mass and weight problem solving

5 Newton’s Laws of Motion

5.4 mass and weight, learning objectives.

By the end of the section, you will be able to:

Explain the difference between mass and weight
Explain why falling objects on Earth are never truly in free fall
Describe the concept of weightlessness

Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but never in the correct units of newtons. In physics, however, there is an important distinction. Weight is the pull of Earth on an object. It depends on the distance from the center of Earth. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon.

Units of Force

The equation [latex] {F}_{\text{net}}=ma [/latex] is used to define net force in terms of mass, length, and time. As explained earlier, the SI unit of force is the newton. Since [latex] {F}_{\text{net}}=ma, [/latex]

Although almost the entire world uses the newton for the unit of force, in the United States, the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb. Thus, a 225-lb person weighs 1000 N.

Weight and Gravitational Force

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law says that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight [latex] \overset{\to }{w} [/latex], or its force due to gravity acting on an object of mass m . Weight can be denoted as a vector because it has a direction; down is, by definition, the direction of gravity, and hence, weight is a downward force. The magnitude of weight is denoted as w . Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g . Using Galileo’s result and Newton’s second law, we can derive an equation for weight.

Consider an object with mass m falling toward Earth. It experiences only the downward force of gravity, which is the weight [latex] \overset{\to }{w} [/latex]. Newton’s second law says that the magnitude of the net external force on an object is [latex] {\overset{\to }{F}}_{\text{net}}=m\overset{\to }{a}. [/latex] We know that the acceleration of an object due to gravity is [latex] \overset{\to }{g}, [/latex] or [latex] \overset{\to }{a}=\overset{\to }{g} [/latex]. Substituting these into Newton’s second law gives us the following equations.

The gravitational force on a mass is its weight. We can write this in vector form, where [latex] \overset{\to }{w} [/latex] is weight and m is mass, as

In scalar form, we can write

Since [latex] g=9.80\,{\text{m/s}}^{2} [/latex] on Earth, the weight of a 1.00-kg object on Earth is 9.80 N:

When the net external force on an object is its weight, we say that it is in free fall , that is, the only force acting on the object is gravity. However, when objects on Earth fall downward, they are never truly in free fall because there is always some upward resistance force from the air acting on the object.

Acceleration due to gravity g varies slightly over the surface of Earth, so the weight of an object depends on its location and is not an intrinsic property of the object. Weight varies dramatically if we leave Earth’s surface. On the Moon, for example, acceleration due to gravity is only [latex] {1.67\,\text{m/s}}^{2} [/latex]. A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

The broadest definition of weight in this sense is that the weight of an object is the gravitational force on it from the nearest large body, such as Earth, the Moon, or the Sun. This is the most common and useful definition of weight in physics. It differs dramatically, however, from the definition of weight used by NASA and the popular media in relation to space travel and exploration. When they speak of “weightlessness” and “microgravity,” they are referring to the phenomenon we call “free fall” in physics. We use the preceding definition of weight, force [latex] \overset{\to }{w} [/latex] due to gravity acting on an object of mass m , and we make careful distinctions between free fall and actual weightlessness.

Be aware that weight and mass are different physical quantities, although they are closely related. Mass is an intrinsic property of an object: It is a quantity of matter. The quantity or amount of matter of an object is determined by the numbers of atoms and molecules of various types it contains. Because these numbers do not vary, in Newtonian physics, mass does not vary; therefore, its response to an applied force does not vary. In contrast, weight is the gravitational force acting on an object, so it does vary depending on gravity. For example, a person closer to the center of Earth, at a low elevation such as New Orleans, weighs slightly more than a person who is located in the higher elevation of Denver, even though they may have the same mass.

It is tempting to equate mass to weight, because most of our examples take place on Earth, where the weight of an object varies only a little with the location of the object. In addition, it is difficult to count and identify all of the atoms and molecules in an object, so mass is rarely determined in this manner. If we consider situations in which [latex] \overset{\to }{g} [/latex] is a constant on Earth, we see that weight [latex] \overset{\to }{w} [/latex] is directly proportional to mass m , since [latex] \overset{\to }{w}=m\overset{\to }{g}, [/latex] that is, the more massive an object is, the more it weighs. Operationally, the masses of objects are determined by comparison with the standard kilogram, as we discussed in Units and Measurement . But by comparing an object on Earth with one on the Moon, we can easily see a variation in weight but not in mass. For instance, on Earth, a 5.0-kg object weighs 49 N; on the Moon, where g is [latex] {1.67\,\text{m/s}}^{2} [/latex], the object weighs 8.4 N. However, the mass of the object is still 5.0 kg on the Moon.

Clearing a Field

A farmer is lifting some moderately heavy rocks from a field to plant crops. He lifts a stone that weighs 40.0 lb. (about 180 N). What force does he apply if the stone accelerates at a rate of [latex] 1.5\,{\text{m/s}}^{2}? [/latex]

We were given the weight of the stone, which we use in finding the net force on the stone. However, we also need to know its mass to apply Newton’s second law, so we must apply the equation for weight, [latex] w=mg [/latex], to determine the mass.

No forces act in the horizontal direction, so we can concentrate on vertical forces, as shown in the following free-body diagram. We label the acceleration to the side; technically, it is not part of the free-body diagram, but it helps to remind us that the object accelerates upward (so the net force is upward).

Figure shows a free-body diagram with vector w equal to 180 newtons pointing downwards and vector F of unknown magnitude pointing upwards. Acceleration a is equal to 1.5 meters per second squared.

[latex] \begin{array}{ccc}\hfill w& =\hfill & mg\hfill \\ \hfill m& =\hfill & \frac{w}{g}=\frac{180\,\text{N}}{9.8\,{\text{m/s}}^{2}}=18\,\text{kg}\hfill \\ \hfill \sum F& =\hfill & ma\hfill \\ \hfill F-w& =\hfill & ma\hfill \\ \hfill F-180\,\text{N}& =\hfill & (18\,\text{kg})(1.5\,{\text{m/s}}^{2})\hfill \\ \hfill F-180\,\text{N}& =\hfill & 27\,\text{N}\hfill \\ \hfill F& =\hfill & 207\,\text{N}=210\,\text{N to two significant figures}\hfill \end{array} [/latex]

Significance

To apply Newton’s second law as the primary equation in solving a problem, we sometimes have to rely on other equations, such as the one for weight or one of the kinematic equations, to complete the solution.

Check Your Understanding

For (Example) , find the acceleration when the farmer’s applied force is 230.0 N.

[latex] a=2.78\,{\text{m/s}}^{2} [/latex]

Can you avoid the boulder field and land safely just before your fuel runs out, as Neil Armstrong did in 1969? This version of the classic video game accurately simulates the real motion of the lunar lander, with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is hard to control.

Use this interactive simulation to move the Sun, Earth, Moon, and space station to see the effects on their gravitational forces and orbital paths. Visualize the sizes and distances between different heavenly bodies, and turn off gravity to see what would happen without it.

Mass is the quantity of matter in a substance.
The weight of an object is the net force on a falling object, or its gravitational force. The object experiences acceleration due to gravity.
Some upward resistance force from the air acts on all falling objects on Earth, so they can never truly be in free fall.
Careful distinctions must be made between free fall and weightlessness using the definition of weight as force due to gravity acting on an object of a certain mass.

Conceptual Questions

What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?

How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?

The astronaut is truly weightless in the location described, because there is no large body (planet or star) nearby to exert a gravitational force. Her mass is 70 kg regardless of where she is located.

Which of the following statements is accurate?

(a) Mass and weight are the same thing expressed in different units.

(b) If an object has no weight, it must have no mass.

(d) Mass and inertia are different concepts.

(e) Weight is always proportional to mass.

When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you?

The force you exert (a contact force equal in magnitude to your weight) is small. Earth is extremely massive by comparison. Thus, the acceleration of Earth would be incredibly small. To see this, use Newton’s second law to calculate the acceleration you would cause if your weight is 600.0 N and the mass of Earth is [latex] 6.00\,×\,{10}^{24}\,\text{kg} [/latex].

How would you give the value of [latex] \overset{\to }{g} [/latex] in vector form?

The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

a. [latex] \begin{array}{ccc}\hfill {w}_{\text{Moon}}& =\hfill & m{g}_{\text{Moon}}\hfill \\ \hfill m& =\hfill & 150\,\text{kg}\hfill \\ \hfill {w}_{\text{Earth}}& =\hfill & 1.5\,×\,{10}^{3}\,\text{N}\hfill \end{array} [/latex]; b. Mass does not change, so the suited astronaut’s mass on both Earth and the Moon is [latex] 150\,\text{kg.} [/latex]

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is [latex] 1.00\,×\,{10}^{4} [/latex] kg. The thrust of its engines is [latex] 3.00\,×\,{10}^{4} [/latex] N. (a) Calculate the module’s magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

A rocket sled accelerates at a rate of [latex] {49.0\,\text{m/s}}^{2} [/latex]. Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body.

a. [latex] \begin{array}{ccc}\hfill {F}_{\text{h}}& =\hfill & 3.68\,×\,{10}^{3}\,\text{N and}\hfill \\ \hfill w& =\hfill & 7.35\,×\,{10}^{2}\,\text{N}\hfill \\ \hfill \frac{{F}_{\text{h}}}{w}& =\hfill & 5.00\,\text{times greater than weight}\hfill \end{array} [/latex];

b. [latex] \begin{array}{ccc}\hfill {F}_{\text{net}}& =\hfill & 3750\,\text{N}\hfill \\ \hfill \theta & =\hfill & 11.3\text{°}\,\text{from horizontal}\hfill \end{array} [/latex]

Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of [latex] {201\,\text{m/s}}^{2} [/latex]. In this problem, the forces are exerted by the seat and the seat belt.

A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?

[latex] \begin{array}{ccc}\hfill w& =\hfill & 19.6\,\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & 5.40\,\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & ma⇒a=2.70\,{\text{m/s}}^{2}\hfill \end{array} [/latex]

A car weighing 12,500 N starts from rest and accelerates to 83.0 km/h in 5.00 s. The friction force is 1350 N. Find the applied force produced by the engine.

A body with a mass of 10.0 kg is assumed to be in Earth’s gravitational field with [latex] g=9.80\,{\text{m/s}}^{2} [/latex]. What is its acceleration?

[latex] 0.60\hat{i}-8.4\hat{j}\,{\text{m/s}}^{2} [/latex]

A fireman has mass m ; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical force he must apply to the pole. (b) If his mass is 90.0 kg and he accelerates at [latex] 5.00\,{\text{m/s}}^{2}, [/latex] what is the magnitude of his applied force?

A baseball catcher is performing a stunt for a television commercial. He will catch a baseball (mass 145 g) dropped from a height of 60.0 m above his glove. His glove stops the ball in 0.0100 s. What is the force exerted by his glove on the ball?

When the Moon is directly overhead at sunset, the force by Earth on the Moon, [latex] {F}_{\text{EM}} [/latex], is essentially at [latex] 90\text{°} [/latex] to the force by the Sun on the Moon, [latex] {F}_{\text{SM}} [/latex], as shown below. Given that [latex] {F}_{\text{EM}}=1.98\,×\,{10}^{20}\,\text{N} [/latex] and [latex] {F}_{\text{SM}}=4.36\,×\,{10}^{20}\,\text{N}, [/latex] all other forces on the Moon are negligible, and the mass of the Moon is [latex] 7.35\,×\,{10}^{22}\,\text{kg}, [/latex] determine the magnitude of the Moon’s acceleration.

Figure shows a circle labeled moon. An arrow from it, pointing up is labeled F subscript EM. Another arrow from it pointing right is labeled F subscript SM.

OpenStax University Physics. Authored by : OpenStax CNX. Located at : https://cnx.org/contents/[email protected]:Gofkr9Oy@15 . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

Mass and weight – problems and solutions

Solved problems in Newton’s laws of motion – Mass, and weight

1. The weight of a 1 kg mass at the surface of the Earth is… g = 9.8 m/s 2

Wanted: weight (w)

m = mass (The SI unit of mass is the kilogram, kg)

w = (1 kg)(9.8 m/s 2 ) = 9.8 kg m/s 2 = 9.8 Newton

w x = the horizontal component of the weight and w y = the vertical component of the weight

The horizontal component of the weight :

w y = w cos 30 o = (9.8 N)(0.5√3) = 4.9√3 Newton

5.4 Mass and Weight

Learning objectives.

By the end of this section, you will be able to:

Explain the difference between mass and weight
Explain why objects falling through the air are never truly in free fall
Describe the concept of weightlessness

Units of Force

The equation F net = m a F net = m a is used to define net force in terms of mass, length, and time. As explained earlier, the SI unit of force is the newton. Since F net = m a , F net = m a ,

Weight and Gravitational Force

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law says that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight w → w → , or its force due to gravity acting on an object of mass m . Weight can be denoted as a vector because it has a direction; down is, by definition, the direction of gravity, and hence, weight is a downward force. The magnitude of weight is denoted as w . Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g . Using Galileo’s result and Newton’s second law, we can derive an equation for weight.

Consider an object with mass m falling toward Earth. It experiences only the downward force of gravity, which is the weight w → w → . Newton’s second law says that the magnitude of the net external force on an object is F → net = m a → . F → net = m a → . We know that the acceleration of an object due to gravity is g → , g → , or a → = g → a → = g → . Substituting these into Newton’s second law gives us the following equations.

The gravitational force on a mass is its weight. We can write this in vector form, where w → w → is weight and m is mass, as

In scalar form, we can write

Since g = 9.80 m/s 2 g = 9.80 m/s 2 on Earth, the weight of a 1.00-kg object on Earth is 9.80 N:

When the net external force on an object is its weight, we say that it is in free fall , that is, the only force acting on the object is gravity. However, when objects on Earth fall downward through the air, they are never truly in free fall because there is always some upward resistance force from the air acting on the object.

Acceleration due to gravity g varies slightly over the surface of Earth, so the weight of an object depends on its location and is not an intrinsic property of the object. Weight varies dramatically if we leave Earth’s surface. On the Moon, for example, acceleration due to gravity is only 1.62 m/s 2 1.62 m/s 2 . A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.6 N on the Moon.

The broadest definition of weight in this sense is that the weight of an object is the gravitational force on it from the nearest large body, such as Earth, the Moon, or the Sun. This is the most common and useful definition of weight in physics. It differs dramatically, however, from the definition of weight used by NASA and the popular media in relation to space travel and exploration. When they speak of “weightlessness” and “microgravity,” they are referring to the phenomenon we call “free fall” in physics. We use the preceding definition of weight, force w → w → due to gravity acting on an object of mass m , and we make careful distinctions between free fall and actual weightlessness.

It is tempting to equate mass to weight, because most of our examples take place on Earth, where the weight of an object varies only a little with the location of the object. In addition, it is difficult to count and identify all of the atoms and molecules in an object, so mass is rarely determined in this manner. If we consider situations in which g → g → is a constant on Earth, we see that weight w → w → is directly proportional to mass m , since w → = m g → , w → = m g → , that is, the more massive an object is, the more it weighs. Operationally, the masses of objects are determined by comparison with the standard kilogram, as we discussed in Units and Measurement . But by comparing an object on Earth with one on the Moon, we can easily see a variation in weight but not in mass. For instance, on Earth, a 5.0-kg object weighs 49 N; on the Moon, where g is 1.67 m/s 2 1.67 m/s 2 , the object weighs 8.4 N. However, the mass of the object is still 5.0 kg on the Moon.

Example 5.8

Clearing a field, significance, check your understanding 5.6.

For Example 5.8 , find the acceleration when the farmer’s applied force is 230.0 N.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction

Authors: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher/website: OpenStax
Book title: University Physics Volume 1
Publication date: Sep 19, 2016
Location: Houston, Texas
Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
Section URL: https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

StickMan Physics

Animated Physics Lessons

Mass and Weight

Learn the difference between mass (m) and weight (F w ). Find out how to convert to mass from weight and from weight to mass.

Watch the video as we go through the content and problems set or go through the same material below

Learning Targets

I know the difference between mass and weight
I can calculate mass from weight and weight from mass using F w = mg
I can draw a Force Diagram of an object on a horizontal surface of any planet

Mass is a measurement of matter (molecular composition) of an object. Since an objects molecular composition remains when location changes, mass never changes.

Weight is a measure of the force of gravity on an objects mass. This is directly related to mass but will change with location as the force and acceleration due to gravity changes.

Weight equals mass times gravity


Weight	F	Newton	N
Mass	m	kilogram	kg
Acceleration due to gravity	g	Meters per second squared	m/s

On the Earth's surface, the accepted value for acceleration due to gravity (g) is 9.81 m/s 2
In some lessons we had you use a less specific rounded number of 10 m/s 2

Weight Changes When (g) Changes

On Earth, your weight is caused by the earths pull on you. In a future lesson we will see that weight is the result of the your mass, the earths mass, and the distance between you and Earth.

We will solve problems on this page using an average surface acceleration due to gravity

More massive interstellar objects have a higher surface acceleration due to gravity ( g ).
The higher the acceleration due to gravity ( g ) the higher the weight ( F w )

Mass, Radius, and Acceleration due to Gravity of Planets

			)
Mercury	3.29 x 10	2.440 x 10	3.70
Venus	4.87 x 10	6.052 x 10	8.88
Earth	5.97 x 10	6.378 x 10	9.81
Mars	6.39 x 10	3.396 x 10	3.72
Jupiter	1.90 x 10	7.149 x 10	24.79
Saturn	5.68 x 10	6.027 x 10	10.44
Uranus	8.68 x 10	2.556 x 10	8.69
Neptune	1.02 x 10	2.476 x 10	11.15

Mass, Radius, and Acceleration due to Gravity of Other Interstellar Objects

			)
Sun	1.99 x 10	6.963 x 10	274.78
Earth’s Moon	7.35 x 10	1.738 x 10	1.62
Pluto	1.31 x 10	1.195 x 10	0.62

Example Questions (Mass and Weight)

1. What is 76 kg Natalia's weight on earth where the acceleration due to gravity is 9.81 m/s 2 ?

See Solution

F w = (76)(9.81)= 745.56 N

2. What is Natalia's weight on the moon where the acceleration due to gravity is 1.62 m/s 2 ?

F w = (76)(1.62)= 123.12 N

3. If 76 kg Natalia went to Neptune where the surface acceleration due to gravity is 11.15 m/s 2 , would her mass or weight change and what would each be?

Mass would still be 76 kg wither location and weight would change

F w = (76)(11.15) = 847.4 N

Normal Force Equals Weight on a Horizontal Surface

Notice in the force diagrams :

Mass ( m ) of 10 kg does not change
Weight ( F w ) changes with the acceleration due to gravity
The normal ( F N )force changes with weight ( F w )

Normal force is the force created by weight on a surface pushing back upwards perpendicular to the surface. Perpendicular to any horizontal surface will be up.

Normal force equals weight on a horizontal surface

Problem Set

1. What is the weight of a 25 kg object on Pluto where the acceleration due to gravity is 0.62 m/s 2 ?

F w = 15.5 N

2. Draw a force diagram including the normal force of this 25 kg object on a horizontal surface of Pluto where the acceleration due to gravity is 0.62 m/s 2 ?

3. What is the mass of a 25 kg object on Pluto where the acceleration due to gravity is 0.62 m/s 2 ?

m = 25 kg (does not change)

4. What is the weight of a 25 kg object on Mars where the acceleration due to gravity is 3.72 m/s 2 ?

5. What is the mass of a 100 N object on the Moon where the acceleration due to gravity is 1.62 m/s 2 ?

6. Draw a force diagram including the normal force of a 100 N object on the surface of the Moon where the acceleration due to gravity is 1.62 m/s 2 ?

7. If you weigh 1177.2 N on Earth where the acceleration due to gravity is 9.81 m/s 2 what is your mass on Uranus where the acceleration due to gravity is 8.69 m/s 2 ?

8. If you weigh 1177.2 N on Earth where the acceleration due to gravity is 9.81 m/s 2 what is your weight on Uranus where the acceleration due to gravity is 8.69 m/s 2 ?

F w = 1042.8 N

Mass and Weight Quiz

Joe has a mass of 54 kg. What is his mass on the moon where the acceleration due to gravity is 1.62 m/s 2 ?

Mass does not change. Weight does depending on the acceleration due to gravity.

Joe has a mass of 54 kg. What is his weight on the moon where the acceleration due to gravity is 1.62 m/s 2 ?

g = 1.62 m/s 2

F w = (54)(1.62) = 87.48 N

Joe has a mass of 54 kg. What is his weight on the earth?

g = 9.8 m/s 2

F w = (54)(9.8) = 529.2 N

Which changes depending on your location?

Mass (kg) never changes because it is a measure of the matter that you are composed of. You are the same matter on earth or on the moon.

Weight (F w ) changes when g changes. g changes depending on your altitude on earth, in space, or on another planet (it is not always 9.8 m/s 2 which is why many classes use a more rounded 10 m/s 2 instead.

Which is the term for the molecules that make up an object.

Matter is composed of the atoms/molecules that make up an object

What would happen to your weight if you were on a planet with twice the acceleration due to gravity?

Your score is

Continue to Newton's Third Law
Back to the Main Forces Page
Back to the Stickman Physics Home Page
Equation Sheet

Terms and Conditions - Privacy Policy

TPC and eLearning
What's NEW at TPC?
Read Watch Interact
Practice Review Test
Teacher-Tools
Subscription Selection
Seat Calculator
Ad Free Account
Edit Profile Settings
Classes (Version 2)
Student Progress Edit
Task Properties
Export Student Progress
Task, Activities, and Scores
Metric Conversions Questions
Metric System Questions
Metric Estimation Questions
Significant Digits Questions
Proportional Reasoning
Acceleration
Distance-Displacement
Dots and Graphs
Graph That Motion
Match That Graph
Name That Motion
Motion Diagrams
Pos'n Time Graphs Numerical
Pos'n Time Graphs Conceptual
Up And Down - Questions
Balanced vs. Unbalanced Forces
Change of State
Force and Motion

Mass and Weight

Match That Free-Body Diagram
Net Force (and Acceleration) Ranking Tasks
Newton's Second Law
Normal Force Card Sort
Recognizing Forces
Air Resistance and Skydiving
Solve It! with Newton's Second Law
Which One Doesn't Belong?
Component Addition Questions
Head-to-Tail Vector Addition
Projectile Mathematics
Trajectory - Angle Launched Projectiles
Trajectory - Horizontally Launched Projectiles
Vector Addition
Vector Direction
Which One Doesn't Belong? Projectile Motion
Forces in 2-Dimensions
Being Impulsive About Momentum
Explosions - Law Breakers
Hit and Stick Collisions - Law Breakers
Case Studies: Impulse and Force
Impulse-Momentum Change Table
Keeping Track of Momentum - Hit and Stick
Keeping Track of Momentum - Hit and Bounce
What's Up (and Down) with KE and PE?
Energy Conservation Questions
Energy Dissipation Questions
Energy Ranking Tasks
LOL Charts (a.k.a., Energy Bar Charts)
Match That Bar Chart
Words and Charts Questions
Name That Energy
Stepping Up with PE and KE Questions
Case Studies - Circular Motion
Circular Logic
Forces and Free-Body Diagrams in Circular Motion
Gravitational Field Strength
Universal Gravitation
Angular Position and Displacement
Linear and Angular Velocity
Angular Acceleration
Rotational Inertia
Balanced vs. Unbalanced Torques
Getting a Handle on Torque
Torque-ing About Rotation
Properties of Matter
Fluid Pressure
Buoyant Force
Sinking, Floating, and Hanging
Pascal's Principle
Flow Velocity
Bernoulli's Principle
Balloon Interactions
Charge and Charging
Charge Interactions
Charging by Induction
Conductors and Insulators
Coulombs Law
Electric Field
Electric Field Intensity
Polarization
Case Studies: Electric Power
Know Your Potential
Light Bulb Anatomy
I = ∆V/R Equations as a Guide to Thinking
Parallel Circuits - ∆V = I•R Calculations
Resistance Ranking Tasks
Series Circuits - ∆V = I•R Calculations
Series vs. Parallel Circuits
Equivalent Resistance
Period and Frequency of a Pendulum
Pendulum Motion: Velocity and Force
Energy of a Pendulum
Period and Frequency of a Mass on a Spring
Horizontal Springs: Velocity and Force
Vertical Springs: Velocity and Force
Energy of a Mass on a Spring
Decibel Scale
Frequency and Period
Closed-End Air Columns
Name That Harmonic: Strings
Rocking the Boat
Wave Basics
Matching Pairs: Wave Characteristics
Wave Interference
Waves - Case Studies
Color Addition and Subtraction
Color Filters
If This, Then That: Color Subtraction
Light Intensity
Color Pigments
Converging Lenses
Curved Mirror Images
Law of Reflection
Refraction and Lenses
Total Internal Reflection
Who Can See Who?
Formulas and Atom Counting
Atomic Models
Bond Polarity
Entropy Questions
Cell Voltage Questions
Heat of Formation Questions
Reduction Potential Questions
Oxidation States Questions
Measuring the Quantity of Heat
Hess's Law
Oxidation-Reduction Questions
Galvanic Cells Questions
Thermal Stoichiometry
Molecular Polarity
Quantum Mechanics
Balancing Chemical Equations
Bronsted-Lowry Model of Acids and Bases
Classification of Matter
Collision Model of Reaction Rates
Density Ranking Tasks
Dissociation Reactions
Complete Electron Configurations
Elemental Measures
Enthalpy Change Questions
Equilibrium Concept
Equilibrium Constant Expression
Equilibrium Calculations - Questions
Equilibrium ICE Table
Intermolecular Forces Questions
Ionic Bonding
Lewis Electron Dot Structures
Limiting Reactants
Line Spectra Questions
Mass Stoichiometry
Measurement and Numbers
Metals, Nonmetals, and Metalloids
Metric Estimations
Metric System
Molarity Ranking Tasks
Mole Conversions
Name That Element
Names to Formulas
Names to Formulas 2
Nuclear Decay
Particles, Words, and Formulas
Periodic Trends
Precipitation Reactions and Net Ionic Equations
Pressure Concepts
Pressure-Temperature Gas Law
Pressure-Volume Gas Law
Chemical Reaction Types
Significant Digits and Measurement
States Of Matter Exercise
Stoichiometry Law Breakers
Stoichiometry - Math Relationships
Subatomic Particles
Spontaneity and Driving Forces
Gibbs Free Energy
Volume-Temperature Gas Law
Acid-Base Properties
Energy and Chemical Reactions
Chemical and Physical Properties
Valence Shell Electron Pair Repulsion Theory
Writing Balanced Chemical Equations
Mission CG1
Mission CG10
Mission CG2
Mission CG3
Mission CG4
Mission CG5
Mission CG6
Mission CG7
Mission CG8
Mission CG9
Mission EC1
Mission EC10
Mission EC11
Mission EC12
Mission EC2
Mission EC3
Mission EC4
Mission EC5
Mission EC6
Mission EC7
Mission EC8
Mission EC9
Mission RL1
Mission RL2
Mission RL3
Mission RL4
Mission RL5
Mission RL6
Mission KG7
Mission RL8
Mission KG9
Mission RL10
Mission RL11
Mission RM1
Mission RM2
Mission RM3
Mission RM4
Mission RM5
Mission RM6
Mission RM8
Mission RM10
Mission LC1
Mission RM11
Mission LC2
Mission LC3
Mission LC4
Mission LC5
Mission LC6
Mission LC8
Mission SM1
Mission SM2
Mission SM3
Mission SM4
Mission SM5
Mission SM6
Mission SM8
Mission SM10
Mission KG10
Mission SM11
Mission KG2
Mission KG3
Mission KG4
Mission KG5
Mission KG6
Mission KG8
Mission KG11
Mission F2D1
Mission F2D2
Mission F2D3
Mission F2D4
Mission F2D5
Mission F2D6
Mission KC1
Mission KC2
Mission KC3
Mission KC4
Mission KC5
Mission KC6
Mission KC7
Mission KC8
Mission AAA
Mission SM9
Mission LC7
Mission LC9
Mission NL1
Mission NL2
Mission NL3
Mission NL4
Mission NL5
Mission NL6
Mission NL7
Mission NL8
Mission NL9
Mission NL10
Mission NL11
Mission NL12
Mission MC1
Mission MC10
Mission MC2
Mission MC3
Mission MC4
Mission MC5
Mission MC6
Mission MC7
Mission MC8
Mission MC9
Mission RM7
Mission RM9
Mission RL7
Mission RL9
Mission SM7
Mission SE1
Mission SE10
Mission SE11
Mission SE12
Mission SE2
Mission SE3
Mission SE4
Mission SE5
Mission SE6
Mission SE7
Mission SE8
Mission SE9
Mission VP1
Mission VP10
Mission VP2
Mission VP3
Mission VP4
Mission VP5
Mission VP6
Mission VP7
Mission VP8
Mission VP9
Mission WM1
Mission WM2
Mission WM3
Mission WM4
Mission WM5
Mission WM6
Mission WM7
Mission WM8
Mission WE1
Mission WE10
Mission WE2
Mission WE3
Mission WE4
Mission WE5
Mission WE6
Mission WE7
Mission WE8
Mission WE9
Vector Walk Interactive
Name That Motion Interactive
Kinematic Graphing 1 Concept Checker
Kinematic Graphing 2 Concept Checker
Graph That Motion Interactive
Two Stage Rocket Interactive
Rocket Sled Concept Checker
Force Concept Checker
Free-Body Diagrams Concept Checker
Free-Body Diagrams The Sequel Concept Checker
Skydiving Concept Checker
Elevator Ride Concept Checker
Vector Addition Concept Checker
Vector Walk in Two Dimensions Interactive
Name That Vector Interactive
River Boat Simulator Concept Checker
Projectile Simulator 2 Concept Checker
Projectile Simulator 3 Concept Checker
Hit the Target Interactive
Turd the Target 1 Interactive
Turd the Target 2 Interactive
Balance It Interactive
Go For The Gold Interactive
Egg Drop Concept Checker
Fish Catch Concept Checker
Exploding Carts Concept Checker
Collision Carts - Inelastic Collisions Concept Checker
Its All Uphill Concept Checker
Stopping Distance Concept Checker
Chart That Motion Interactive
Roller Coaster Model Concept Checker
Uniform Circular Motion Concept Checker
Horizontal Circle Simulation Concept Checker
Vertical Circle Simulation Concept Checker
Race Track Concept Checker
Gravitational Fields Concept Checker
Orbital Motion Concept Checker
Angular Acceleration Concept Checker
Balance Beam Concept Checker
Torque Balancer Concept Checker
Aluminum Can Polarization Concept Checker
Charging Concept Checker
Name That Charge Simulation
Coulomb's Law Concept Checker
Electric Field Lines Concept Checker
Put the Charge in the Goal Concept Checker
Circuit Builder Concept Checker (Series Circuits)
Circuit Builder Concept Checker (Parallel Circuits)
Circuit Builder Concept Checker (∆V-I-R)
Circuit Builder Concept Checker (Voltage Drop)
Equivalent Resistance Interactive
Pendulum Motion Simulation Concept Checker
Mass on a Spring Simulation Concept Checker
Particle Wave Simulation Concept Checker
Boundary Behavior Simulation Concept Checker
Slinky Wave Simulator Concept Checker
Simple Wave Simulator Concept Checker
Wave Addition Simulation Concept Checker
Standing Wave Maker Simulation Concept Checker
Color Addition Concept Checker
Painting With CMY Concept Checker
Stage Lighting Concept Checker
Filtering Away Concept Checker
InterferencePatterns Concept Checker
Young's Experiment Interactive
Plane Mirror Images Interactive
Who Can See Who Concept Checker
Optics Bench (Mirrors) Concept Checker
Name That Image (Mirrors) Interactive
Refraction Concept Checker
Total Internal Reflection Concept Checker
Optics Bench (Lenses) Concept Checker
Kinematics Preview
Velocity Time Graphs Preview
Moving Cart on an Inclined Plane Preview
Stopping Distance Preview
Cart, Bricks, and Bands Preview
Fan Cart Study Preview
Friction Preview
Coffee Filter Lab Preview
Friction, Speed, and Stopping Distance Preview
Up and Down Preview
Projectile Range Preview
Ballistics Preview
Juggling Preview
Marshmallow Launcher Preview
Air Bag Safety Preview
Colliding Carts Preview
Collisions Preview
Engineering Safer Helmets Preview
Push the Plow Preview
Its All Uphill Preview
Energy on an Incline Preview
Modeling Roller Coasters Preview
Hot Wheels Stopping Distance Preview
Ball Bat Collision Preview
Energy in Fields Preview
Weightlessness Training Preview
Roller Coaster Loops Preview
Universal Gravitation Preview
Keplers Laws Preview
Kepler's Third Law Preview
Charge Interactions Preview
Sticky Tape Experiments Preview
Wire Gauge Preview
Voltage, Current, and Resistance Preview
Light Bulb Resistance Preview
Series and Parallel Circuits Preview
Thermal Equilibrium Preview
Linear Expansion Preview
Heating Curves Preview
Electricity and Magnetism - Part 1 Preview
Electricity and Magnetism - Part 2 Preview
Vibrating Mass on a Spring Preview
Period of a Pendulum Preview
Wave Speed Preview
Slinky-Experiments Preview
Standing Waves in a Rope Preview
Sound as a Pressure Wave Preview
DeciBel Scale Preview
DeciBels, Phons, and Sones Preview
Sound of Music Preview
Shedding Light on Light Bulbs Preview
Models of Light Preview
Electromagnetic Radiation Preview
Electromagnetic Spectrum Preview
EM Wave Communication Preview
Digitized Data Preview
Light Intensity Preview
Concave Mirrors Preview
Object Image Relations Preview
Snells Law Preview
Reflection vs. Transmission Preview
Magnification Lab Preview
Reactivity Preview
Ions and the Periodic Table Preview
Periodic Trends Preview
Chemical Reactions Preview
Intermolecular Forces Preview
Melting Points and Boiling Points Preview
Bond Energy and Reactions Preview
Reaction Rates Preview
Ammonia Factory Preview
Stoichiometry Preview
Nuclear Chemistry Preview
Gaining Teacher Access
Algebra Based Physics Course
Tasks and Classes
Tasks - Classic
Subscription
Subscription Locator
1-D Kinematics
Newton's Laws
Vectors - Motion and Forces in Two Dimensions
Momentum and Its Conservation
Work and Energy
Circular Motion and Satellite Motion
Thermal Physics
Static Electricity
Electric Circuits
Vibrations and Waves
Sound Waves and Music
Light and Color
Reflection and Mirrors
About the Physics Interactives
Task Tracker
Usage Policy
Newtons Laws
Vectors and Projectiles
Forces in 2D
Momentum and Collisions
Circular and Satellite Motion
Balance and Rotation
Electromagnetism
Waves and Sound
Atomic Physics
Forces in Two Dimensions
Work, Energy, and Power
Circular Motion and Gravitation
Sound Waves
1-Dimensional Kinematics
Circular, Satellite, and Rotational Motion
Einstein's Theory of Special Relativity
Waves, Sound and Light
QuickTime Movies
About the Concept Builders
Pricing For Schools
Directions for Version 2
Measurement and Units
Relationships and Graphs
Rotation and Balance
Vibrational Motion
Reflection and Refraction
Teacher Accounts
Task Tracker Directions
Kinematic Concepts
Kinematic Graphing
Wave Motion
Sound and Music
About CalcPad
1D Kinematics
Vectors and Forces in 2D
Simple Harmonic Motion
Rotational Kinematics
Rotation and Torque
Rotational Dynamics
Electric Fields, Potential, and Capacitance
Transient RC Circuits
Light Waves
Units and Measurement
Stoichiometry
Molarity and Solutions
Thermal Chemistry
Acids and Bases
Kinetics and Equilibrium
Solution Equilibria
Oxidation-Reduction
Nuclear Chemistry
Newton's Laws of Motion
Work and Energy Packet
Static Electricity Review
NGSS Alignments
1D-Kinematics
Projectiles
Circular Motion
Magnetism and Electromagnetism
Graphing Practice
About the ACT
ACT Preparation
For Teachers
Other Resources
Solutions Guide
Solutions Guide Digital Download
Motion in One Dimension
Work, Energy and Power
Algebra Based Physics
Honors Physics
Other Tools
Frequently Asked Questions
Purchasing the Download
Purchasing the CD
Purchasing the Digital Download
About the NGSS Corner
NGSS Search
Force and Motion DCIs - High School
Energy DCIs - High School
Wave Applications DCIs - High School
Force and Motion PEs - High School
Energy PEs - High School
Wave Applications PEs - High School
Crosscutting Concepts
The Practices
Physics Topics
NGSS Corner: Activity List
NGSS Corner: Infographics
About the Toolkits
Position-Velocity-Acceleration
Position-Time Graphs
Velocity-Time Graphs
Newton's First Law
Newton's Second Law
Newton's Third Law
Terminal Velocity
Projectile Motion
Forces in 2 Dimensions
Impulse and Momentum Change
Momentum Conservation
Work-Energy Fundamentals
Work-Energy Relationship
Roller Coaster Physics
Satellite Motion
Electric Fields
Circuit Concepts
Series Circuits
Parallel Circuits
Describing-Waves
Wave Behavior Toolkit
Standing Wave Patterns
Resonating Air Columns
Wave Model of Light
Plane Mirrors
Curved Mirrors
Teacher Guide
Using Lab Notebooks
Current Electricity
Light Waves and Color
Reflection and Ray Model of Light
Refraction and Ray Model of Light
Classes (Legacy)
Teacher Resources
Subscriptions

Newton's Laws
Einstein's Theory of Special Relativity
About Concept Checkers
School Pricing
Newton's Laws of Motion
Newton's First Law
Newton's Third Law

Launch Concept Builder

practice problem 1

Use the weight formula.

W = mg

Solve for mass. Substitute one newton for weight and one standard earth gravity for gravity.

=		=	1 N
			9.8 m/s
=	0.102 kg = 102 g

The 96.7 gram tangerine comes closest to this value. Not all tangerines weigh 98.7 grams, however, so this is only a rule of thumb. There are certainly apples, bananas, oranges, tomatoes, and other fruits out there with a mass of approximately 102 grams and thus a weight of approximately one newton.

Those of you familiar with multiple choice tests should have eliminated the chicken egg as a possible answer. A chicken egg is only metaphorically the "fruit of the chicken".

practice problem 2

Here's the way I usually do it — using values I've memorized from years of use.

=
2.2 lb =	(1 kg)(9.8 m/s )
1 lb =	4.45… N

Here's a more accurate way to do it — using values that are exact by definition.

=
1 lb =	(0.45359237 kg)( )
1 lb =	4.448221615… N

Not quite a quarter pound, but you get the idea.

0.20 lb	<	0.224808943… lb	<	0.25 lb
⅕ lb	<	1 N	<	¼ lb

The fraction 9 40 gives a decimal expansion of 0.225, which is accurate to three significant figures. Not my favorite fraction, but it gets the job done. With sixteen avoirdupois ounces in a pound, one newton is also about 3½ ounces.

1 N ≈	9 lb	×	16 oz	=	18 oz	= 3½ oz
	40		1 lb		5

practice problem 3

Practice problem 4.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Course: 3rd grade > Unit 13

Understanding mass (grams and kilograms)
Estimate mass (grams and kilograms)

Word problems with mass

Your answer should be
an integer, like 6 ‍
an exact decimal, like 0.75 ‍
a simplified proper fraction, like 3 / 5 ‍
a simplified improper fraction, like 7 / 4 ‍
a mixed number, like 1 3 / 4 ‍

Or search by topic

Number and algebra

The Number System and Place Value
Calculations and Numerical Methods
Fractions, Decimals, Percentages, Ratio and Proportion
Properties of Numbers
Patterns, Sequences and Structure
Algebraic expressions, equations and formulae
Coordinates, Functions and Graphs

Geometry and measure

Angles, Polygons, and Geometrical Proof
3D Geometry, Shape and Space
Measuring and calculating with units
Transformations and constructions
Pythagoras and Trigonometry
Vectors and Matrices

Probability and statistics

Handling, Processing and Representing Data
Probability

Working mathematically

Thinking mathematically
Mathematical mindsets
Cross-curricular contexts
Physical and digital manipulatives

For younger learners

Early Years Foundation Stage

Advanced mathematics

Decision Mathematics and Combinatorics
Advanced Probability and Statistics

Resources tagged with: Mass and weight

There are 20 NRICH Mathematical resources connected to Mass and weight , you may find related items under Measuring and calculating with units .

Seesaw Shenanigans

A group of animals has made a seesaw in the woods. How can you make the seesaw balance?

Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Order, Order!

Can you place these quantities in order from smallest to largest?

All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Being Resilient - Primary Measures

Measure problems at primary level that may require resilience.

Being Resourceful - Primary Measures

Measure problems at primary level that require careful consideration.

Being Collaborative - Primary Measures

Measure problems for primary learners to work on with others.

Being Curious - Primary Measures

Measure problems for inquiring primary learners.

Watermelons

These watermelons have been entered into a competition. Use the information to work out the number of points each one was awarded.

2010: A Year of Investigations

This article for teachers suggests ideas for activities built around 10 and 2010.

Weighing Fruit

Can you use this information to estimate how much the different fruit selections weigh in kilos and pounds?

Working with Dinosaurs

This article for teachers suggests ways in which dinosaurs can be a great context for discussing measurement.

Measure for Measure

This article, written for students, looks at how some measuring units and devices were developed.

Weigh to Go

This article for teachers recounts the history of measurement, encouraging it to be used as a spring board for cross-curricular activity.

Money Measure

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Do You Measure Up?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

Oranges and Lemons

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

What's My Weight?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

5 Newton’s Laws of Motion

5.4 Mass and Weight

Learning objectives.

By the end of the section, you will be able to:

Explain the difference between mass and weight
Explain why falling objects on Earth are never truly in free fall
Describe the concept of weightlessness

Units of Force

The equation [latex]{F}_{\text{net}}=ma[/latex] is used to define net force in terms of mass, length, and time. As explained earlier, the SI unit of force is the newton. Since [latex]{F}_{\text{net}}=ma,[/latex]

Weight and Gravitational Force

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law says that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight [latex]\mathbf{\overset{\to }{w}}[/latex], or its force due to gravity acting on an object of mass m . Weight can be denoted as a vector because it has a direction; down is, by definition, the direction of gravity, and hence, weight is a downward force. The magnitude of weight is denoted as w . Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g . Using Galileo’s result and Newton’s second law, we can derive an equation for weight.

Consider an object with mass m falling toward Earth. It experiences only the downward force of gravity, which is the weight [latex]\mathbf{\overset{\to }{w}}[/latex]. Newton’s second law says that the magnitude of the net external force on an object is [latex]{\mathbf{\overset{\to }{F}}}_{\text{net}}=m\mathbf{\overset{\to }{a}}.[/latex] We know that the acceleration of an object due to gravity is [latex]\mathbf{\overset{\to }{g}},[/latex] or [latex]\mathbf{\overset{\to }{a}}=\mathbf{\overset{\to }{g}}[/latex]. Substituting these into Newton’s second law gives us the following equations.

The gravitational force on a mass is its weight. We can write this in vector form, where [latex]\mathbf{\overset{\to }{w}}[/latex] is weight and m is mass, as

In scalar form, we can write

Since [latex]g=9.80\,{\text{m/s}}^{2}[/latex] on Earth, the weight of a 1.00-kg object on Earth is 9.80 N:

Acceleration due to gravity g varies slightly over the surface of Earth, so the weight of an object depends on its location and is not an intrinsic property of the object. Weight varies dramatically if we leave Earth’s surface. On the Moon, for example, acceleration due to gravity is only [latex]{1.67\,\text{m/s}}^{2}[/latex]. A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

The broadest definition of weight in this sense is that the weight of an object is the gravitational force on it from the nearest large body, such as Earth, the Moon, or the Sun. This is the most common and useful definition of weight in physics. It differs dramatically, however, from the definition of weight used by NASA and the popular media in relation to space travel and exploration. When they speak of “weightlessness” and “microgravity,” they are referring to the phenomenon we call “free fall” in physics. We use the preceding definition of weight, force [latex]\mathbf{\overset{\to }{w}}[/latex] due to gravity acting on an object of mass m , and we make careful distinctions between free fall and actual weightlessness.

It is tempting to equate mass to weight, because most of our examples take place on Earth, where the weight of an object varies only a little with the location of the object. In addition, it is difficult to count and identify all of the atoms and molecules in an object, so mass is rarely determined in this manner. If we consider situations in which [latex]\mathbf{\overset{\to }{g}}[/latex] is a constant on Earth, we see that weight [latex]\mathbf{\overset{\to }{w}}[/latex] is directly proportional to mass m , since [latex]\mathbf{\overset{\to }{w}}=m\mathbf{\overset{\to }{g}},[/latex] that is, the more massive an object is, the more it weighs. Operationally, the masses of objects are determined by comparison with the standard kilogram, as we discussed in Units and Measurement . But by comparing an object on Earth with one on the Moon, we can easily see a variation in weight but not in mass. For instance, on Earth, a 5.0-kg object weighs 49 N; on the Moon, where g is [latex]{1.67\,\text{m/s}}^{2}[/latex], the object weighs 8.4 N. However, the mass of the object is still 5.0 kg on the Moon.

Clearing a Field

Significance

Check Your Understanding

For (Example) , find the acceleration when the farmer’s applied force is 230.0 N.

[latex]a=2.78\,{\text{m/s}}^{2}[/latex]

Mass is the quantity of matter in a substance.
The weight of an object is the net force on a falling object, or its gravitational force. The object experiences acceleration due to gravity.
Some upward resistance force from the air acts on all falling objects on Earth, so they can never truly be in free fall.
Careful distinctions must be made between free fall and weightlessness using the definition of weight as force due to gravity acting on an object of a certain mass.

Conceptual Questions

What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?

How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?

Which of the following statements is accurate?

(a) Mass and weight are the same thing expressed in different units.

(b) If an object has no weight, it must have no mass.

(d) Mass and inertia are different concepts.

(e) Weight is always proportional to mass.

When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you?

How would you give the value of [latex]\mathbf{\overset{\to }{g}}[/latex] in vector form?

The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

a. [latex]\begin{array}{ccc}\hfill {w}_{\text{Moon}}& =\hfill & m{g}_{\text{Moon}}\hfill \\ \hfill m& =\hfill & 150\,\text{kg}\hfill \\ \hfill {w}_{\text{Earth}}& =\hfill & 1.5\times {10}^{3}\,\text{N}\hfill \end{array}[/latex]; b. Mass does not change, so the suited astronaut’s mass on both Earth and the Moon is [latex]150\,\text{kg.}[/latex]

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is [latex]1.00\times {10}^{4}[/latex] kg. The thrust of its engines is [latex]3.00\times {10}^{4}[/latex] N. (a) Calculate the module’s magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

A rocket sled accelerates at a rate of [latex]{49.0\,\text{m/s}}^{2}[/latex]. Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body.

a. [latex]\begin{array}{ccc}\hfill {F}_{\text{h}}& =\hfill & 3.68\times {10}^{3}\,\text{N and}\hfill \\ \hfill w& =\hfill & 7.35\times {10}^{2}\,\text{N}\hfill \\ \hfill \frac{{F}_{\text{h}}}{w}& =\hfill & 5.00\,\text{times greater than weight}\hfill \end{array}[/latex];

b. [latex]\begin{array}{ccc}\hfill {F}_{\text{net}}& =\hfill & 3750\,\text{N}\hfill \\ \hfill \theta & =\hfill & 11.3^\circ\,\text{from horizontal}\hfill \end{array}[/latex]

Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of [latex]{201\,\text{m/s}}^{2}[/latex]. In this problem, the forces are exerted by the seat and the seat belt.

A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?

[latex]\begin{array}{ccc}\hfill w& =\hfill & 19.6\,\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & 5.40\,\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & ma\Rightarrow a=2.70\,{\text{m/s}}^{2}\hfill \end{array}[/latex]

A car weighing 12,500 N starts from rest and accelerates to 83.0 km/h in 5.00 s. The friction force is 1350 N. Find the applied force produced by the engine.

A body with a mass of 10.0 kg is assumed to be in Earth’s gravitational field with [latex]g=9.80\,{\text{m/s}}^{2}[/latex]. What is its acceleration?

[latex]0.60\mathbf{\hat{i}}-8.4\mathbf{\hat{j}}\,{\text{m/s}}^{2}[/latex]

A fireman has mass m ; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical force he must apply to the pole. (b) If his mass is 90.0 kg and he accelerates at [latex]5.00\,{\text{m/s}}^{2},[/latex] what is the magnitude of his applied force?

When the Moon is directly overhead at sunset, the force by Earth on the Moon, [latex]{F}_{\text{EM}}[/latex], is essentially at [latex]90^\circ[/latex] to the force by the Sun on the Moon, [latex]{F}_{\text{SM}}[/latex], as shown below. Given that [latex]{F}_{\text{EM}}=1.98\times {10}^{20}\,\text{N}[/latex] and [latex]{F}_{\text{SM}}=4.36\times {10}^{20}\,\text{N},[/latex] all other forces on the Moon are negligible, and the mass of the Moon is [latex]7.35\times {10}^{22}\,\text{kg},[/latex] determine the magnitude of the Moon’s acceleration.

Share This Book

Mass and Weight worksheet with answers for Grade 6 Standard

Mass and Weight worksheet with answers for Grade 6 Standard. This Worksheet includes MCQ, Fill in the blanks, True / False, Short Answer Questions, Long Answer Questions.

a) It doubles

b) Gravity decreases with altitude

c) Gravity remains the same at all altitudes

5.) Which factor affects the weight of an object the most?

c) Its shape

Answer: b) Pounds

7.) Which force keeps us on the ground and is responsible for our weight?

9.) Which of the following materials has the most mass?

d) A rubber ball

c) The object’s temperature and size

b) 10 kilograms

Answer: d) Venus

c) It remains the same

5.) If you were on the Moon, your weight would be the same as on Earth.

8.) An astronaut in space experiences zero gravity.

Answer: Weight

Answer: Weight is the force that acts on an object due to Earth’s gravitational force.

Weighty Problems

Thanks for visiting NZMaths. We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

This unit comprises six problems for students to apply and interpret measurement of mass. Students are also introduced to the concepts of net and gross mass.

Select the appropriate standard unit of measurement for a specific application.
Measure masses with appropriate measuring devices.
Measure net and gross mass.

Mass is the force created by gravity acting of on an object. Mass is felt as weight, a force that pulls the object towards the centre of the Earth. Mass is measured in units based on grams, and tonnes. Larger or smaller units are created by combining or equally partitioning these units. One kilogram is a combination of 1000 grams (kilo means 1000). One milligram is 1/1000 of a gram and one microgram is 1/ 1 000 000 of a gram. The units for mass come from the mass of water. One cubic metre of water has a mass of 1 tonne, or 1000 kilograms. One millilitre of water has a mass of one gram.

Note that in the New Zealand Curriculum document, “weight” and “mass” are used interchangeably. In a science context, the definition of “force created by gravity acting on an object” would often be equated with weight, not mass. Consider the scientific knowledge of your students (e.g. are they studying forces in science). It may be more appropriate to define mass as the amount of matter in an object (measured in kilograms) and weight using the adorementioned definition (measured in Newtons, N).

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

letting students attempt problems using physical materials as much as possible, so they develop a ‘feel’ for the benchmark units
directly modelling measurement with tools, like digital scales for mass
providing opportunities for students to copy the correct use of tools
clarifying the language of measurement units, such as “kilogram” as a mass that is made up of 1000 grams
clarifying the meaning of symbols, e.g. 45g as 45 grams, and 45kg as 45 kilograms; 45t as 45 tonnes
encouraging students to work collaboratively (mahi tahi) to share and justify their ideas
easing the calculation demands by providing calculators where appropriate.

Tasks can be varied in many ways including:

reducing the complexity of the numbers involved in the station tasks, e.g. whole number versus fraction dimensions. The choice of measurement units influences the difficulty of calculation as well as the level of precision
allowing physical solutions with manipulatives before requiring abstract (in the head) anticipation of measures
creating or using models of standard units, e.g. 1 litre of water for the mass of 1 kilogram
reducing the demands for a product, e.g. less calculations and words, and more diagrams and models.

The context for this unit can be adapted to suit the interests and cultural backgrounds of your students. Use the interests of your students to create contexts that will engage them. Students may be interested in the mass of rugby players. Students from large whānau, or who prepare food for large numbers of people, may relate to measuring quantities to scale up recipes. Carrying heavy objects was a major problem for pre-European Māori. How did they carry heavy loads, or move waka? Counting on Frank by Rod Clement may inspire some students to look for eccentric ways to apply measurement to their daily lives. For example, the human body is 60% water, by mass. How much water is in their body?

Te reo Māori vocabulary terms such as maihea (weight / mass), karamu (gram), manokaramu (kilogram), and tana (tonne) could be introduced in this unit and used throughout other mathematical learning.

Station 1: Copymaster 1 , $1, $2 and 50c coins, scales (preferably digital and able to weigh in grams), metre ruler
Station 2: Copymaster 2 , calculator
Station 3: Copymaster 3 , calculator
Station 4: Copymaster 4 , access to the internet.
Station 5: Copymaster 5 , 1L measuring jug, five different sized plastic containers, scales, eyedropper
Station 6: Copymaster 6 , can of dog food, supermarket bags, calculator

The following six stations provide a range of problems for students to apply and interpret measurement of mass. Consider what would be the most effective method for introducing these to your class. You could work on them as a whole class and provide support to groups of students. Alternatively, you could use another relevant igniting activity to introduce the context for learning, before directing students to work on one or more of these stations independently, or in small groups. These stations could serve as the basis for learning in different sessions, or could be used as one session. At the conclusion of these stations, students draw on the problems presented and create their own stations to be used in other lessons.

Station 1: A kilo of coins

You have won a prize which can be just one of the following:

1 kilogram of $1 coins
A 1.5 metre long trail of $2 coins (lying flat and touching)
A 0.5 metre high stack of 50c coins

What is your choice?

1 kg of $1 coins (1000 ÷ 8 = 125 coins, so $125)

1.5 metre of $2 coins (1500 ÷ 26.5 = 57 coins, so $114)

0.5 metre stack of 50c coins (500 ÷ 1.7 = 294 coins, so $147)

Station 2: Largest Lasagne

This problem could be adapted to reflect food that is meaningful to your students (e.g. the largest tray of pani popo).

The world’s largest lasagne was made in 2012 at a restaurant in Wieliczka, Poland. It weighed 4865 kg and measured 25 m x 2.5 m.

The ingredients were:

2500kg of pasta, 800kg of mince, 400kg of mozzarella cheese, 100kg of peas, 100kg of carrots, and equal amounts of white sauce and tomato sauce.

How much did the white sauce and tomato sauce weigh?
What would be the size of a 500g piece from the lasagne?
How many people could be fed with the whole lasagne? Show how you arrived at your estimate.
The other ingredients total 3900kg so the sauces must weigh 4865 – 3900 = 965 kg. 500L of each sauce was used. Does that sound right?
A 500g piece would be about 1/10 000 of the whole lasagne. One way is to cut both the length and width into 100 parts, since 100 x 100 = 10 000. A single piece would measure 25cm x 2.5cm. That’s a bit skinny so 12.5cm x 5cm might work better.
The lasagne was actually cut into 10 000 pieces so that’s how many people were fed. Each piece had a mass of 0.486 kg or 486 grams. That is a good serving of lasagne.

Station 3: Weighing Tonnes

Konsihiki was the largest active sumo wrestler in the world with a mass of 287 kg. Now he is retired.

How many Konishikis weigh as much as 1 tonne?

Make a table of tonne weights using objects in the classroom. Remember that 1000 kg is a tonne.

Object	Mass	Number in a tonne
Konsihiki	287 kg
School bag	5 kg	200

The number of Konshihikis in 1 tonne equals 3.48, about 3 and ½ of him.

To find how many of any object make 1 tonne, divided 1 000 by the weight of the object in kilograms. For example, if a schoolbag weighs 5kg then 1 000 ÷ 5 = 200 make 1 tonne.

Station 4: Jumbo facts

Find out facts about the mass of very large animals and make a report about these animals for the class. To get you started here are some facts about the Blue Whale, which can be seen in New Zealand waters.

The blue whale is the largest animal living on Earth. It can reach up to nearly 30 metres in length and weigh up to 180 tonnes (t). Their tongues alone can weigh as much as some elephants and their hearts are huge, weighing a whopping 180kg. They have the largest babies on Earth. When they are first born they can be 8 metres (m) in length and weigh 4000kg. Imagine a jet engine that registers at 140 decibels. A blue whale, when it calls, registers at 188 decibels. Compare the facts about the Blue Whale with the large African elephant

The African elephant is the biggest animal on land. Fully grown the male can be 7 metres long, 3.2 metres tall at the shoulder and have a mass of 6500kg. Its tusks can weigh as much as 100kg each. The largest pair of tusks on record are in the British Museum and weigh 133kg each. What combination of animals could be equal to the elephant's weight?

For example, it takes 6500 ÷ 5 = 1300 big domestic cats to weigh 1 elephant or 130 big dogs.

How many rhinoceroses, lions, giraffes, or hippopotamuses weigh the same as an elephant?

Answers will vary depending on what other animals your students research.

Station 5: Mass of water

Measure out one litre (l) of water.

What is the mass of one litre of water? If 1L = 1000ml, what is the mass of 1mL of water?

For each container, estimate the capacity of the container, measure it to check, estimate the mass of water when the container is full, and find the mass of the water using scales.

Record your results like this:

Container	Estimate capacity	Measure actual capacity	Estimate mass of water	Measure actual mass
A
B
C
D
E

How many drops of water are needed to fill each container?
What is the mass of a single drop?
1 litre (l) of water has a mass of 1 kilogram (1000 grams). 1 millilitre (mL) of water has a mass of 1 gram.

Answers depend on the size of the containers. Here is an example:

Container	Estimate capacity	Measure actual capacity	Estimate mass of water	Measure actual mass
A	400 mL	450 mL	390 g	450g

About 20 drops make 1 ml of water. Find the capacity of the container in mL then multiply by 20 to get the number of drops.
A single drop has a mass of 1/20 of 1g, that’s 0.05g.

Station 6: Frank’s arms

Counting on Frank by Rod Clement (1990; Harper Collins Publishers: Sydney) has some great ideas for measurement investigations. You can view readings of the book on YouTube if you cannot source a copy of the book. One of the ideas introduced in the story is about Frank carrying a trolley load of cans to the supermarket.

Trolleys measure 60 litres or 80 litres. What do those measures mean?
How heavy do you think Frank’s load of cans is?
How many cans are you able to carry in a reusable supermarket bag?

How did you work that out?

Here is another task based on Counting on Frank that you may choose to use.

1 litre is a unit of capacity, but it is also used as a unit of volume. One litre measures 10cm x 10cm x 10cm. 60 litres is 60 times that size.
Frank has 47 cans. They could be 420g cans so they would weigh 47 x 420g = 19 740g or 19.740 kg (about 20 kg). If the cans are bigger, say 820g, then the mass equals 47 times the mass of one can.
You could get 24 x 420g cans in a supermarket bag, or 36 cans if you add another layer. The mass of the bag would be 24 x 420g = 10.080 kg or 36 x 420g = 15.12 kg.

Dear family and whānau,

In class we have talked a lot about weight this week. In particular, we discovered that Konshiki, the largest Sumo wrestler, weighs 226kg, a Blue Whale weighs 180 tonnes and an elephant weighs 6500kg. What do you think the Blue Whale weighs in kg?

Your child has been asked to look for other facts associated with weight by reading the newspaper or doing some reading on the internet. They should record what they find out. Please encourage them to discuss their findings with you.

You could support them further by weighing items at home or cooking with them.

Figure It Out

Some links from the Figure It Out series which you may find useful are:

Measurement, Level 3-4: Can You, page 5; Breaking Bags, page 9; Egging you on, page 21
Sport, Level 3-4, Scrum Power, page 20
Measurement, Level 4: Taking Off, pages 6 & 7; Weighty Water, pages 12 & 13

Printer-friendly version

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Newton’s Laws of Motion

Mass and Weight

Learning objectives.

By the end of the section, you will be able to:

Explain the difference between mass and weight
Explain why falling objects on Earth are never truly in free fall
Describe the concept of weightlessness

Units of Force

${F}_{\text{net}}=ma$

Weight and Gravitational Force

$\stackrel{\to }{w}$

In scalar form, we can write

${1.67\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$

$\stackrel{\to }{g}$

Solution No forces act in the horizontal direction, so we can concentrate on vertical forces, as shown in the following free-body diagram. We label the acceleration to the side; technically, it is not part of the free-body diagram, but it helps to remind us that the object accelerates upward (so the net force is upward).

Significance To apply Newton’s second law as the primary equation in solving a problem, we sometimes have to rely on other equations, such as the one for weight or one of the kinematic equations, to complete the solution.

Check Your Understanding For (Figure) , find the acceleration when the farmer’s applied force is 230.0 N.

$a=2.78\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$

Mass is the quantity of matter in a substance.
The weight of an object is the net force on a falling object, or its gravitational force. The object experiences acceleration due to gravity.
Some upward resistance force from the air acts on all falling objects on Earth, so they can never truly be in free fall.
Careful distinctions must be made between free fall and weightlessness using the definition of weight as force due to gravity acting on an object of a certain mass.

Conceptual Questions

What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?

How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?

Which of the following statements is accurate?

(a) Mass and weight are the same thing expressed in different units.

(b) If an object has no weight, it must have no mass.

(d) Mass and inertia are different concepts.

(e) Weight is always proportional to mass.

When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you?

$6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{24}\phantom{\rule{0.2em}{0ex}}\text{kg}$

The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

$\begin{array}{ccc}\hfill {w}_{\text{Moon}}& =\hfill & m{g}_{\text{Moon}}\hfill \\ \hfill m& =\hfill & 150\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ \hfill {w}_{\text{Earth}}& =\hfill & 1.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \end{array}$

A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?

$\begin{array}{ccc}\hfill w& =\hfill & 19.6\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & 5.40\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & ma⇒a=2.70\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}\hfill \end{array}$

A car weighing 12,500 N starts from rest and accelerates to 83.0 km/h in 5.00 s. The friction force is 1350 N. Find the applied force produced by the engine.

$0.60\stackrel{^}{i}-8.4\stackrel{^}{j}\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$

${F}_{\text{EM}}$

WORD PROBLEMS INVOLVING MASS AND WEIGHT

The mass of an object is the amount of matter it contains.

Example 1 :

If one egg has a mass of 55 g, find the total mass of eggs in 50 cartons, each containing 12 eggs.

Mass of 1 egg = 55 g

Number of eggs in each carton = 12

Total number of cartons = 50

Total mass = 55 x 12 x 50

= 33000 g

1000g = 1 kg

= 33 kg

Example 2 :

Find the total mass of 32 chocolates, each of mass 28 grams.

Number of chocolates = 32

Mass of each chocolate = 28 grams

Total mass = 32 x 28

= 896 grams

Example 3 :

If a clothes peg has a mass of 6.5 g, how many pegs are there in a 13 kg box?

Mass of 1 cloth peg = 6.5 g

Mass of box = 13 kg

1000 grams = 1 kg

Converting kg to grams, we get

= 13000 grams

Number of pegs = 13000/6.5

= 2000 pegs

Example 4 :

If a roof tile has mass 1.25 kilograms, how many tiles could a van with a load limit of 8 tonnes carry?

1000 kg = 1 tonne

8 tonnes = 8(1000)

= 8000 kg

Mass of 1 roof tile = 1.25 kg

Number of roof tiles carried by the van = 8000/1.25

= 6400 tiles

Example 5 :

Find the total mass in tonnes of 3500 books, each with mass 800 grams.

Mass of each book = 800 grams

Total number of books = 3500

Mass of 3500 books = 800 x 3500

= 2800000 grams

= 2800000/1000

= 2800 kg

1000 kg = 1 tonne

= 2800/1000

= 2.8 tonnes

Example 6 :

If the mass of 8000 oranges is 1.04 tonnes, what is the average mass of one orange?

Total number of oranges = 8000

Weight of oranges = 1.04 tonnes

= 1.04 (1000)

= 1040 kg

= 1040(1000)

= 1040000 grams

Average weight of 1 orange = 1040000 / 8000

= 130 grams

So, mass of 1 orange is 130 grams.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to [email protected]

We always appreciate your feedback.

Sat Math Practice
SAT Math Worksheets
PEMDAS Rule
BODMAS rule
GEMDAS Order of Operations
Math Calculators
Transformations of Functions
Order of rotational symmetry
Lines of symmetry
Compound Angles
Quantitative Aptitude Tricks
Trigonometric ratio table
Word Problems
Times Table Shortcuts
10th CBSE solution
PSAT Math Preparation
Privacy Policy
Laws of Exponents

Recent Articles

Best way to learn mathematics.

Jul 01, 24 02:18 PM

Derivative Problems and Solutions (Part - 1)

Jun 30, 24 11:56 PM

Algebra Word Problems Involving Geometry (Video Solutions)

Jun 30, 24 01:17 PM

These are our mass and weight Word Problems worksheets for 2nd grade math school. Click on the previews to go to download page.

Worksheet by math grade levels:

Our grade 2 math worksheets are free and printable in PDF format. Based on the Singaporean math curriculum for second graders, these math worksheets are made for students in grade level 2. However, also students in other grade levels can benefit from doing these math worksheets. Feel free to print them. Our math worksheets cover important math topics such as: whole numbers, spelling, place value, skip counting, addition and subtraction, multiplication tables, basic division facts, fractions, mixed operations, geometry, graphing, picture graphs, measurement of time, mass, length and volume.

Our first grade math worksheets are free and printable in PDF format. Based on the Singaporean math school curriculum for grade 1 students, these 1st level math worksheets are made for students in school, tutoring or online math education. Our grade 1 math worksheets cover topics such as: whole numbers, spelling of basic numbers up to 10 or 100 and first grade math operations, grade 1addition and subtraction, place value, skip counting, introduction to division and multiplication, first grade geometry and basic shapes, easy picture graphs, length, volume and mass measurement and beginners number patterns.

Reading & Math for K-5

Kindergarten
Learning numbers
Comparing numbers
Place Value
Roman numerals
Subtraction
Multiplication
Order of operations
Drills & practice
Measurement
Factoring & prime factors
Proportions
Shape & geometry
Data & graphing
Word problems
Children's stories
Leveled Stories
Sentences & passages
Context clues
Cause & effect
Compare & contrast
Fact vs. fiction
Fact vs. opinion
Main idea & details
Story elements
Conclusions & inferences
Sounds & phonics
Words & vocabulary
Reading comprehension
Early writing
Numbers & counting
Simple math
Social skills
Other activities
Dolch sight words
Fry sight words
Multiple meaning words
Prefixes & suffixes
Vocabulary cards
Other parts of speech
Punctuation
Capitalization
Narrative writing
Opinion writing
Informative writing
Cursive alphabet
Cursive letters
Cursive letter joins
Cursive words
Cursive sentences
Cursive passages
Grammar & Writing

Breadcrumbs

Word Problems
Mass / weight

$Math Workbooks for Grade 5$

Download & Print From only $2.60

Mass word problems

Measurement word problems.

Below are our grade 5 word problems worksheets involving the measurement of mass or weight . The worksheets are in customary units (ounces, lbs), metric units (gm, kg) or mixed units. No conversions of units between the two systems are needed.

Ounces, pounds:

Grams, kilograms:

These worksheets are available to members only.

Join K5 to save time, skip ads and access more content. Learn More

What Is and Isn’t Accurate About BMI (Body Mass Index)

BMI Accuracy
BMI Inaccuracy
Other Ways to Assess Health
A Healthy BMI

The body mass index (BMI) is commonly used to categorize weight ranges (from underweight to obese) because it is accessible, no-cost, and quick. Using a formula or BMI calculator, it is relatively easy to plug in height and weight measurements and get a figure meant to represent a measure of body fat and, by extension, related health risks.

While there is a noted correlation between high BMI and obesity-related health risks, such as cardiovascular disease and type 2 diabetes, BMI has flaws and is not meant to be a diagnostic tool for individuals. BMI does not consider other variables that influence health risks, such as muscle and bone mass, lifestyle, sex or gender, ethnicity, race , and family history.

The American Medical Association (AMA) recommends against healthcare providers using BMI as a sole indicator of health and as a means to diagnosis obesity. Rather, the AMA argues, it should be used along with other measures, such as waist circumference, cholesterol tests, and other tools to gain a more comprehensive picture of an individual's health and care needs.

This article will discuss the accuracy and inaccuracies of BMI, how to assess health beyond BMI values, and how to determine a healthy BMI for an individual.

ruizluquepaz / Getty Images

Use of Gendered Language

Overwhelmingly, the data and research on BMI use binary gender measures of male and female, and does not account for gender diversity. This article uses binary gender language to reflect the current research, while recognizing that more research is needed that considers how BMI affects those who are not cisgender.

BMI Accuracy: What Is True?

BMI is calculated using weight and height measurements—namely, weight in kilograms divided by the square of height in meters.

BMI is not a precise measure of body fat or health but can be used as a screening tool. It gives a measure that corresponds to weight categories (underweight, normal weight, overweight/pre-obesity, obesity classes 1, 2, and 3 ). BMI levels alone do not indicate a person's health status, but BMI is moderately correlated with more direct measures of body fat.

Higher BMI levels are also correlated with elevated mortality risk , and with an elevated risk for conditions such as cardiovascular disease, type 2 diabetes, and other health issues associated with overweight and obesity.

BMI is not an individual diagnostic tool, but it is useful for examining overall population trends and can be used as a starting point for determining an individual's obesity-related health risks.

The World Health Organization (WHO) categorizes BMI for adults as:

Underweight : Less than or equal to 18.5
Normal weight : 18–24.9
Overweight/pre-obesity : 25.0-29.9
Class 1 obesity : 30.0–34.9
Class 2 obesity : 35.0–39.9
Class 3 obesity : Greater than or equal to 40

These values are based on cisgender white men, and may need to be adjusted according to factors such as race and sex.

BMI is calculated differently for children and adolescents than it is for adults. Adult BMI measures and ranges cannot be used to assess BMI for people under 20 years old.

BMI Inaccuracy: What’s Untrue?

BMI does not give a precise measure of body fat, and it cannot be used alone to determine an individual's health. It is not a diagnostic tool; it just gives a general idea of body fat .

There are many factors that can affect BMI, but BMI is calculated using only height and weight. In addition, a BMI figure alone can have different implications depending on other contributing factors. Two people can have the same BMI, but have different levels of body fat and/or different health risks.

For example, at the same BMI:

Women tend to have more body fat than men.
Older adults tend to have more body fat than younger adults.
Athletes tend to have less body fat than nonathletes.
People of different racial and ethnic groups tend to have more or less body fat than other racial or ethnic groups.

Some of this discrepancy stems from the origins of the BMI. The concept for a calculation like BMI was invented by a mathematician in Belgium about 200 years ago. He based the data on European White men, without accounting for variables in sex, race, and ethnicity.

Several studies have found that the current BMI ranges do not correlate accurately with some health risks, such as type 2 diabetes, for Asian Americans .

The WHO has noted that people of Asian descent can have a higher risk for some metabolic conditions at lower BMIs than the current classification ranges indicate.

BMI may be less accurate for certain ethnic groups, such as:

Aboriginal and Torres Strait Islander peoples
Chinese people
Japanese people
Maori people
Pacific Islanders
South Asian people

Available data also suggests that the association between BMI and body fat, dyslipidemia , metabolic syndrome, and all-cause mortality may be weaker for Black Americans than for White Americans. This may affect how BMI should be interpreted for this racial group.

More research is also needed on the accuracy of BMI with other racial and ethnic groups, such as people of Middle Eastern descent.

In addition, BMI does not take into consideration body makeup, such as the weight percentage due to fat, muscle, bone density, etc.

In general, BMI tends to be a less accurate tool for people such as:

Pregnant people
People with a physical disability
Certain athletes, such as bodybuilders, weight lifters, or some high-performance athletes
People under 20 years old

How BMI is used can also be problematic. Because it is a simple, easy-to-use tool, there can be a tendency to use it as a sole indicator of health or to make health recommendations.

This may lead to important assessments being missed, such as dismissing heart health risks in someone whose BMI is in the normal range, or unnecessarily pressuring someone with a BMI above the normal range but without additional risk factors to lose weight.

Other potential downsides to BMI include:

Fostering of weight-based shame, which may discourage some people from seeking medical care
Possibility of mistrust for the healthcare provider, if too focused on BMI
Missed or misdiagnosis if healthcare provider incorrectly attributes symptoms to weight
Arbitrariness of the BMI cut-off points in terms of identifying health risks
Overreliance on BMI to the exclusion of other measures of health

Why Is My BMI High If I Am Not Overweight?

BMI does not account for body makeup. A person with increased muscle mass and lower body fat may have a BMI that classifies them as overweight or obese , but their body size may be smaller than someone with the same BMI who has a higher amount of body fat.

Assessing Health Beyond BMI Values

BMI is one of many tools that can be used to assess health related to body fat.

Waist circumference is another tool commonly used to assess potential health risks. Excessive abdominal fat is associated with an increased risk of conditions such as cardiovascular disease, type 2 diabetes, and high blood pressure (hypertension).

To measure your waist, do the following:

Use a tape measure over bare skin or one layer of light clothing.
Place the tape measure in the area between your lowest rib and the top of your hip bone (about belly button level).
Breathe out normally and wrap the tape around your waist snugly (without squeezing the skin) to measure.

You may have a higher risk of obesity -related health conditions if your waist circumference is more than:

Men : 40 inches
Women : 35 inches

As with BMI, waist circumference is another screening tool that can be used as part of a health assessment, but not as a sole indicator of health. Waist circumference measurement is not appropriate for:

People under 18 years
People with a medical condition that causes a very enlarged abdomen
People from certain non-European backgrounds

The AMA recommends additional measures for diagnosing obesity , such as:

Body adiposity index (hip and height measurement)
Relative fat mass
Measurements of visceral fat (found deep in the abdominal cavity)
Body composition (percentage of fat, bone, and muscles)
Genetic/metabolic factors

Tools healthcare providers may use include:

Caliper measurements of skinfold thickness
Underwater weighing
Bioelectrical impedance
Dual-energy X-ray absorptiometry (DXA)
Isotope dilution

These are less readily available, and some can be expensive. They should be performed by professionals trained to use these tools.

As part of a comprehensive health assessment, healthcare providers may also do other checks, such as:

Blood pressure
Cholesterol
Blood glucose (sugar)

What Is a Healthy BMI for Me?

What a healthy BMI is for any individual depends on more factors than just which range the number falls in, including genetic factors, fitness levels, lean mass, health behaviors, environmental risks, and more. BMI alone should not be used as a health assessment but rather one screening tool among many.

Rather than rely on the one BMI reading, it's best to see a healthcare provider for a comprehensive health assessment.

To calculate your BMI, visit the Centers For Disease Control and Prevention (CDC) website for the following calculators:

A tool for measuring BMI in people age 20 years and older
A tool for measuring BMI in children and teens

BMI is a popular tool used to categorize body mass based on height and weight. It is helpful as a screening tool when used alongside other measures of health, but it can be inaccurate or misleading when used on its own to assess an individual's health risks.

BMI doesn't take into consideration factors such as body composition, age , sex, race and ethnicity, genetics, and other variables that contribute to an individual's health status and health risks. Instead of relying solely on BMI , see your healthcare provider for a comprehensive health assessment.

Yale Medicine. Why you shouldn’t rely on BMI alone .

American Medical Association. AMA: Use of BMI alone is an imperfect clinical measure .

Centers For Disease Control and Prevention. Body Mass Index (BMI) .

Gutin I. In BMI we trust: reframing the body mass index as a measure of health . Soc Theory Health. 2018;16(3):256-271. doi:10.1057/s41285-017-0055-0

World Health Organization. A healthy lifestyle - WHO recommendations .

National Health Service. Obesity .

Hsu WC, Araneta MRG, Kanaya AM, Chiang JL, Fujimoto W. Bmi cut points to identify at-risk asian americans for type 2 diabetes screening . Diabetes Care. 2015;38(1):150-158. doi:10.2337/dc14-2391

Healthdirect. Body mass index (BMI) and waist circumference .

Jackson CL, Wang N, Yeh H, Szklo M, Dray‐Spira R, Brancati FL. Body‐mass index and mortality risk in US Blacks compared to Whites . Obesity. 2014;22(3):842-851. doi:10.1002/oby.20471

Obesity Medicine Association. Is BMI outdated? An analysis of body mass index and health .

Harvard T.H. Chan School of Public Health. BMI a poor metric for measuring people’s health, say experts .

Centers For Disease Control and Prevention. Assessing your weight .

NurseJournal. BMI has fallen out of favor as a measurement tool: here’s what nurses need to know .

University of Rochester Medical Center. Is BMI accurate? New evidence says no .

By Heather Jones Jones is a freelance writer with a strong focus on health, parenting, disability, and feminism.

IMAGES

Problem solving using weights up to 200g
Mass Problem Solving
Primary weight and mass resources
Year 1
Measure Mass (kg): Reasoning and Problem Solving
Mass Problem Solving 2

VIDEO

#difference_between mass & weight #mass #weight #physics #class9th #science
Mass & Weight [Brief Comparison]
Difference between mass and weight
I'm Fat Because Food Is My Comfort
Understanding Mass and Weight
Chapter 8 weight Problem Solving

COMMENTS

5.4 Mass and Weight
Explain the difference between mass and weight; ... To apply Newton's second law as the primary equation in solving a problem, we sometimes have to rely on other equations, such as the one for weight or one of the kinematic equations, to complete the solution. ... [latex] {201\,\text{m/s}}^{2} [/latex]. In this problem, the forces are exerted ...
Mass and weight
3. The mass of a box is 1 kg and acceleration due to gravity is 9.8 m/s 2. Find (a) weight (b) the horizontal component and the vertical component of the weight. Solution. Weight : w = m g = (1 kg)(9.8 m/s 2) = 9.8 kg m/s 2 = 9.8 Newton. The horizontal component of the weight :
5.4 Mass and Weight
A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.6 N on the Moon. The broadest definition of weight in this sense is that the weight of an object is the gravitational force on it from the nearest large body, such as Earth, the Moon, or the Sun. This is the most common and useful definition of weight in physics.
Mass and Weight
Weight Changes When (g) Changes. On Earth, your weight is caused by the earths pull on you. In a future lesson we will see that weight is the result of the your mass, the earths mass, and the distance between you and Earth. We will solve problems on this page using an average surface acceleration due to gravity
Mass and Weight
Mass and Weight. The Mass and Weight Concept Builder is a tool that challenges the learner to distinguish between the concepts of mass and weight. In addition to the conceptual aspect of these two concepts, students will also perform calculations of mass and weight. There are a total of 28 questions organized into nine different Question Groups ...
6.12: Mass and Weight
Be aware that weight and mass are different physical quantities, although they are closely related. Mass is an intrinsic property of an object: It is a quantity of matter. ... To apply Newton's second law as the primary equation in solving a problem, we sometimes have to rely on other equations, such as the one for weight or one of the ...
Mass and Weight Questions
Weight and mass are independent of any physical state of a matter, such as solid, gas, liquid, or plasma. Weight and mass have definite units and dimensions. Both mass and weight are measurable quantities. Weight and mass depend on the amount of matter in a body. 4. The mass of an object can be zero. True. False.
Weight
solution. Use the weight formula. Solve for mass. Substitute one newton for weight and one standard earth gravity for gravity. The 96.7 gram tangerine comes closest to this value. Not all tangerines weigh 98.7 grams, however, so this is only a rule of thumb. There are certainly apples, bananas, oranges, tomatoes, and other fruits out there with ...
Converting Between Mass and Weight: Example Problems
Are mass and weight the same thing? This video explains the difference between mass and weight. This video also has four different example problems for how t...
Word problems with mass (practice)
Word problems with mass. Emily needs 4 eggs for baking her cake. All of the eggs have the same mass. Emily knows the mass of 1 egg (shown below). What is the total mass of 4 eggs? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.
Weight and Mass Example Problems
AP Physics. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket
Resources tagged with: Mass and weight
Resources tagged with: Mass and weight Types All types Problems Articles Games Age range All ages 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level There are 20 NRICH Mathematical resources connected to Mass and weight , you may find related items under Measuring and calculating with units .
Grade 4 mass and weight word problem worksheets
These word problems involve mass or weight. Problems involve the addition, subtraction, multiplication or division of amounts with units of mass. There are worksheets on both customary units (ounces & pounds) and metric units (gm, kg). Students are not asked to convert between the two systems. Ounces, pounds:
5.4 Mass and Weight
1.7 Solving Problems in Physics. 1 Chapter Review. 2 Vectors. Introduction. 2.1 Scalars and Vectors. 2.2 Coordinate Systems and Components of a Vector. 2.3 Algebra of Vectors. ... Explain the difference between mass and weight; Explain why falling objects on Earth are never truly in free fall;
Mass and Weight Problems and Solutions
Mass and Weight Problems and Solutions - Free download as PDF File (.pdf), Text File (.txt) or read online for free. (a) Draw force of gravity (weight) that act on the object when object is at rest on a table, as shown in figure (a). (b) Draw force of gravity (weight) and it's components that act on an object sliding down an incline, as shown in figure (b)
Mass and Weight worksheet with answers for Grade 6 Standard
Answer: True. 4.) The weight of an object depends on its location in the universe. Answer: True. 5.) If you were on the Moon, your weight would be the same as on Earth. Answer: False. 6.) The relationship between mass and weight is direct; as mass increases, weight also increases.
Weighty Problems
Mass is the force created by gravity acting of on an object. Mass is felt as weight, a force that pulls the object towards the centre of the Earth. Mass is measured in units based on grams, and tonnes. Larger or smaller units are created by combining or equally partitioning these units. One kilogram is a combination of 1000 grams (kilo means 1000).
Grade 3 mass and weight word problems
These measurement word problems involve the addition, subtraction, multiplication or division of amounts measured in standard (ounces, pounds) and metric (grams, kilograms) units of mass. No conversion of units is required. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.
Mass and Weight
Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but never in the correct units of newtons. ... To apply Newton's second law as the primary equation in solving a problem, we sometimes have to rely on other equations, such as the one for weight or one ...
Word Problems Involving Mass and Weight
Total mass = 55 x 12 x 50 = 33000 g. 1000g = 1 kg = 33 kg. Example 2 : Find the total mass of 32 chocolates, each of mass 28 grams. Solution : Number of chocolates = 32. Mass of each chocolate = 28 grams. Total mass = 32 x 28 = 896 grams. Example 3 : If a clothes peg has a mass of 6.5 g, how many pegs are there in a 13 kg box? Solution :
Weight Formula With Solved Examples
Problem 1: Compute the weight of a body on the moon if the mass is 60Kg? g is given as 1.625 m/s 2. g = 1.625 m/s 2. Problem 2: Compute the weight of a body on earth whose mass is 25 kg? g = 9.8 m/s 2. The formula for weight is given as the product of mass and acceleration due to gravity. The solved numericals helps in understanding the formula ...
Grade 2 mass and weight Word Problems math school worksheets for
These are our mass and weight Word Problems worksheets for 2nd grade math school. Click on the previews to go to download page. Mass Problems (level 2) Mass Problems (level 2) Mass Problems (level 2) Worksheet by math grade levels: Grade 1 sheets. Grade 2 sheets. Grade 3 sheets. Grade 4 sheets.
Mass and weight word problems for grade 5
Below are our grade 5 word problems worksheets involving the measurement of mass or weight. The worksheets are in customary units (ounces, lbs), metric units (gm, kg) or mixed units. No conversions of units between the two systems are needed. Ounces, pounds: Worksheet #1 Worksheet #2. Grams, kilograms:
What Is and Isn't Accurate About BMI (Body Mass Index)
The body mass index (BMI) is commonly used to categorize weight ranges (from underweight to obese) because it is accessible, no-cost, and quick. Using a formula or BMI calculator, it is relatively easy to plug in height and weight measurements and get a figure meant to represent a measure of body fat and, by extension, related health risks.

5 Newton’s Laws of Motion

Units of Force

Weight and Gravitational Force

Clearing a Field

Significance

Check Your Understanding

Conceptual Questions

Mass and weight – problems and solutions

Share this:

5.4 Mass and Weight

Units of Force

Weight and Gravitational Force

Example 5.8

Mass and Weight

Weight equals mass times gravity

Weight Changes When (g) Changes

Mass, Radius, and Acceleration due to Gravity of Planets

Mass, Radius, and Acceleration due to Gravity of Other Interstellar Objects

Example Questions (Mass and Weight)

Normal Force Equals Weight on a Horizontal Surface

Problem Set

Mass and Weight

Launch Concept Builder

practice problem 1

practice problem 2

practice problem 3

Course: 3rd grade > Unit 13

Word problems with mass

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

For younger learners

Advanced mathematics

Resources tagged with: Mass and weight

Seesaw Shenanigans

Place Your Orders

Discuss and Choose

Order, Order!

All in a Jumble

Being Resilient - Primary Measures

Being Resourceful - Primary Measures

Being Collaborative - Primary Measures

Being Curious - Primary Measures

Watermelons

2010: A Year of Investigations

Weighing Fruit

Working with Dinosaurs

Measure for Measure

Weigh to Go

Money Measure

Do You Measure Up?

Oranges and Lemons

What's My Weight?

5.4 Mass and Weight

Units of Force

Weight and Gravitational Force

Clearing a Field

Significance

Check Your Understanding

Conceptual Questions

Share This Book

Mass and Weight worksheet with answers for Grade 6 Standard

Leave a Reply Cancel reply

Weighty Problems

Station 1: A kilo of coins

Station 2: Largest Lasagne

Station 3: Weighing Tonnes

Station 4: Jumbo facts

Station 5: Mass of water

Station 6: Frank’s arms

Figure It Out

Mass and Weight

Units of Force

Weight and Gravitational Force

Conceptual Questions

WORD PROBLEMS INVOLVING MASS AND WEIGHT

Recent Articles

Derivative Problems and Solutions (Part - 1)

Algebra Word Problems Involving Geometry (Video Solutions)