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Example Physics Problems and Solutions

Learning how to solve physics problems is a big part of learning physics. Here’s a collection of example physics problems and solutions to help you tackle problems sets and understand concepts and how to work with formulas:

Physics Homework Tips Physics homework can be challenging! Get tips to help make the task a little easier.

Unit Conversion Examples

There are now too many unit conversion examples to list in this space. This Unit Conversion Examples page is a more comprehensive list of worked example problems.

Newton’s Equations of Motion Example Problems

Equations of Motion – Constant Acceleration Example This equations of motion example problem consist of a sliding block under constant acceleration. It uses the equations of motion to calculate the position and velocity of a given time and the time and position of a given velocity.

Equations of Motion Example Problem – Constant Acceleration This example problem uses the equations of motion for constant acceleration to find the position, velocity, and acceleration of a breaking vehicle.

Equations of Motion Example Problem – Interception

This example problem uses the equations of motion for constant acceleration to calculate the time needed for one vehicle to intercept another vehicle moving at a constant velocity.

Vertical Motion Example Problem – Coin Toss Here’s an example applying the equations of motion under constant acceleration to determine the maximum height, velocity and time of flight for a coin flipped into a well. This problem could be modified to solve any object tossed vertically or dropped off a tall building or any height. This type of problem is a common equation of motion homework problem.

Projectile Motion Example Problem This example problem shows how to find different variables associated with parabolic projectile motion.

Accelerometer and Inertia Example Problem Accelerometers are devices to measure or detect acceleration by measuring the changes that occur as a system experiences an acceleration. This example problem uses one of the simplest forms of an accelerometer, a weight hanging from a stiff rod or wire. As the system accelerates, the hanging weight is deflected from its rest position. This example derives the relationship between that angle, the acceleration and the acceleration due to gravity. It then calculates the acceleration due to gravity of an unknown planet.

Weight In An Elevator Have you ever wondered why you feel slightly heavier in an elevator when it begins to move up? Or why you feel lighter when the elevator begins to move down? This example problem explains how to find your weight in an accelerating elevator and how to find the acceleration of an elevator using your weight on a scale.

Equilibrium Example Problem This example problem shows how to determine the different forces in a system at equilibrium. The system is a block suspended from a rope attached to two other ropes.

Equilibrium Example Problem – Balance This example problem highlights the basics of finding the forces acting on a system in mechanical equilibrium.

Force of Gravity Example This physics problem and solution shows how to apply Newton’s equation to calculate the gravitational force between the Earth and the Moon.

Coupled Systems Example Problems

Coupled systems are two or more separate systems connected together. The best way to solve these types of problems is to treat each system separately and then find common variables between them. Atwood Machine The Atwood Machine is a coupled system of two weights sharing a connecting string over a pulley. This example problem shows how to find the acceleration of an Atwood system and the tension in the connecting string. Coupled Blocks – Inertia Example This example problem is similar to the Atwood machine except one block is resting on a frictionless surface perpendicular to the other block. This block is hanging over the edge and pulling down on the coupled string. The problem shows how to calculate the acceleration of the blocks and the tension in the connecting string.

Friction Example Problems

These example physics problems explain how to calculate the different coefficients of friction.

Friction Example Problem – Block Resting on a Surface Friction Example Problem – Coefficient of Static Friction Friction Example Problem – Coefficient of Kinetic Friction Friction and Inertia Example Problem

Momentum and Collisions Example Problems

These example problems show how to calculate the momentum of moving masses.

Momentum and Impulse Example Finds the momentum before and after a force acts on a body and determine the impulse of the force.

Elastic Collision Example Shows how to find the velocities of two masses after an elastic collision.

It Can Be Shown – Elastic Collision Math Steps Shows the math to find the equations expressing the final velocities of two masses in terms of their initial velocities.

Simple Pendulum Example Problems

These example problems show how to use the period of a pendulum to find related information.

Find the Period of a Simple Pendulum Find the period if you know the length of a pendulum and the acceleration due to gravity.

Find the Length of a Simple Pendulum Find the length of the pendulum when the period and acceleration due to gravity is known.

Find the Acceleration due to Gravity Using A Pendulum Find ‘g’ on different planets by timing the period of a known pendulum length.

Harmonic Motion and Waves Example Problems

These example problems all involve simple harmonic motion and wave mechanics.

Energy and Wavelength Example This example shows how to determine the energy of a photon of a known wavelength.

Hooke’s Law Example Problem An example problem involving the restoring force of a spring.

Wavelength and Frequency Calculations See how to calculate wavelength if you know frequency and vice versa, for light, sound, or other waves.

Heat and Energy Example Problems

Heat of Fusion Example Problem Two example problems using the heat of fusion to calculate the energy required for a phase change.

Specific Heat Example Problem This is actually 3 similar example problems using the specific heat equation to calculate heat, specific heat, and temperature of a system.

Heat of Vaporization Example Problems Two example problems using or finding the heat of vaporization.

Ice to Steam Example Problem Classic problem melting cold ice to make hot steam. This problem brings all three of the previous example problems into one problem to calculate heat changes over phase changes.

Charge and Coulomb Force Example Problems

Electrical charges generate a coulomb force between themselves proportional to the magnitude of the charges and inversely proportional to the distance between them. Coulomb’s Law Example This example problem shows how to use Coulomb’s Law equation to find the charges necessary to produce a known repulsive force over a set distance. Coulomb Force Example This Coulomb force example shows how to find the number of electrons transferred between two bodies to generate a set amount of force over a short distance.

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How to solve a physics problem (with an example)?

Pankaj Kumar

This article will see how to solve a physics problem from scratch, step by step. To demonstrate this, we will  solve a physical pendulum problem with a detailed explanation as given in a textbook.

Question: A uniform steel bar swings from a pivot at one end with a period of 1.2 seconds. How long is the bar?

This problem deals with PHYSICAL PENDULUM and calculating its period. We will explain the solution to this problem right from scratch. We will not use any secondary formulas, and all the steps will be based only on the most fundamental equations. 

Also, we will explain how to approach and solve a problem, where to start from, and what strategy to adopt to solve it most efficiently and logically.

It is explained in such a way that anyone knowing even fundamental physics can understand it easily.

We will try not to solve the problem step by step but also provide helpful insight into what goes on while solving a problem. It will help us solve other problems in your Physics Homework as well.

Approaching the problem

The bar given is uniform. By this, we mean the dimensions are uniform, and the density is the same everywhere in the bar. 

This situation is entirely different from a simple pendulum where the mass “m” is concentrated in the bob at a distance “l” from the pivot point. Here the whole mass “m” is distributed uniformly throughout the length of the bar pendulum.

The FBD of the Physical pendulum is as below:

Building our strategy

We know from our experience that when we displace a uniform rod pivoted at one end slightly by a small angle “θ,” it oscillates about the pivot. So, our analysis should start from the point where the uniform bar gets displaced from its equilibrium position or the vertical position by a small angle “θ.” The bar will try to come back to its original position. When it comes back to its equilibrium position (vertical), the bar gets kinetic energy due to loss in gravitational potential energy. This momentum does not let the rod settle and instead takes it away again from the vertical position. This cycle continues till it loses all its energy and becomes upright again. 

The Physics and Math with explanations

We will assume the bar’s mass as “m” and its length as “l.”

Since the bar is uniform, its center of mass must be at its geometrical center; for a linear rod, the center of mass is at a distance of “l/2” from any end.

The component of the weight W=mg which is normal to the rod, is “mg*sinθ.”

It acts at “l/2” from the pivot point, so the moment of this restoring torque about the pivot point is 

T= (l/2) *mg*sinθ and for small angles sinθ= θ this becomes T= (l/2) mgθ

Moment of inertia about the pivot is 

The resulting angular acceleration α is:

α=T/I= (l/2)*mg*θ/(1/3*ml^2)

Which is α= 3gθ/2l

The SHM criteria is α= w^2*θ

It satisfies the SHM criteria with angular velocity w= sqrt(3g/2l)

Now the period is T=2*pi/w

So, T=2pi*sqrt(2l/3g)

It completes our derivation.

In the given problem, the period is 1.2 seconds. 

Plug this in, and we will get

1.2=2pi*sqrt(2l/3*9.81)

Solving this, we will get l= 0.537 m

Finally, it completes our explanation. 

If you follow the logic and strategy that we used to solve this problem, you will be able to solve physics problems better in the future.

If you need a private online physics tutor who can logically explain physics problems in easy-to-understand steps, contact us on WhatsApp . 

I am the founder of My Engineering Buddy (MEB) and the cofounder of My Physics Buddy. I have 15+ years of experience as a physics tutor and am highly proficient in calculus, engineering statics, and dynamics. Knows most mechanical engineering and statistics subjects. I write informative blog articles for MEB on subjects and topics I am an expert in and have a deep interest in.

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Fueled by problem-solving

Undergraduate research helped feed physics and eecs major thomas bergamaschi’s post-mit interest in tackling challenges..

“Every time I try to solve a problem — whether it be physics or computer science — I always try to find an elegant solution,” says MIT senior Thomas Bergamaschi, who spent four years learning how to solve problems while an Undergraduate Research Opportunities Program ( UROP ) student in the Engineering Quantum Systems (EQUS) laboratory at MIT.

“Of course,” he adds, “there are many times where a problem doesn’t have an elegant solution, or finding an elegant solution is much harder than a normal solution, but it is something I always try to do, as it helps me understand at most something. Another compelling reason is that these solutions are usually the simplest to teach other people, which is always appealing to me.”

Now, as the physics and electrical engineering and computer science (EECS) major ponders post-graduation life, he believes he’s ready to tackle challenges in his career as a software engineer at Five Rings, where he had an internship. “There are a lot of hard and interesting problems to be solved there,” he says. “Challenges are something that fuels me.”

STEM family

Born in Brazil, Bergamaschi lived in the United States until he was 6, when his family moved back to a small town in rural Sao Paulo called Vinhedo. His Brazilian father is a software engineer, and his mother, who is from England, studied biology in college and now teaches English. He followed in the footsteps of his older brother, Thiago, who was the first in the family to be drawn to physics. And when his brother entered physics competitions in high school, Thomas did too.

He had high school teachers who encouraged him to study physics beyond the usual curriculum. “One teacher accompanied me on many bus and plane rides to physics competitions and classes,” he recalls. “She was a huge motivator for me to continue studying physics and helped find me new books and problems throughout high school.”  

The younger Bergamaschi went on to win silver medals at the International Physics Olympiad and at the International Young Physicists’ Tournament , and more than a dozen other medals in national and regional Brazilian science competitions in physics, math, and astronomy.

Thiago Bergamaschi ’21 joined MIT as a physics and EECS major in 2017, and his brother wasn’t far behind him, entering MIT in 2019.

Bergamaschi ended up spending nearly all four years at MIT as a UROP student in the Engineering Quantum Systems (EQUS) laboratory, under the supervision of PhD student Tim Menke and Professor William Oliver . That’s when he was introduced to quantum computing — his supervisors were constructing a device that had a phenomenon where many qubits could interact simultaneously.

“This type of interaction is very useful for quantum computers, as it gives us a possible way that we can map problems we are interested in onto a quantum computer,” he says. “My project was to try to answer the question of how we can actually measure things, and prove that the constructed device actually had this coupling term we were interested in.”

He proposed and analyzed methods to experimentally detect many-body quantum systems. “These systems are extremely important and interesting as they have many cool applications, and in particular can be used to map computationally hard problems — such as route optimization, Boolean satisfiability, and more — to quantum computers in an easy way.”

This project was supposed to be a warmup project for his UROP. “However, we soon noticed that the problem of accurately measuring these effects was a pretty tricky problem. I ended up working on this problem for around six months — my summer, the fall semester, and the beginning of IAP [Independent Activities Period] — trying to figure out how we can measure these effects.”

He presented his research at the 2021 and 2022 American Physical Society March meetings, and published “Distinguishing multi-spin interactions from lower-order effects” in Physical Review Applied .   

“The experience of presenting my work in a conference and publishing a paper is a huge highlight from my time at MIT and gave me a taste of scientific communication and research, which was invaluable for me,” Bergamaschi says. “Being able to do research with the help of Tim Menke and Professor Oliver was inspiring, and is one of the largest highlights from my time at MIT.”

He also worked with William Isaac Jay, a postdoc at the MIT Center for Theoretical Physics , on lattice quantum field theory. He studies quantum theories at the microscopic level, where strong nuclear interactions are relevant. “This is particularly appealing as we can simulate these theories on a computer — albeit usually a huge supercomputer — and try to make predictions about phenomena involving atoms at a minuscule scale. I UROP’d in this lab over both my junior and senior year, and my project involved implementing techniques from one of these computer simulations, how can we go back to the real world and obtain something that an experiment would measure.”

Brazil blues

Bergamaschi missed Brazil but found community playing soccer with intramural teams  Ousadia and Alegria Futebol Clube, and eating churrasco with his friends at Oliveira’s Brazilian-style steakhouse in Somerville, Massachusetts. He also loved going to college with his brother, who graduated in 2021 and is now pursuing his PhD in physics at the University of California at Berkeley.

“One of my favorite memories of MIT is from my sophomore spring, when I managed to take two classes with him just before he graduated,” he recalls. “It was a lot of fun discussing physics problem sets and projects with him.”

What also keeps him in touch with his homeland is working with Brazilian high school students competing in physics tournaments. He is part of an academic committee that creates and grades the physics problems taken by the top 100 Brazilian high school students. Those with top scores go on to the International Physics Olympiad . He says he sees this as a way to pay forward what his high school teacher did for him: to encourage others to study physics.

“These olympiads were one of the main reasons for my interest in physics and me coming to MIT, and I hope that other Brazilian students can have these same opportunities as I had,” he says. “These students are all incredibly talented. A large amount of them end up coming to MIT after they graduate high school, so it’s a very gratifying and incredible experience for me to be able to participate and help in their physics education.”

Post-graduation thoughts

What will he miss most at MIT? “Late-night problem set sessions immediately before a deadline, trying to find a free food event across campus, and getting banana lounge bananas and coffee.”

And what were his biggest lessons? He says that MIT taught him how to work with other people, “handle imposter syndrome,” and most importantly, unravel complicated challenges.

“I think one of my major motivators is my desire to learn new things, whether it be physics or computer science. So, I am a big fan of very difficult problems or projects which require continual work but have large payoffs at the end. I think there are many instances during my time at MIT in which I worked all night for a project, just to get up and hop back on because of the excitement of obtaining a result or solution.”

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How to Solve Problems: For Success in Freshman Physics, Engineering, and Beyond 5th Edition

• ISBN-10 0962200859
• ISBN-13 978-0962200854
• Edition 5th
• Publisher Dosoris Pr
• Publication date January 1, 1998
• Language English
• Dimensions 6 x 0.25 x 9.25 inches
• Print length 118 pages
• See all details

Editorial Reviews

From library journal.

He concludes the handbook with challenging physics and engineering problems. Yes, the systematic strategies and solutions are also included. -- M. Jenice French, The Physics Teacher, 34, 120 February 1996

From the Publisher

Step by step explanations of how to describe problems exactly, draw diagrams, define variables, standardize units, calculate clearly, and state answers accurately are illustrated by solved examples of typical introductory physics and engineering problems. The problem-solving style learned by working these simple examples can be used for all problems, including those that are complex, open ended, or design oriented.

Product details

• Publisher ‏ : ‎ Dosoris Pr; 5th edition (January 1, 1998)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 118 pages
• ISBN-10 ‏ : ‎ 0962200859
• ISBN-13 ‏ : ‎ 978-0962200854
• Item Weight ‏ : ‎ 8 ounces
• Dimensions ‏ : ‎ 6 x 0.25 x 9.25 inches
• #52,664 in Physics (Books)
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• Problem of the Week

During each week from 2002 to 2004, I posted a problem on this page. Some problems are new, and some are classics. Half of them are physics (the odd weeks), and half are math (the even weeks). In most cases they're quite difficult. After all, I call them "Problems of the Week," and not "Problems of the Hour"! Many of the math problems can be found in my book: The Green-Eyed Dragons and Other Mathematical Monsters . And many of the physics problems can be found in my classical mechanics textbook  for the Physics 16 course here at Harvard.

-  David Morin

© 2004 by David Morin 

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NSF launches new investment to accelerate the transition of privacy-enhancing technologies to practice

The new pdasp program aligns with a tasking in the recent 'executive order on the safe, secure, and trustworthy development and use of artificial intelligence'.

The U.S. National Science Foundation yesterday published a new investment to advance privacy-enhancing technologies (PETs) and promote their use to solve real-world problems. The Privacy-Preserving Data Sharing in Practice (PDaSP) program, which aligns with a tasking in the recent " Executive Order on the Safe, Secure, and Trustworthy Development and Use of Artificial Intelligence " (AI EO), will enhance the ability to privately share and analyze data for a range of use cases and applications, including those of significant interest to federal agencies.   

"The explosive growth of data and computational power in today’s world provide tremendous opportunities to accelerate scientific discovery and innovation," said Erwin Gianchandani, NSF assistant director for TIP. "NSF is uniquely positioned to lead efforts to enable and promote data sharing in a privacy-preserving and responsible manner to harness the power and insights of data for public good. Through this program, NSF will prioritize use-inspired and translational research that empowers federal agencies and the private sector to adopt leading-edge PETs in their work."  

PDaSP is led by the NSF Directorate for Technology, Innovation and Partnerships (TIP) in collaboration with the NSF Directorate for Computer and Information Science and Engineering, as well as Intel Corporation and VMware LLC, as industry partners, and the U.S. Department of Transportation Federal Highway Administration and U.S. Department of Commerce National Institute of Standards and Technology as federal agency partners.  

"PDaSP reflects NSF's commitment to accelerate the translation of promising research outputs to the market and society by promoting use-inspired research, systems development and implementation projects," said Thyaga Nandagopal, director of the Division of Innovation and Technology Ecosystems within TIP. "We are pleased to address, through the PDaSP program, key priorities put forward in the National Strategy to Advance Privacy-Preserving Data Sharing and Analytics (PPDSA). The PDaSP program also answers mandates of the AI EO by prioritizing research, development and availability of testing environments to support the maturation and deployment of PETs in application-specific contexts."   

The PDaSP program welcomes proposals from qualified researchers and multidisciplinary teams in the following tracks with expected funding ranges for proposals as shown below.  

• Track 1: Advancing key technologies to enable practical PPDSA solutions: Projects are expected to be in the $500K - $1 million range for up to two years.  
• Track 2: Integrated and comprehensive solutions for trustworthy data sharing in application settings:  Projects are expected to be in the $1 million - $1.5 million range for up to three years.  
• Track 3: Usable tools and testbeds for trustworthy sharing of private or otherwise confidential data: Projects are expected to be in the $500K - $1.5 million range for up to three years.  

For more information, visit the PDaSP program webpage or register for an upcoming informational webinar on July 12 or July 23 .  

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Bibliometrics & citations, view options, recommendations, certified pde-constrained parameter optimization using reduced basis surrogate models for evolution problems.

We consider parameter optimization problems which are subject to constraints given by parametrized partial differential equations. Discretizing this problem may lead to a large-scale optimization problem which can hardly be solved rapidly. In order to ...

Reduced Basis Method for quadratically nonlinear transport equations

If many numerical solutions of parametrised partial differential equations have to be computed for varying parameters, usual Finite Element Methods (FEM) suffer from too high computational costs. The RBM allows to solve parametrised problems faster than ...

Approximated Lax pairs for the reduced order integration of nonlinear evolution equations

A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, ...

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Aerospace engineering student uses black soldier flies to grow pea plants in simulated Martian soil

by Felysha Walker, Texas A&M University

Once we travel to another planet, we'll face the next challenge—how to survive. Emmanuel Mendoza began tackling that problem in his parent's garage during his senior year of high school.

"I've always been interested in human space systems, specifically, how we grow or how humans live in long-term space environments," said Mendoza, an aerospace engineering student at Texas A&M University.

This interest began with a high-school science project testing if radishes would grow in Martian regolith (simulated Martian soil). Today, he's upgraded from a garage to the Forensic Laboratory for Investigative Entomological Sciences (FLIES) Facility at Texas A&M, where he experiments with growing pea plants in simulated Martian soil with the help of black soldier flies.

Insects: The astronaut's best friend

During his freshman year at A&M, Mendoza scrolled through the Aggie Research Program's website for an undergraduate research opportunity that would allow him to bridge his interests in aerospace engineering and sustainable agriculture. One project caught his eye. Noah Lemke, a Texas A&M graduate student, was researching black soldier flies under the direction of entomology professor Dr. Jeffery Tomberlin.

"Black soldier flies are on the rise due to their ability to break down basically any organic matter —feces, animal waste, organic waste, plant matter—a lot of things that are generally non-useful," said Mendoza.

As a byproduct of digesting this biomatter, the black soldier fly larvae produce frass, which is essentially insect waste.

"Because of the way their gut works, it is found to be a really good soil supplement, like fertilizer to plants," said Mendoza. "I saw this and thought, if you can use this for plants, what's to prevent you from using it with something that doesn't usually support life?"

Since then, Mendoza has been experimenting with pea plant growth in Martial soil using varying amounts of frass. He potted pea plants in regular and Martian soil and experimented using 0% to 100% frass.

To his surprise, green pods sprouted from the red regolith.

Taking root in red soil

Mendoza found that exceeding anything greater than 50% frass would destroy the plant's ability to grow but adding 10% frass to the Martian soil was the optimum amount for plant growth.

"This tells us that frass is being used by the soil. It's also showing us the plants are definitely up-taking something from the soil," he said. "It definitely shows that the Martian regolith is not so inert that plants will not grow. It's showing us that there is a certain functionality, a certain usefulness in Martian regolith."

Even with 0% frass, he saw flowering and pod growth in plants potted entirely in Martian soil.

"That was really interesting. It shows that plants are super resilient. They can learn togreen plants on mars thrive and grow in even the most austere conditions, and that we can do a lot with the things that we already have on hand and species that already exist," he said. "And we can do a lot to make those environments more favorable."

Mendoza presented his findings at the 2023 Entomological Society of America Conference in Washington, D.C.

Planning ahead

In addition to being an aerospace engineering major, Mendoza has a double minor in agricultural systems management and mathematics. He hopes that his education and ability to layer his interests will lead him to the forefront of sustainable agriculture—for space and for Earth.

"Looking at long-term work not necessarily space-related, we need to find additional soil supplements to grow things on Earth in order to continue having sustainable agriculture ," said Mendoza.

"We need to have options to grow things in environments that we really haven't grown them in before, and I think that's where this comes in because Martian regolith is the hardest. If you can master that, then I think you can work backward and develop good novel farming techniques for growing things on Earth."

Now, in his second year of experiments, he is focusing on soil analysis and plant mass analysis. With every potted pea plant, he gathers data that intersects agriculture, entomology and aerospace engineering .

"I want to focus on the life support and the food science aspect of supporting astronauts in their field. I want to build a system that demonstrates this is possible in zero gravity," said Mendoza.

Until he begins building that system, he continues growing plants and gathering data on how fly larvae may be humanity's golden ticket to survival.

Provided by Texas A&M University

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