### Dynamics practice problems

The following are a bunch of pulley exercises and problems. If you can work through and understand them you should be able to solve most standard pulley problems. When working through pulley problems in Engineering Dynamics, we will usually make the following assumptions.

With just a little extra work it is possible to determine the tension too. The tension might be surprising. Here is a classical pulley problem that asses your understanding of basic mechanics concepts.

It is a multiple choice problem. In Part A below, we draw free body diagrams, write equations of motion, and begin working out the pulley kinematics. It also make you think more deeply about whether a pulley problem is well posed or not. Here is Part 1 of the video solution. In it, I derive equations of motion, and work out the pulley kinematics. We can neglect the mass of the pulley.

The following video explains how these assumptions make solving pulley problems easier. Unless stated otherwise, we will regard these assumptions as valid. We work through the answer in the video below. Pulley Multiple Choice Here is a classical pulley problem that asses your understanding of basic mechanics concepts. In Part B, we finish the pulley kinematics and solve for the acceleration. In Part 2, I solve for tension and interpret the result.A satellite of mass Small thrusters are used to maneuver the satellite in its orbit.

An elevator car of mass kg is raised and lowered by a cable. A balloon of a known mass or weight is dropped from a known height and timed. Determine the average amount of air resistance that acts on it.

An object that weighs A certain rope has a tensile strength of 5. Suppose this rope is used for rappelling. What is the maximum deceleration of a Repeat for a An object of mass 5. As shown in the diagram below a mass m is pulled by two forces but remains at rest due to a third force — gravity. Two astronauts aboard the space station bump into one another. Astronaut Jones, mass If Smith is accelerated 2.

A doomed skydiver of mass He exerts a downward force of Use a CBR to measure a book of known weight that falls and is caught by a student. Use the velocity vs. A student of mass A bowling ball is prevented from rolling down an incline of Based on the known weight of the ball determine the normal force that acts upon it and the amount of force that the student has to exert.

A A force of A man of mass Every time the man lifts himself a bit higher he accelerates upward 0. Determine the maximum tension in the rope that occurs during his climb to the top. At what part of the rope does this occur?Dynamics Force problems ask you to relate motion to the forces causing it.

You know many forces such as gravity, tension, and normal force that are present even if not listed in the problem. In other cases, it is harder to recognize 2nd Law problems. You may know forces that are present without having force ever mentioned in the problem, and you may be asked for things like how fast an object moves in a circle or how much of an object is underwater. When you approach force problems, a free body diagram will allow you to both picture what is happening and directly map the picture into the equation.

All the physics is done in the process of drawing the diagram—only algebra remains after this step. The first thing that you will need to do is to identify what object s will be the focus of the diagram—in other words, what system do you need to consider in order to answer the question. In some cases, you will need to consider several objects as separate systems. In those cases, you will draw free body diagrams and set up equations for each object separately.

Once you have identified your system, think about all forces on that system, discard any that are too small to matter. Only forces acting on the object should be shown, since you are trying to understand what causes the motion of the object.

Acceleration is the result not the cause—if you wish to sketch the acceleration, make sure that you do so off to the side and not on the sketch of forces. Math is always easiest if you pick one axis to be along the direction of acceleration. That way, one component of a will be zero and you will have fewer linked equations. This true no matter what you are asked to find.

If any additional information is needed, it will become apparent as you work through the problem. Think carefully about the direction of each force and include the appropriate sign. Once you have filled your forces into these equations, you have only algebra left and can solve the equations in any way that works. Once you have completed the problem, look at it again. Does your answer make sense?

Did it give the behavior you intuitively expected to find? Can you now do steps that caused you problems earlier? Can you explain in words what is happening? If you only recognized it as a 2nd Law problem because of the section heading in your text book, identify the information that you would use to recognize a problem like this on the final exam.

One of the most common mistakes is to think too hard. Check Definition and Ratio problems to see if you can find a useful example.

It is also possible that your problem is better solved using kinematics description of motion or energy and momentum.

Can you clearly explain to yourself that your problem requires you to relate the cause of motion forces to the effect of those forces acceleration or changing velocity? In that case, think more broadly about what makes a useful example. Remember, you were given your assignment to practice the problem solving approachnot because the answers to your problems are particularly interesting.

### AP Physics 1

An example in which you merely substitute your numbers for those in the problem will give you practice entering numbers on your calculator but will teach you nothing about physics, and when you take your exam every problem on it will feel new and different to you.

So think about your example as support for helping you to practice the problem solving approach. And every single problem in this section uses the very same approach, so any problem is an appropriate example to help you approach your problem.

That said, different situations require you to do different side problems along the way. So if your problem has any of these features, you may find it useful to pick an example that does as well. Problems Dynamics.Determine the magnitude of the acceleration of the car. If the radius of the motion is 0. Assume all other parameters stay constant except that noted in the description of the change.

Of course, the object would have to be forced differently to keep the speed the same if the mass changes. List the standard lab apparatuses needed to make the measurements and the calculations a student can make with the measurements to determine the acceleration.

Measurement devices needed: A long measuring tape A stopwatch Step 1: Use the measuring tape to determine the radius r of the path of the car on the circular racetrack. Model the car as a point particle. Use the geometric center of the car as the location of this point.

Step 2: Use the stopwatch to determine the time T needed for the car to move once around the track. Example: If the actual radius is This is the largest expected error that is too high.

However, one can also determine an answer that is too low. Determine the velocity and acceleration when the particle is at: a. Find the magnitude of the acceleration. When, if ever, is the acceleration zero? When, if ever, is the speed zero? All rights reserved. Get Ready. Be Prepared. Understand the Big Ideas.A child throws a ball downward from a tall building. Note that the ball is thrown, not dropped and disregard air resistance.

What is the acceleration of the ball immediately after it leaves the child's hand? You are driving along an empty straight road at a constant speed u. At some point you notice a tall wall at a distance D in front of you. Would it require a larger force to a continue moving straight and decelerate to a full stop before the wall, or b turn left or right to avoid the wall?

How fast should the earth spin in order for a lb human not to be able to walk on the ground? In the film A Space Odyssey, a wheel like space station achieves artificial gravity by spinning around its axis.

If the station had a size of 2 km, how fast should it be spinning for the people inside to feel the same gravitational acceleration as on earth? A boy of mass 40 kg wishes to play on pivoted seesaw with his dog of mass 15 kg. When the dog sits at 3 m from the pivot, where must the boy sit if the 6.

The drawing shows three particles far away from any other objects and located on a straight line. Find the magnitude and direction of the net gravitational force acting on each of the three particles the direction to the right is positive.

As part a of the drawing shows, two blocks are connected by a rope that passes over a set of pulleys.

The block 1 has a weight of N, and the block 2 has a weight of N. The rope and the pulleys are massless and there is no friction. Find the acceleration of the remaining block. Part a of the drawing shows a block suspended from the pulley; the tension in the rope is 80 N.

Part b shows the same block being pulled up at a constant velocity. What is the tension in the rope in part b?Mr Trask's Physics. Search this site. Unit 0 - Introduction. Unit 1 - Kinematics in 1D. Unit 2 - Kinematics in 2D. Unit 3 - Dynamics. Unit 4 - Momentum and Energy. Unit 5 - Circular Motion and Gravitation. Unit 6 - Equilibrium. Unit 7 - Rotational Dynamics. Unit 9 - Electric Circuits. Unit 1 - Electrostatics. Unit 2 - RC Circuits.

Unit 3 - Electromagnetism. Unit 4 - Fluid Mechanics. Unit 5 - Thermodynamics. Unit 6 - Waves and Optics. Unit 7 - Nuclear and Quantum. Unit 8 - Review. Unit 1. Unit 2. Unit 3. Unit 4. Unit 5. Unit 6. Unit 7. Unit 8. Year End Review. Unit 1 Vector Kinematics. Unit 2 - Dynamics. Unit 3 - Equilibrium. Unit 4 - Work, Energy, Power, Momentum. Unit 6 - Electrostatics. Unit 7 - Electric Circuits. Unit 8 - Electromagnetism. Capacitance and Resistivity.

Center of Mass. Unit 1 - Safety and Review. Unit 2 - The Mole.This course is an introduction to the study of bodies in motion as applied to engineering systems and structures. We will study the dynamics of particle motion and bodies in rigid planar 2D motion. This will consist of both the kinematics and kinetics of motion.

Kinematics deals with the geometrical aspects of motion describing position, velocity, and acceleration, all as a function of time.

## AP Physics 1

Kinetics is the study of forces acting on these bodies and how it affects their motion. You will find a book like this useful as a reference and for completing additional practice problems to enhance your learning of the material.

Wayne Whiteman. Any other use of the content and materials, including use by other academic universities or entities, is prohibited without express written permission of the Georgia Tech Research Corporation.

Interested parties may contact Dr. Wayne Whiteman directly for information regarding the procedure to obtain a non-exclusive license. The Georgia Institute of Technology is one of the nation's top research universities, distinguished by its commitment to improving the human condition through advanced science and technology.

Georgia Tech's campus occupies acres in the heart of the city of Atlanta, where more than 20, undergraduate and graduate students receive a focused, technologically based education.

In this section students will learn about particle kinematics, Newton's Laws and Euler's Laws, motion of particles and mass centers of bodies.

In this section students will learn about planar 2D rigid body kinematics, relative velocity equation, rotation about a fixed axis, instantaneous center of zero velocity, and relative acceleration equations. In this section students will continue to learn about planar 2D rigid body kinematics, relative velocity equation, rotation about a fixed axis, instantaneous center of zero velocity, and relative acceleration equations.

In this section students will learn about planar 2D rigid body kinetics, translation, moment of momentum - angular momentum, and equations of motion. In this section students will continue to learn about planar 2D rigid body kinetics using the Work-Energy Method.

In this section students will continue to learn about planar 2D rigid body kinetics using the Impulse-Momentum Method and Conservation of Momentum. A brilliant course, gave me a great foundation for more advanced courses in mechanical engineering.

Centripetal Acceleration & Force - Circular Motion, Banked Curves, Static Friction, Physics Problems

When ever i use some of the things i learned in this course in my work i think of Whiteman. I would just like to say that Prof. Whiteman is a great explainer.

## CP1 ("Regular") Physics 1

I would like to complete most of the courses by him that are available on Coursera. Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.