University of Maryland Physics Education Research Group


Activity Based Physics Thinking Problems in Mechanics: Forces

PERG Info | PERG materials | PERG HOMEPAGE | PER on the web | Resources on the web

    Activity Based Physics Thinking Problems in Mechanics: Forces

    1) A Frenchman, filling out a form writes "78 kg" in the space marked Poids (weight). However, weight is a force and the kg is a mass unit. What do the French (among others) have in mind when they use a mass to report their weight? Why don't they report their weight in newtons? How many newtons does this Frenchman weigh? How many pounds?

    2) An old Yiddish joke is told about a farmer in Chelm, a town famous for the lack of wisdom of its inhabitants. One day the farmer was going to the mill to have a bag of wheat ground into flour. He was riding to the mill on his donkey, with the sack of wheat thrown over the donkey's back behind him. On his way, he met a friend. His friend chastised him. "Look at you! You must weigh 200 pounds and that sack of flour must weigh 100. That's a very small donkey! Together, you're too much weight for him to carry!" On his way to the mill the farmer thought about what his friend had said. On his way home, he passed his friend again, confident that this time the friend would be satisfied. The farmer still rode the donkey, but this time he carried the 100 pound bag of flour on his own shoulder!

    Analyze the problem by considering the following simplified picture: two blocks resting on a scale. One block weighs 10 N, the other 25 N. In case 1 the blocks are arranged on the scale as shown in the figure below. In case 2 the blocks are arranged as shown on the right. Each system has come to rest.

    Analyze the forces on the blocks and on the scale in the two cases by isolating the objects -- each block and the scale -- and using Newton's laws, show that the force exerted on the scale must be the same in both cases. 

    3) Your pickup truck gets stuck in some soft dirt driving across a field. Fortunately, you have a winch connected to the truck and a rope. You connect the rope from the winch to a nearby tree and wind it as tightly as you can. Unfortunately, the truck is still stuck. However, you remember your physics class and go to the middle of the taut rope and push in a direction perpendicular to the rope as shown in the top-view diagram below.

    You push with a force of 100 pounds and the rope bends inward a distance of 1 foot. If the car is 50 feet from the tree, find the force the rope exerts on the car.

    4) Discuss the difference between the physical content of the two laws F = ma and F = mg. (Do NOT just give a one sentence statement describing each. Think about what they mean and how they are used. Are they similar in some ways? Are they different in some ways? What I am looking for here is a thoughtful discussion that shows some insight into what these laws mean.)

    5) Suppose you are standing on the ground in a shed and are pulling vertically downward on a string that is attached to the bottom of a block that hangs from the ceiling on a rope. 

    • Draw well separated force diagrams for your body, the string, the block, the rope, the shed, and the earth. 
    • Describe each force in words, indicating the nature of the force and say what object is exerting the force on what other object. 
    • Show the relative sizes of the force by using a longer arrow for a larger force and equal-length arrows for equal forces. 
    • Identify third law pairs. 

    Repeat the exercise if you are pulling the string at 45 degrees from the vertical.

    6) A carpenter swings a 3-kg hammer so that its speed is 5 m/s just before it strikes a nail. The nail is driven 6 mm into a block of wood.

    • Assuming that a constant force resisted the motion of the nail, what must have been the magnitude of the force? 
    • Compare the force to the weight of the hammer. 

    7) You have placed two of your books on a table, one on top of the other as shown in the figure below.

    (a) You press down on the top book with a force F. Consider the forces on the book marked Tipler. Draw a diagram showing all the forces acting on this book. Be sure to indicate the type of each force and the agent responsible for it. What can you say about the magnitudes of these forces? Write down any relations you can between them and specify how you know them.
    (b) Specify all the forces acting on the book marked Jurassic Park, giving the comparable information to that requested for the forces on Tipler.
    (c) Can you identify any relations between the forces acting on Tipler and those acting on Jurassic Park? Which ones? How do you know?

    8) A bowling ball sits on a hard floor at a point which we take to be the origin. The ball is hit some number of times by a hammer. The ball moves along a line back and forth across the floor as a result of the hits. The region to the right of the origin is taken to be positive, but during its motion the ball is at times on both sides of the origin. A graph showing the ball's velocity is given below. 

    Answer the following questions with the symbols R (right), L (left), N (neither), or C (can't say which). Each question only refers to the time interval displayed.

    (a) Which side of the origin is the ball at for the time marked A?
    (b) At the time marked B, in which direction is the ball moving?
    (c) Between the times A and C, what is the direction of the ball's displacement?
    (d) The ball receives a hit at the time marked D. What is the direction the ball is moving after that hit?
    (e) The ball receives a hit at the time marked D. What is the direction of the force on the ball produced by that hit?

    9) A toy car is moving along a straight track. Its motion is restricted to the + distance axis. For the situations described below, choose the letter of the one correct acceleration vs. time graph which could correspond to the motion described. If you think that none is correct, answer N. You may use a graph more than once.

    (a). The car speeds up at a steady rate, moving away from the origin.
    (b) The car slows down at a steady rate, moving away from the origin.
    (c). The car moves at a constant speed toward the origin.
    (d). The car speeds up at a steady rate, moving toward the origin.

    10) Discuss what we mean in physics by "a force". How do we know when an object is feeling a force? What kinds of forces are there? Write a brief (one to two page) essay discussing what a physicist means by a "force". Include a discussion of what the different kinds of forces are that we have talked about in this class and some of their properties.

    11) A student (whom we will call Bill) was about to go out on a date when his roommate, Bob, asked him to hold a pail against the ceiling with a broom for a moment. After Bill had complied, Bob mentioned that the pail was filled with water and left. 

    (a) Draw a free-body diagram showing all the forces acting on the pail. Be sure for each force you identify the kind of force and the object whose interaction with the pail is responsible for the force. 
    (b) Suppose Bill wants to slide the pail a few feet to one side so he can get to a chair in the room. Are any other forces not specified in your answer to part (a) that become relevant? 
    (c) Suppose the pail weighs 1 pound, it has 6 pounds of water in it, the coefficient of friction between the broom and pail is 0.3, and the coefficient of friction between the pail and the ceiling is 0.5. Can Bill slide the pail? Explain. 

    12) Jack left the lights in his truck on while in a truck stop in Kansas and his battery went dead. Fortunately, his friend Al was there. Unfortunately, Al was driving his Geo Metro. Fortunately, the road was very flat. Jack was able to convince Al to give his truck a long slow push to get it up to 20 miles/hour. At this speed, Jack can let in the truck's clutch and the truck's engine should start up. 

    (a) Al begins to push the truck. It takes him 5 minutes to get the truck up to a speed of 20 miles/hour. During the time that Al's Geo is pushing the truck, draw separate free body diagrams for the Geo and for the truck. Order all the horizontal forces by magnitude from largest to smallest. If any are equal, state that explicitly. Explain your reasoning. 
    (b) If the truck was accelerating uniformly over the 5 minutes, how far did Al have to push the truck before Jack could let in the clutch? 
    (c) Suppose the mass of the truck is 4000 kg, the mass of the car is 800 kg, and the coefficient of friction between the vehicles and the road is 0.1. At one instant when they were trying to get the truck moving, the car was pushing the truck and exerting a force of 1000 N, but neither vehicle moved. What was the frictional force between the truck and the road? Explain your reasoning.


    13) A worker is pulling a heavy crate along the floor with a rope. The crate has a mass M and the coefficient of friction between the crate and the floor is m

    (a) If the worker is pulling so that the crate is moving at a constant velocity, v0, what force is the worker using? Explain how you know. 
    (b) Does how hard she has to pull depend on whether her little brother (mass = m) is sitting on top of the crate? Explain your reasoning. 
    (c) If her little brother is sitting on top of the crate, and if M = 50 kg, m = 30 kg, m = 0.4, and v0 = 4 m/s, how hard does she have to pull to keep it moving? 

    14) When I release a book in midair it falls to the ground. When I put it on a table, the book stays where it is. Discuss why the book on the table does not fall. How does the table know what to do?

    15) The shelves in a refrigerator are metal lattices that are held up by being slipped into two small (about 1 inch long) hollow boxes or "pockets" attached to the interior back wall of the refrigerator. If a full gallon of milk is put on the shelf, is it more likely to break the pocket if it is placed near to the back of the refrigerator or near to the front? Explain your answer in terms of the physics we have learned. If the milk is the only thing on the shelf, estimate the downward force that the shelf exerts on the front of the pocket when the milk is placed at the front of the shelf.


These problems written and collected by E. F. Redish. Photos and figures by E. F. Redish. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity Based Physics Thinking Problems in Physics site is mentioned and the URL given. Webpage edited by K.A. Vick

To contribute problems to this site, send them to

Go back to the Activity Based Physics page
Go back to the Thinking Problems page
Go back to the Thinking Problems in Mechanics page

Information about PERG Resource materials from PERG PERG Homepage PER elsewhere on the web Resource materials for teachers

Maintained by University of Maryland PERG
Comments and questions may be directed to E. F. Redish
Last modified June 21, 2002