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 topview 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. Repeat the exercise if you are pulling the string at 45 degrees from the vertical. 6) A carpenter swings a 3kg 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. 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. 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? 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.
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.
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.
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, v_{0}, what force is the worker using? Explain
how you know. 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?

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
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Last modified June 21, 2002