9.2 The Second Condition for Equilibrium
Which of the following is not an example of an object undergoing a torque?
- A car is rounding a bend at a constant speed.
- A merry-go-round increases from rest to a constant rotational speed.
- A pendulum swings back and forth.
- A bowling ball rolls down a bowling alley.
Five forces of equal magnitude, labeled A–E, are applied to the object shown below. If the object is anchored at point P, which force will provide the greatest torque?
- Force A
- Force B
- Force C
- Force D
- Force E
Using the concept of torque, explain why a traffic cone placed on its base is in stable equilibrium, while a traffic cone placed on its tip is in unstable equilibrium.
9.4 Applications of Statics, Including Problem-Solving Strategies
A child sits on the end of a playground see-saw. Which of the following values is the most appropriate estimate of the torque created by the child?
- 6 N•m
- 60 N•m
- 600 N•m
- 6000 N•m
A group of students is stacking a set of identical books, each one overhanging the one below it by 1 inch. They would like to estimate how many books they could place on top of each other before the stack tipped. What information below would they need to know to make this calculation?
- The mass of each book
- The width of each book
- The depth of each book
- I only
- I and II only
- I and III only
- II only
- I, II, and III
A 10 N board of uniform density is 5 meters long. It is supported on the left by a string bearing a 3 N upward force. In order to prevent the string from breaking, a person must place an upward force of 7 N at a position along the bottom surface of the board. At what distance from its left edge would they need to place this force in order for the board to be in static equilibrium?
- 5 m
A bridge is supported by two piers located 20 meters apart. Both the left and right piers provide an upward force on the bridge, labeled FL and FR respectively.
- If a 1000 kg car comes to rest at a point 5 meters from the left pier, how much force will the bridge provide to the left and right piers?
- How will FL and FR change as the car drives to the right side of the bridge?
An object of unknown mass is provided to a student. Without using a scale, design an experimental procedure detailing how the magnitude of this mass could be experimentally found. Your explanation must include the concept of torque and all steps should be provided in an orderly sequence. You may include a labeled diagram of your setup to help in your description. Include enough detail so that another student could carry out your procedure.
9.5 Simple Machines
As a young student, you likely learned that simple machines are capable of increasing the ability to lift and move objects. Now, as an educated AP Physics student, you are aware that this capability is governed by the relationship between force and torque.
In the space below, explain why torque is integral to the increase in force created by a simple machine. You may use an example or diagram to assist in your explanation. Be sure to cite the mechanical advantage in your explanation as well.
Figure 9.24(a) shows a wheelbarrow being lifted by an applied force Fi. If the wheelbarrow is filled with twenty bricks massing 3 kg each, estimate the value of the applied force Fi. Provide an explanation behind the total weight w and any reasoning toward your final answer. Additionally, provide a range of values over which you feel the force could exist.
9.6 Forces and Torques in Muscles and Joints
When you use your hand to raise a 20 lb dumbbell in a curling motion, the force on your bicep muscle is not equal to 20 lb.
- Compare the size of the force placed on your bicep muscle to the force of the 20 lb dumbbell lifted by your hand. Using the concept of torque, which force is greater and explain why the two forces are not identical.
- Does the force placed on your bicep muscle change as you curl the weight closer toward your body? (In other words, is the force on your muscle different when your forearm is 90° to your upper arm than when it is 45° to your upper arm?) Explain your answer using torque.