AP50 Fall 2014
Problem Set 3
due Thursday, Oct 16 in class
Instructions:
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use 8.5 x 11” paper
no staples — use a paperclip (we’ll have some on hand)
blue or black ink (no light pencils and no red)
name on each page
single-sided (no writing on back)
leave margins blank
no-dog ears or torn out of ring-bound notebook
Many of these problems require energy and/or free-body diagrams. Please include when appropriate.
1. A company thinks that there is a market for ultralight umbrellas. While developing these umbrellas, the design
team was confronted with the following question: Is the force of the rain falling on an opened umbrella a force
that needs to be taken into consideration in designing an umbrella? You have been hired as a consultant to this
firm. Your task is to estimate the magnitude of this force. You are allowed to use anything that you feel may assist
you. You must be able to justify your solution before the members of the design team.
Hint: You might have to factor in terminal velocity.
2. Spring into action
On a low-friction track, a 0.36-kg cart initially moving to the right at 2.05m/s collides elastically with a 0.12-kg
cart initially moving to the left at 0.13m/s. The 0.12-kg cart bounces off of the other cart and then compresses a
spring attached to the right end of the track.
(𝑎) At the instant of maximum compression of the spring, how much elastic potential energy is stored in
the spring?
(𝑏) If the spring then returns all of this energy to the cart, and the two carts collide again, what is the final
velocity of each cart?
3. Going up?
Penny wants to test out her new scale. Suppose Penny’s inertia is 45 kg. She does five experiments (A-E).
A: Penny stands on a scale in her bathroom and notes the scale reading.
B: Penny stands on a scale that is at rest with respect to an elevator that is moving upward at a constant speed.
C: Penny stands on a scale that is at rest with respect to an elevator that is moving downward at a constant speed.
D: Penny stands on a scale that is at rest with respect to an elevator that is accelerating up at 2 m/s2.
E: Penny stands on a scale that is at rest with respect to an elevator that is accelerating downward at 2 m/s2.
(𝑎) Draw free-body diagrams for the elevator cabin, Penny, and the scale, respectively, labeling the forces
using the notation introduced in the book. Make sure the lengths of the force vectors are appropriate
to the magnitudes of the forces.
(𝑏) State the magnitudes of as many forces as possible and identify all the forces that form interaction
pairs. Explain briefly how you obtained these magnitudes.
(𝑐) In which, if any, of these experiments (A-E) does the scale reading register a value that is less than the
reading when Penny stands on the scale at home.
AP50 Fall 2014
4. Quick shot
A bullet of inertia 𝑚 traveling at speed 𝑣 is fired into a wooden block that has inertia 4𝑚 and rests on a level
𝑣
surface. The bullet passes through the block and emerges with speed , taking a negligible amount of the wood
3
with it. The block moves to the right but comes to rest after traveling a distance 𝑑.
(𝑎) What is the magnitude of the frictional force between the block and the surface while the block is
moving?
(𝑏) What is the ratio of the energy dissipated as the bullet passes through the block to the energy dissipated
by friction between the surface and the bottom face of the block?
5. Working hard or hardly working?
In the block-and tackle arrangement shown in the figure, three segments of the single
rope pull on the block.
𝑐
(𝑎) Show that the magnitude 𝐹𝑝𝑟
of the force exerted by a person on the rope to
raise the block at constant speed is 𝑚𝑔/3 , where 𝑚 is the inertia of the block.
(𝑏) One worker uses this arrangement to lift a heavy block, while another hauls
up an identical block with a straight rope. After both blocks have been raised
to the same second-floor window, the workers argue about whether they have
done the same amount of work.