Week 6 HW answers
1. When an ice skater is spinning, she pulls her arms in to increase her angular velocity. How does
this work if there is no torque acting on her?
a. When she pulls her arms in, her rotational inertia decreases. If angular momentum is to
be conserved, her angular velocity must increase.
2. Two cars collide in a head-on collision and come to a complete stop. Each car was traveling the
same speed and had the same mass. Their momentum has seemingly disappeared. Did it?
Explain why or why not.
a. If considering the total momentum of the system before the crash, it would equal zero
since the cars have the same momentum in opposite directions. After the crash, neither
car is moving, so the total momentum is zero. Momentum is conserved.
3. A group of children are on a spinning carousel. Another child jumps on and everyone notices the
angular velocity decreases. Why is this so?
a. With an additional child, the rotational inertia increases. If there are no torques acting
on the carousel, the angular momentum must be conserved, so angular velocity
decreases.
4. Your friend has run out of gas in his car. You are helping to push it. If you exert a force of 15,000
N for a total of 13 seconds on his 1500 kg car, what impulse have you provided?
a. Impulse = 15,000 N x 13 sec = 195,000 N∙s.
5. Extra credit: A ball has been thrown straight up and eventually stops due to gravity. If
momentum is conserved, where did the momentum of the ball go?
a. Consider the combined momentum of the earth and the ball. As the ball is slowing down
because of the force of gravity from the earth, the earth is increasing in velocity
(towards the ball) due to the force of the ball on the earth. Although, virtually
unmeasurable, the increased speed of the earth towards the ball results in increased
momentum for the earth that equals the decreased momentum of the ball.
Chapter 3 Questions
1. In what way does the string of a bow and arrow behave like a spring?
E.1
As you draw the string away from its equilibrium shape, it experiences a restoring force proportional to its
displacement.
2. As you wind the mainspring of a mechanical watch or clock, why does the knob get harder and harder to turn?
E.2
As the mainspring winds farther and farther from its equilibrium shape, the restoring force it exerts on its end gets
stronger. You must overcome this increasing force as you twist the knob.
3. Curly hair behaves like a weak spring that can stretch under its own weight. Why is a hanging curl straighter at the top than at
the bottom?
E.3
The top of the curl supports more weight than the bottom.
4. When you lie on a spring mattress, it pushes most strongly on the parts of you that stick into it the farthest. Why doesn’t it
push up evenly on your entire body?
E.4
The deeper you dent the mattress's surface at any given point, the stronger the local restoring force becomes.
5. If you pull down on the basket of a hanging grocery store scale so that it reads 15 N, how much downward force are you
exerting on the basket?
E.5
15 N.
6. While you’re weighing yourself on a bathroom scale, you reach out and push downward on a nearby table. Is the weight
reported by the scale high, low, or correct?
E.6
The scale reads low; it reports less than your actual weight.
E.6
The upward force that the table exerts on your hand contributes to the force supporting you against gravity and
allows the scale to exert a smaller upward force on you.
7. There’s a bathroom scale on your kitchen table and your friend climbs up to weigh himself on it. One of the table’s legs is
weak and you’re afraid that he’ll break it, so you hold up that corner of the table. The table remains level as you push upward on
the corner with a force of 100 N. Is the weight reported by the scale high, low, or correct?
E.7
Correct.
8. If you put your bathroom scale on a ramp and stand on it, will the weight it reports be high, low, or correct?
E.8
The scale will read less than your actual weight.
E.8
The scale only reports how hard it pushes perpendicular to its surface. When you weigh yourself on a ramp, your
weight doesn't push directly toward the scale's surface and so the scale doesn't push back directly perpendicular to its
surface. The perpendicular component of its force on you is less than you full weight.
9. When you step on a scale, it reads your weight plus the weight of your clothes. Only your shoes are touching the scale, so
how does the weight of the rest of your clothes contribute to the weight reported by the scale?
E.9
You support your clothes and the scale supports you.
10. To weigh an infant you can step on a scale once with the infant and then again without the infant. Why is the difference
between the scale’s two readings equal to the weight of the infant?
E.10 When you weigh yourself with the child, the scale reports the total force needed to support you both. When you
weigh yourself alone, the scale reports only the force needed to support you. The difference between these two
reported values is the force needed to support only the child.
11. An elastic ball that wastes 30% of the collision energy as heat when it bounces on a hard floor will rebound to 70% of the
height from which it was dropped. Explain the 30% loss in height.
E.11 A 30% loss of rebound height is a 30% loss of gravitational potential energy—equal to the energy that became
thermal energy.
12. The best running tracks have firm but elastic rubber surfaces. How does a lively surface assist a runner?
E.12 An elastic track stores energy as it dents when the runner's foot presses against it and then returns that energy to the
runner as it undents.
13. Why is it so exhausting to run on soft sand?
E.13
You do work on the sand as you step on it, but the sand doesn’t return this energy to you as you
lift your foot back up again.