Cases – Chapter 3
1. A spring bathroom scale is designed to report the amount of upward force it’s exerting on the objects touching its surface.
a. When you first step on the scale, you usually have some downward velocity because you “land” on the scale. As it slows
your motion to bring you to rest, does the scale report your correct weight, or does it report more than your weight or less than
your weight?
b. If you stand motionless on one foot, rather than two feet, what fraction of your weight does the scale report?
c. If you jump upward, what does the scale report as you push yourself upward?
d. You stand motionless on two identical bathroom scales, one foot on the left scale and one foot on the right scale. What can
you say about the weights that the two scales report?
*e. You stand motionless on two identical bathroom scales stacked on top of each other. Each scale weighs 10 N. What weights
do the two scales report?
2. You are seated in a subway car, facing forward with your eyes closed. The only way that you can tell where you are going is
by feeling the effects of motion on your body.
a. When the car is traveling at a steady speed on a straight section of track, what is the net force on your body?
b. Why is it very difficult to feel which way the car is going when it’s traveling at a constant velocity?
c. Explain the sensations you experience as the car increases or decreases its forward speed.
d. How can you tell when the car turns to the left or the right?
3. A trampoline has an elastic surface, supported at the edges by springs or elastic bands so that it’s normally flat. This surface
stores energy during a bounce so that you can jump very high on it.
a. When you get on a particular trampoline and stand in its center, its surface distorts downward 10 cm. It’s behaving like a
spring that’s distorted away from its equilibrium shape. The distorted trampoline surface is exerting a restoring force on you in
which direction?
*b. If someone with twice your weight climbed into the middle of the empty trampoline, how far downward would its surface
distort?
c. You begin bouncing up and down on the trampoline. As you land on the trampoline during one of the bounces, its surface
distorts downward 30 cm. Your weight hasn’t changed, so how can you make it distort so far downward?
d. While you are in the air above the trampoline, nothing is pushing on you except gravity. On both your way upward and your
way downward (while in the air), do you feel weightless, your normal weight, or particularly heavy?
e. While you are touching the trampoline during a bounce, its surface is pushing upward on you. Near the bottom of the
bounce, you distort the trampoline’s surface downward more than 10 cm. On both your way downward and your way upward
(while the surface is distorted downward more than 10 cm), do you feel weightless, your normal weight, or particularly heavy?
4. Bumper cars are a popular ride at many amusement parks. You drive about an enclosed area in a small, electrically powered
vehicle. This vehicle has a large rubber bumper wrapped all the way around its exterior.
a. Half the fun of driving a bumper car is crashing into other people’s cars. When you drive forward at high speed and slam
into the car in front of you, you find yourself thrown forward in your car. Which way is your car accelerating?
b. When you are stopped and someone else slams into the front of your car, you find yourself thrown forward in your car.
Which way is your car accelerating?
c. What would happen to the support forces between cars and to the accelerations those cars experience if the soft rubber
bumpers were replaced by hard, steel bumpers?
d. Suppose that all of the cars are traveling at 10 km/h in various directions, as viewed by the people waiting in line for a turn.
You crash first into a car that’s heading in about the same direction as yours and feel a gentle thud. You then crash into a car
that’s heading toward you and experience a tremendous jolt. Explain briefly why these two collisions are different.
e. If you were to fill your car with metal bars so that its mass were 10 times that of any other bumper car, how would it affect
the jolts you experience during crashes, as compared to riding in a normal car?
5. The body of a car is suspended above the four wheels on four huge coil springs. The road supports the wheels, the wheels
support the springs, and the springs support the body.
*a. When the manufacturer placed the body of the car on the springs, the springs were compressed downward 10 cm. The body
weighs 10,000 N. When you and your friends climb into the car, the body descends an additional 2 cm. How much do you and
your friends weigh?
*b. While you and your friends are driving down a straight, level highway at a constant speed of 100 km/h, what is the net
force on the car body and which way (if any) is it accelerating?
*c. The car now passes over a very sudden rise in the pavement. The wheels move upward about 5 cm, instantly compressing
the springs by that same amount. Which way does the car body now accelerate, and how large is the acceleration compared to
the acceleration due to gravity?
*d. If the car body were attached directly to the wheels, with no springs in between, and it passed over the 5-cm rise in the
pavement, which way would the car body accelerate and how large would that acceleration be relative to the acceleration due to
gravity? (You must make some assumptions here; justify those assumptions.)
e. Use your answers to parts c and d to explain why cars have spring suspensions.
6. You’re taking a step aerobics class. In front of you is a small platform that you step onto and off of during the course of the
exercises. Most of the time, one foot remains stationary on the platform and you use it to lift your body up and down.
a. As you step up onto the platform, your leg does work on your body. What characteristics of you and the platform determine
how much work your leg must do?
b. How much work is your leg doing on your body as it lowers you gently back down to the ground?
c. If you let yourself drop back down to the ground, rather than lowering yourself gently, you could injure the leg you land on.
Why does wearing padded shoes reduce your risk of injury?
*d. The platforms are all identical and are made of a sturdy plastic that acts like a stiff spring. When you step up onto your
platform it distorts downward by about 4 mm. You’re curious about the weight of the person to your right, so you watch the
platform as that person steps onto it. It distorts downward by 8 mm. How much does that person weigh?
7. If you attach a string to a ball and begin swinging it around your head, the ball will travel in a circle. Let’s suppose that the ball
is traveling counterclockwise, as viewed from overhead.
a. Although the ball is traveling with a constant speed, it is accelerating. Which way is it accelerating?
b. In which direction is the net force on the ball?
c. In which direction is the ball traveling at the moment it passes directly in front of you?
d. If you let go of the string at the moment the ball passes directly in front of you, which way will the ball travel? Why?
e. You feel an outward tug on the string, yet there is no outward force on the ball. The only way that the ball can tug on the
string is if the string is tugging on the ball. What effect does the string’s pull have on the ball if there isn’t any outward force on
the ball?
8. A lazy Susan is a rotating tray that sits in the middle of a dinner table and makes it easy for everyone to help themselves to its
contents. The flat circular tray turns on ball bearings when you push it to the right or left.
a. Why is it harder to spin the tray when it’s heavily loaded with dishes?
b. Why does the tray continue to rotate (for a while) even after you stop pushing on it?
c. What eventually stops the tray from rotating after you stop pushing on it?
d. If you spin the tray too quickly, objects begin to fly off it. Why do they leave the tray and in what direction do they travel
once they leave?
9. You want to weigh a horse with several bathroom scales. The bathroom scales can only handle about 1500 N (337 lb.) and the
horse weighs about 4000 N (900 lb.).
a. Your friend suggests stacking four bathroom scales on top of one another and placing the horse on the upper scale. He
claims that each scale will then read exactly a quarter of the horse’s weight. Why isn’t this right?
b. Another friend suggests placing one scale under each of the horse’s four feet. She claims that each scale will then read
exactly a quarter of the horse’s weight. Although a much better suggestion, this isn’t quite right, either. Why not?
c. You place one scale under each of the horse’s four feet and correctly determine the horse’s weight from the readings of the
four scales. How?
d. If the horse lifts its foot off one of the scales and holds it in the air, what will happen to the readings of the other three
scales?
e. If the horse now places that foot on the ground, what will happen to the readings of the other three scales?
10. A foam rubber pillow is relatively springy.
a. When you drop your head onto the foam pillow, your head bounces. How is energy stored and returned during this collision
between your head and the pillow?
b. Your head only bounces once or twice and then settles down. Explain this settling process.
c. Why is dropping your head onto a foam pillow so much more comfortable than dropping it onto a wooden pillow?
d. How is the distortion of the pillow related to the weight of your head?
e. As the pillow ages, your head settles deeper into it. What is happening to the relationship between the pillow’s distortion and
the restoring force it exerts on your head?