Due Monday, October 23, 1995, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1: (Case 5 from Chapter 2)
A trampoline has an elastic surface, supported at the edges by springs or elastic bands so that it is 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 is behaving like a spring that is distorted away from its equilibrium shape. The distorted trampoline surface is exerting a restoring force on you in what 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?
Question 2: (Case 6 from Chapter 2)
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 experienced if the soft rubber bumpers were replaced by hard, steel bumpers?
(D) Suppose that all of the cars are traveling at 20 km/h in various directions, as viewed by the people waiting in line for a turn. You crash first into a car that is heading in about the same direction as yours and feel a gentle thud. You then crash into a car that is 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 was 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?
Question 3: (Case 4 from Chapter 3)
A scuba diver swims below the surface of the water, breathing air from the steel tanks of an aqualung.
(A) It is easiest for her to maintain a constant depth if the buoyant force on her and her equipment exactly balances their weight. The air tanks float by themselves so she wears a heavy weight belt to compensate. How should her average density compare with that of the water around her?
(B) When she is 20 m below the surface of the water, what is the pressure pushing inward on her chest?
(C) When she breathes, she expects air to flow into her lungs. She can change the pressure in her lungs slightly, using the muscles in her chest and diaphragm. How must the pressure in her mouth compare with that in her lungs in order for air to begin flowing into her lungs?
(D) If instead of taking compressed air with her, she were to try to breathe surface air through a straw, the air entering her mouth would be at atmospheric pressure. What would happen when she tried to breathe?
(E) The special pressure regulator of an aqualung delivers air to her mouth at exactly the same pressure as that of the surrounding water. She can breathe this air easily. However, the deeper she dives, the faster she consumes air molecules from the tanks and the sooner she must return to the surface. Explain.
Question 4: (Case 6 from Chapter 4)
You and your best friend live on the 58th floors of two adjacent high-rise apartment buildings. You have windows that face one another across an open courtyard. One day, the city turns off all the water to your friend's building. You decide to help your friend obtain water. You immediately buy about 500 meters of garden hose, enough to reach from either apartment to the ground at least two times.
(A) Your first thought is to run water from the gardener's faucet, which is at street level in the courtyard, up to your friend's apartment. Although water runs briefly into the hose, it never reaches your friend's apartment. Why not?
(B) You decide to obtain water from a faucet in your apartment. You run the hose out of your window, down to the courtyard, and up to your friend's apartment. To your surprise, the hose bursts in the courtyard when you turn on the water. Why does the hose burst?
(C) You patch the hose and decide not to let it droop down to the courtyard. With the hose running almost directly across the gap between windows, you turn on the faucet. What happens this time?
(D) Water is flowing rapidly through all 500 meters of hose as your friend fills a bathtub. To stop the flow, your friend suddenly makes a kink in the end of the hose. The pressure in the hose surges upward, and the hose bursts. What produced this pressure surge?
(E) As water flows out of the narrow split in the hose, it accelerates to very high speed. What happens to its pressure as its speed increases?
Question 5: (Case 3 from Chapter 4)
You are watching a downhill ski race. In this race, the skiers are trying to descend a mountain as quickly as possible without crashing. The veteran skier standing nearby makes a number of observations about the racers that actually have a sound scientific basis.
(A) The veteran points out that one of the skiers is skidding around corners and that such skids slow her down. During a skid, the ski slips sideways across the snow rather than sliding straight forward through it. Why will skidding always slow the skier down?
(B) The veteran notes that a skier also slows down by remaining airborne too long after passing over a jump. Why should the skier regain contact with the slope as soon as possible after the jump?
(C) A skier loses control and skis off the course into a net. The veteran remarks that it is much better to hit a net than a tree. In terms of force and momentum, why is the skier less likely to be injured by crashing into a net than by crashing into a tree?
(D) The veteran is impressed by one skier's consistent compact form, a tight tucked shape. Why doesn't she want to push on the air during her descent?
(E) The veteran remarks about the high air pressure that skiers feel in front of them as they travel swiftly downhill. What causes this high pressure?