Due Monday, September 18, 1995, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1: (Case 15 from Chapter 1)
A popular exercise machine in a modern weight room simulates the act of climbing stairs. You stand on two pedals and move your feet up and down. The pedals move with your feet and hidden machinery inside the device makes a whirring sound. It takes a lot of force to push each pedal downward but that pedal rises upward easily as you lift your foot. As long as you keep moving your feet up and down at the right pace, you remain stationary. If you slow your pace, you begin to sink downward. If you speed up, you begin to rise upward.
(A) When you're moving your feet up and down at the right pace, so that you remain stationary, how much total downward force are you exerting on the two pedals?
(B) As you push your foot downward, you exert a large downward force on the pedal. Between your foot and the pedal, which is doing work on which?
(C) As you lift your foot upward, the pedal exerts a small upward force on your foot. Between your foot and the pedal, which is doing work on which?
(D) On the average, what is doing work on what (you and the machine)?
(E) Clearly, energy is being transferred out of you and into the machine. The machine converts that energy into a form that can be carried away in the air. What is that final form of energy?
Question 2: (Case 12 from Chapter 1)
Imagine that you're sledding alone down a steep hill on a toboggan and that you left the top of the hill at the same time as an identical toboggan, loaded with six people.
(A) Neglecting the effects of air resistance and friction, which toboggan will reach the bottom of the hill first?
(B) During the descent, your toboggan brushes up against the six person toboggan. Which toboggan will experience the largest change in velocity as the result of the impact?
(C) If you take a steeper route down the hill, how will that affect your arrival time? Explain.
(D) Before each downhill run, you must pull the toboggan back to the top of the hill. Explain how the toboggan's gravitational potential energy changes on the way up the hill and on the way down it.
(E) When are you doing work on the toboggan and when is gravity doing work on the toboggan?
Question 3: (Case 9 from Chapter 1)
Imagine that you're standing on a slick ice-skating rink. No matter how hard you try, you can't move closer to the railing. You're initially at rest in the middle of the rink and you have no initial velocity.
(A) To escape from the ice, you throw your boot toward one side of the rink. Which ends up moving faster: the boot or you, or do you end up with equal but oppositely-directed velocities? Explain.
(B) Once you begin to slide across the ice, why do you continue to slide (assuming there is no air resistance or friction)?
(C) If you throw the boot forward with your right hand extended well out to your right, you will experience a torque. How will that torque affect your subsequent motion?
(D) Suppose that you didn't have a boot to throw away. Your lungs are full of air. If you pushed on that air, what would happen?
(E) Which direction should you push on the air, and in which direction will you then move?
Question 4: (Case 7 from Chapter 1)
Diving boards and platforms offer a nearly ideal opportunity in which to experience the various laws of motion. When you jump off the high diving board, you're the falling object and, if you can keep your presence of mind as you fall, you can learn something about physics. Imagine yourself diving off a platform 10 m above the water below and neglect air resistance.
(A) If you walk very slowly off the platform, so that you fall directly downward, roughly how long will it take for you to reach the water? Look at Fig. 1.1.3 and make a reasonable estimate.
(B) In the situation described in part (A), about how fast will you be traveling downward when you reach the water? Estimate your velocity from Fig. 1.1.3.
(C) If you jump upward as you leave the platform, so that you begin with a modest upward velocity, will your final downward velocity be more or less than in Part (B)?
(D) You leave the platform simultaneously with a friend. She walks slowly off the platform and you jump to give yourself a modest initial upward velocity. Who will reach the water first?
(E) You leave the platform simultaneously with a friend. He walks slowly off the platform and you run off the platform, so that your initial velocity is in the horizontal direction. Who will reach the water first?
Question 5: (Case 21 from Chapter 1)
Even though it has nothing preventing it from turning, the giant door to the local museum is surprisingly hard to open. You're inside the museum, trying to open the door so you can leave.
(A) As you push on the door handle, the door begins to open. It turns more and more quickly as time passes. What kind of influence are you exerting on the door that causes it to begin turning?
(B) If you try to open the door by pushing on the hinged side of the door, it won't open. Why does it matter where on the door you push?
(C) If you stop pushing on the door after is has begun to turn, it will continue turning until it crashes into the outside wall of the museum. What keeps it turning?
(D) What kind of influence does the wall exert on the door as the door crashes into it and how does this influence compare to the one you exerted on the door to start it opening?
(E) The museum has decided to make the door easier to open and close by reducing its mass. To have the greatest effect, from which part of the door should they remove the most mass: (1) the hinged edge, (2) the top edge, (3) the doorknob edge, (4) the bottom edge, or (5) the middle of the door? Why?