Due Monday, February 5, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1: (Case 14 from Chapter 1)
Revolving doors are popular in northern hotels and office buildings as a way to prevent cold outside air from blowing directly into the lobby. Most revolving doors have 4 panels arranged in a cross, as viewed from above. You step in between two panels of the door and push on the panel in front of you. The revolving door begins to rotate and once you reach the inside of the building, you step out into the lobby.
a. It is much easier to make the revolving door rotate by pushing on the panel far from the central pivot than it is by pushing near the pivot. Why?
b. As you push on the door, it begins to turn more and more quickly. What is your pushing doing to the door?
c. One of the dangers of revolving doors is being hit by the panel behind you as you step out of the door. The door tends to keep on turning after you stop pushing on it and it can bump you if you're not careful. Why does it keep on turning after you stop pushing?
d. What eventually stops the revolving door when no one uses it for a minute of two?
e. The people who built the revolving door want it to be easy to start and stop. They had to be most careful to minimize the mass of which edge of each door panel: the upper edge, lower edge, inside edge (nearest the pivot), or the outside edge (farthest from the pivot)?
Question 2: (Case 16 from Chapter 1)
You're a pilot for the Navy. For your airplane to be able to lift itself off the ground, it must be traveling forward with a speed of 130 miles-per-hour. At this take-off speed your airplane will have about 50,000,000 newton-meters (or 50,000,000 J) of kinetic energy.
a. During takeoff, your airplane's jet engine exerts a force of 250,000 N in the backward direction on the air leaving the engine. What force does that same air exert on the airplane (specify the amount and the direction of force)?
b. The force exerted by the air on the airplane causes it to accelerate down the runway. How long must the runway be for the airplane to reach its take-off speed?
c. An aircraft carrier runway is only about 100 m long. As your answer to b indicates, this distance is not enough for the airplane to reach take-off speed on its own. The aircraft carrier must assist the airplane by exerting an extra force on it. The aircraft carrier uses a steam-powered catapult to help push the airplane forward. How much additional force should the catapult exert on the airplane to bring the airplane to take-off speed at the end of the 100 m runway?
d. During an aircraft carrier take-off, the airplane and the catapult exert forces on one another. Which of these two objects does work on the other and which object transfers some of its energy to the other?
e. During an aircraft carrier landing, the airplane hooks onto a cable that slows the airplane to a stop. The airplane and cable exert forces on one another. Which of these two object does work on which and which object transfers some of its energy to the other?
Question 3: (Case 19 from Chapter 1)
You have recently taken up track and field as a way to keep in shape. You soon begin to notice how simple physical laws appear in many of the events.
a. You notice that great sprinters have extremely strong legs. Why is it so important that a sprinter be able to push back very hard on the starting blocks at the beginning of a race?
b. You find that throwing a heavy metal shot is far more difficult than throwing a baseball. Weight isn't the whole problem. Even if you try to throw the shot horizontally or downward, so that weight is not an issue, you have great difficulty getting the shot moving quickly. Why?
c. As you land on the soft, foam pad beneath the pole vault, you realize that its job is to bring you to rest by accelerating you upward gradually with only modest support forces. If there were no pad there, only concrete, what would the acceleration and support forces be like during your landing?
d. You cross the finish line at the end of a race. The net force on your body points in what direction as you slow down?
e. In the long jump, you run rapidly down a path and then leap into the air. You find that the best distance comes from pushing yourself upward rather than forward during the leap. Why is it so important to have a large upward component of velocity at the start of the leap?
Question 4: (Case 22 from Chapter 1)
Local fairs and amusement parks usually offer games in which you can win a large prize by performing a seemingly easy task. In many cases, these tasks are made surprisingly difficult by simple physical principles and few people receive prizes. Here are several of those games.
a. A pitching game requires that you knock over three milk bottles with a baseball. The bottles are filled with sand. Why does filling the bottles with sand make them so hard to knock over with the baseball?
b. A tossing game requires that you throw a coin forward and have it come to a stop on a smooth glass plate. Why doesn't the coin stop when it hits the smooth glass plate?
c. Another game requires that you knock over a wooden peg with a ball hanging from a string. The string is suspended from a point directly above the peg. To win, you must swing the ball past the peg and have the ball knock over the peg on its return swing. This feat can't be done. The ball keeps circling around and around the peg. The ball's suspension prevents it from experiencing any torques about an axis that includes the peg and the ball keeps swinging around and around the peg. What law of motion keeps it swinging around that peg?
d. Still another tossing game requires that you throw a basketball into a shallow basket that is tipped toward you. Whenever you throw the ball into the basket, it bounces back, rolls out of the basket, and falls onto the floor. What conserved physical quantity is the basketball unable to get rid of in time to remain in the basket?
e. A pitching game measures the speed at which you can throw a baseball. While many people can reach 80 km/h (50 mph) with a pitch, almost no one can throw a ball twice that fast. Use the concept of kinetic energy to explain why this is not surprising.
Question 5: (Case 2 from Chapter 11)
A Van der Graaf generator is an electrostatic device that uses a moving non-conductive belt to carry electric charge into a hollow metal sphere. This sphere is insulated from the ground and can accumulate charge until enormous voltages are reached. Small Van der Graaf generators are exciting novelties while large ones are used in research and industry.
a. A typical Van der Graaf generator uses a rubber belt to carry negatively charged electrons from its base to the sphere. As the belt passes through the sphere, it is touched by a metal brush. Electrons leave the belt and flow through a wire to the surrounding sphere. Why do the electrons flow onto the sphere rather than staying on the belt?
b. As negative charge builds up on the sphere, the belt motor begins to strain. Why does it become harder and harder for the motor to move the belt?
c. The amount of charge that can build up on the sphere depends on many things. For one, the sphere must be very smooth. Why is it important that there be no sharp points on the sphere?
d. As you move your hand close to the negatively charged sphere, your hand becomes positively charged and a spark may leap from the sphere to your hand. How does you hand acquire a positive charge?
e. If you insulate yourself from the ground and put your hand on the sphere, negative charge will accumulate on you as well as the sphere. Explain why your hair stands up.