Actual Exam Will Be Given Friday, Oct. 6, 1995, at 1:00 PM
Actual Exam will have 25 Multiple Choice Questions and 3 Short Answer Questions
PART I: MULTIPLE CHOICE QUESTIONS
Please mark the correct answer for each question on the bubble sheet. Fill in the dot completely with #2 pencil. Part I is worth 67% of the grade on the midterm examination.
Problem 1:
A speedboat is pulling a water-skier with a rope, exerting a large forward force on her. The skier is traveling forward in a straight line path at a constant speed. The net force experienced by the skier is
(A) in the backward direction.
(B) in the forward direction.
(C) zero.
(D) in the upward direction.
Answer: (C) zero.
Why: The water-skier is traveling at constant velocity and is not accelerating. The net force on the skier must be zero.
Problem 2:
You are riding on a swing at the local playground. As you swing back and forth, you begin to think about your speed and kinetic energy (this is obviously a fictional story). These two quantities clearly change between the top of each swing (when you are reversing directions) and the bottom of each swing (when you are passing directly beneath the supporting beam). You wonder when each of these two quantities is at its maximum value. Actually, your speed is at its maximum
(A) at the bottom of a swing and your kinetic energy is at its maximum at the bottom of a swing.
(B) at the bottom of a swing and your kinetic energy is at its maximum at the top of a swing.
(C) at the top of a swing and your kinetic energy is at its maximum at the bottom of a swing.
(D) at the top of a swing and your kinetic energy is at its maximum at the top of a swing.
Answer: (A) at the bottom of a swing and your kinetic energy is at its maximum at the bottom of a swing.
Why: At the bottom of the swing, you are traveling as fast as you ever will. Since kinetic energy depends on speed (actually, the square of speed), your kinetic energy is at its maximum when your speed is at its maximum.
Problem 3:
You are doing exercises at the gym. When you lift a weight over your head, you push upward on it both as you lift it and as you lower it. However, when you work out with a particular exercise machine, you push upward as you lift its bar but must pull downward to lower that bar. When you use that exercise machine,
(A) you do work on the bar as you raise it but it does work on you as you lower it.
(B) its bar does work on you as you raise it but you do work on it as you lower it.
(C) you do work on the bar as you raise it and as you lower it.
(D) its bar does work on you as you raise it and as you lower it.
Answer: (C) you do work on the bar as you raise it and as you lower it.
Why: When you raise this bar, you push it upward and it moves upward. Since your force and its motion are in the same direction, you do work on the bar. The same holds for lowering the bar: you pull it downward and it moves downward, so you do work on it.
Problem 4:
You are watching a child is flying a kite at the park. The kite is hovering motionless in the sky, about 100 m above the ground. The wind is blowing smoothly toward the east. The net force on the kite is
(A) in the upward direction.
(B) toward the west.
(C) toward the east.
(D) zero.
Answer: (D) zero.
Why: Once again, the kite is traveling at constant velocity (which happens to be zero velocity). Since it's not accelerating, the net force on it is zero.
Problem 5:
Even when you are driving at a constant 60 miles-per-hour along a straight, level road, your car's engine must be running. As the engine turns the car's wheels, friction between the ground and the tires exerts a forward force on the car. The car needs this forward force from the ground because
(A) air drag (air resistance) exerts a backward force on the car.
(B) an object that is moving requires a net force to keep it moving. In the absence of any net force, objects are motionless.
(C) an object's velocity points in the direction of the net force on that object.
(D) the car has a velocity and is thus accelerating. In order to accelerate, the car must be experiencing a net force.
Answer: (A) air drag (air resistance) exerts a backward force on the car.
Why: When your car is traveling at constant velocity, the net force on it must be zero. Since it needs a forward force from the ground, something must be exerting a backward force on it. On a level road, that something can only be air resistance.
Problem 6:
A gymnast doing a double back flip leaps off the floor with her arms and legs extended and then pulls herself into a very compact position. In her compact shape, she rotates very rapidly and completes two full rotations before opening back up to land on the floor. During the time that she is not touching the floor, the one aspect of her motion that is constant is her
(A) angular momentum.
(B) angular velocity.
(C) momentum.
(D) velocity.
Answer: (A) angular momentum.
Why: The gymnast is free of torques while she is in the air. She is not free of forces because gravity exerts a force on her. Since her angular momentum can't change as long as she experiences no torques, her angular momentum is constant. Everything else in the list does change during her flight through the air.
Problem 7:
Ball bearings permit a wheel to turn freely on an axle without creating any heat because they form a mechanical system that involves
(A) no friction of either type.
(B) no electricity.
(C) no sliding friction.
(D) no static friction.
Answer: (C) no sliding friction.
Why: Ball bearing do experience static friction as the inner disk of the bearing turns relative to the outer disk. But nothing slides across another surface, so there is no sliding friction in the bearing. Since static friction doesn't produce thermal energy, the bearing allows the wheel to turn without wasting energy.
Problem 8:
If you drop a golf ball and a bowling ball simultaneously from roof of your home, they will both hit the ground at the same moment. The two ball travels downward side-by-side because gravity gives them identical
(A) masses.
(B) downward momenta.
(C) weights.
(D) downward accelerations.
Answer: (D) downward accelerations.
Why: Gravity makes everything accelerate at the same rate because it pulls downward on objects with a force that is exactly proportional to their masses. Although large objects have larger masses, weigh more, and acquire larger downward momenta as they fall, they reach the ground at the same time as smaller objects that were dropped at the same moment (neglecting air resistance).
Problem 9:
You have been running track races in smooth-soled shoes. During each start, you have been wasting 100 joules of energy as thermal energy because of friction between your shoes and the track. To help this situation, you purchase a pair of spiked shoes. Now when you start a race, the frictional force your feet experience from the track is increased by a factor of 5 and the shoes do not slide across the track at all. During each start, the amount of energy you now waste as thermal energy because of friction between your spiked shoes and the track is
(A) 0 joules.
(B) 4 joules.
(C) 500 joules.
(D) 20 joules.
Answer: (A) 0 joules.
Why: Only sliding friction turns ordered energy into thermal energy. Since your spiked shoes prevent your feet from sliding on the track, you waste no energy at all as thermal energy due to friction between your shoes and the track.
Problem 10:
The total energy of a rubber ball in a box is contained in the ball's gravitational potential energy, its kinetic energy of motion, and its thermal energy. Energy can be transferred from one of these forms to another as the ball moves around. You throw the ball into the box and leave it for 10 minutes. When you return, most of the ball's energy will have
(A) turned into thermal energy.
(B) turned into gravitational potential energy.
(C) turned into kinetic energy of motion.
(D) turned into random bouncing of the ball around the box.
Answer: (A) turned into thermal energy.
Why: After a while, the ball will stop bouncing. It will have as little gravitational potential energy as possible, because it will be in the bottom of the box. It won't be moving, so its kinetic energy will be zero. And it won't be hopping around the box, so it won't have any random bouncing. Instead, all of its energy will have become thermal energy.
PART II: SHORT ANSWER QUESTIONS
Please give a brief answer in the space provided. Part II is worth 33% of the grade on the midterm examination.
Problem 1:
Many doors are equipped with simple mechanical devices that close them automatically when no one is holding the door open. One of the simplest automatic door closers is a spring that connects the top corner of the door to the door frame. As you open the door, the spring stretches beyond its equilibrium length. The system now contains stored mechanical energy.
(A) When you hold this spring-equipped door open and stationary, what is the net torque on the door? Zero.
Why: Since the door isn't rotating, its angular velocity is constant (at zero). It isn't experiencing angular acceleration and it must not have any net torque on it.
(B) Use words like "force" and "distance" to show that, when you let go of the door and it begins to close, work is done by one object on the other: The spring exerts a force on the door and the door moves in the direction of that force, so the spring does work on the door.
Why: To show which object does work on the other, you need to show that one object pushes on the other and that the second object moves in the direction of that push.
(C) What object contains most of the system's original energy in the moments just before the door shuts completely and latches? The door.
Why: The spring has done work on the door, which is moving quickly just before it shuts completely. The system's energy is kinetic energy in the door, which contains most of the original energy.
(D) More sophisticated door closers bring the door closed very gently and quietly. This type of door closer still contains a spring, but it also contains a damping device that always oppose the door's motion. What kind of force must the damping device use and what becomes of the system's original mechanical energy? The damping device must use sliding friction or air resistance (or any other friction-like force) to turn the system's mechanical energy into thermal energy.
Why: To stop everything from moving, something must get rid of the system's original energy. Otherwise, the door will keep bouncing around forever. By turning that energy into thermal energy, using some friction-like force, the door closer prevents this bouncing.
Problem 2:
You are part of a team designing an energy-efficient escalator system for a new department store. The store has two floors and patrons will ride between the floors on the escalator. Your team plans to use a single belt of stairs that will travel from the ground floor up to the second floor and then return to the ground floor in a perfectly symmetrical arrangement. The belt will then travel underneath the first floor and reemerge at its starting point. A single motor will turn the belt and convey all of the people up and down between floors.
(A) The belt moves at a very steady pace so that a person riding it upward toward the second floor travels at constant velocity. What is the amount and direction of the net force on that person? Zero net force (no direction).
Why: The person is moving at constant velocity and is not accelerating, so the net force on the person is zero.
(B) As that person rides upward toward the second floor, is there any (positive) work being done and, if so, is it being done by the person or by the belt of stairs? The belt of stairs is doing positive work on the person.
Why: The stairs are pushing the person upward and the person is moving at least partially upward. Since the force and the direction of motion are somewhat in the same direction (not at right angles and not in opposite directions), the belt of stairs is doing work on the person.
(C) The total weight of patrons on the escalators is 10,000 newtons (about 2,200 pounds). Half the people (weight 5,000 newtons) are riding the upward escalator and half (weight 5,000 newtons) are riding the downward escalator. The belt advances 1 meter each second. Neglecting friction and air resistance, how much power must the motor provide to the belt? Zero.
Why: The belt is raising the same mass of people on one side as it's lowering on the other. The people going down do work on the belt and this work is just enough to raise the other people. The motor doesn't have to do any work (except to overcome friction and air resistance, which we're neglecting).
(D) If the only person on the escalators is riding down from the second floor toward the first floor, energy is being transferred from what to what? From the person to the belt of stairs.
Why: The person riding down is pushing downward on the stairs and they are moving at least partially downward. Thus the person is doing work on the stairs, transferring energy to those stairs.