Physics 105 - How Things Work - Fall, 1995

Midterm Examination - Problems and Solutions


IMPORTANT NOTE:

This is a special version of the exam in which every multiple choice question has (A) as the correct answer. The questions will appear in a different order on your exam and the correct answers may be (A), (B), (C), or (D). Use this version of the exam when trying to determine which questions you missed from the exam results page.


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:

You're bicycling swiftly down a hill, traveling in a straight line at a steady speed. The wind is blowing in your face and you're pedaling furiously. The net force on you is

(A) zero.

(B) uphill.

(C) downhill.

(D) directly downward.

Answer: (A) zero.

Why: You're traveling at constant velocity so you are not accelerating. Thus the net force on you is zero. Although you may be experiencing many individual forces, they evidently cancel one another perfectly.

Problem 2:

You're trying to sleep on a train that is traveling forward at high speed. Suddenly you find yourself thrown toward the right. Your eyes are closed, so you can't see what happened but you know that the train has just

(A) turned toward the left.

(B) turned toward the right.

(C) begun to ascend a hill.

(D) begun to descend a hill.

Answer: (A) turned toward the left.

Why: You experience fictitious forces in the directions opposite your accelerations. Since the fictitious force you experience here is toward the right, the train must be accelerating toward the left.

Problem 3:

As you ride on a merry-go-round, you feel a strong outward pull that feels just like the force of gravity. This fictitious force occurs because

(A) you are accelerating toward the center of the merry-go-round and experience a fictitious force in the direction opposite your acceleration.

(B) you are accelerating away from the center of the merry-go-round and experience a fictitious force in the direction of your acceleration.

(C) your velocity is toward the center of the merry-go-round and you experience a fictitious force in the direction opposite your velocity.

(D) your velocity is away from the center of the merry-go-round and you experience a fictitious force in the direction of your velocity.

Answer: (A) you are accelerating toward the center of the merry-go-round and experience a fictitious force in the direction opposite your acceleration.

Why: On a merry-go-round, you are traveling in a circle at a steady speed. This motion is uniform circular motion and you are experiencing a centripetal force (a force toward the center of the circle). You are thus accelerating toward the center of the circle and experience an outward fictitious force.

Problem 4:

When you jump while standing on a bathroom scale, it briefly reads more than your actual weight. During that moment, it's exerting an upward force on you that is greater than your weight and

(A) you are accelerating upward.

(B) you are accelerating downward.

(C) your velocity is constant but upward.

(D) your velocity is constant but downward.

Answer: (A) you are accelerating upward.

Why: The scale reads more than your weight because the upward force it's exerting on you is more than your weight. Since the upward force on you is greater than your downward weight, you have an upward net force on you. You accelerate upward.

Problem 5:

You are trying to knock over a stack of weighted bottles at the state fair. You can throw either a super ball or a bean bag. Since both objects have identical masses, the most effective choice is

(A) the super ball because it transfers the most momentum to the bottles when it hits and rebounds.

(B) the bean bag because it transfers the most momentum to the bottles when it hits and stops.

(C) the super ball because it weighs more than the bean bag.

(D) the bean bag because it weighs more than the super ball.

Answer: (A) the super ball because it transfers the most momentum to the bottles when it hits and rebounds.

Why: When it hits the bottles, the superball pushes on them as it comes to a stop and it pushes some more as it rebounds. Overall, it transfers more momentum to the bottles by bouncing than the bean bag does in coming to a stop. The bouncing ball comes away from the bottles with momentum in the opposite direction from before, having transferred all of its original momentum to the bottles as it comes to a stop, and then transferring even more to the bottles as it rebounds.

Problem 6:

Like a baseball bat, a tennis racket has a sweet spot at its center of percussion. If a tennis ball hits this center of percussion, the racket's handle doesn't accelerate. That's because

(A) the racket's center of mass accelerates backward while its handle rotates forward and the two motions cancel one another at the handle.

(B) an impact at the center of percussion transfers no momentum to the racket and doesn't cause the racket to accelerate.

(C) an impact at the center of percussion exerts no torque about the racket's center of mass and doesn't cause the racket to undergo angular acceleration.

(D) the racket's velocity doesn't change when the ball hits its center of percussion.

Answer: (A) the racket's center of mass accelerates backward while its handle rotates forward and the two motions cancel one another at the handle.

Why: When a ball hits the racket's center of percussion, the racket accelerates backward overall (its center of mass accelerates backward), but it begins to rotate about that center of mass. The combination of these two motions leaves the racket's handle moving smoothly.

Problem 7:

A bean bag will bounce higher when you drop it onto a soft rubber surface than it will when you drop it onto a hard rubber surface. That's because

(A) the soft rubber deforms more as it slows the falling bean bag and it stores more of the collision energy.

(B) the bean bag has more momentum when it hits the soft rubber than when it hits the hard rubber.

(C) the hard rubber is less dense than the soft rubber and exerts a smaller buoyant force on the bean bag.

(D) the hard rubber exerts less torque on the bean bag.

Answer: (A) the soft rubber deforms more as it slows the falling bean bag and it stores more of the collision energy.

Why: A springy surface can make anything bounce if the collision with that surface stores some energy in it. In this case, the soft rubber deforms more during the collision and stores more of the energy (more work is done on the surface because it deforms more). The hard rubber may be springy, but it doesn't deform enough to receive any of the collision energy. Instead, the bean bag does all of the deforming and receives all of the collision energy. Since it doesn't return any of that collision energy, it doesn't rebound.

Problem 8:

After clearing the bar in the high jump, you land softly on a giant mattress. Landing on the mattress is much more comfortable than landing on a sand heap of equal size because

(A) the force that the mattress exerts on you to stop your descent is much less than the force that the sand heap would have exerted on you.

(B) you transfer less momentum to the mattress in coming to a stop than you would have transferred to the sand heap in coming to a stop.

(C) you transfer more momentum to the mattress in coming to a stop than you would have transferred to the sand heap in coming to a stop.

(D) your velocity is less as you land on the mattress than it would have been if you'd landed on the sand heap.

Answer: (A) the force that the mattress exerts on you to stop your descent is much less than the force that the sand heap would have exerted on you.

Why: When you land on a soft object, you slow to a stop gradually. You still give up all your downward momentum but you do it slowly and with modest forces. Since large forces can injure you, this slow deceleration is a good thing. That's why you want to land on a mattress.

Problem 9:

You are floating along in a hot air balloon. You look up and notice that the bottom of the balloon is open. Hot air remains inside the balloon despite this opening because

(A) the air pressure inside the balloon's opening is the same as the air pressure outside that opening.

(B) hot air has more inertia than cold air and doesn't accelerate easily.

(C) the propane burner located below the opening keeps pushing the hot air back into the balloon.

(D) hot air has a lower pressure than cold air, so hot air is drawn into the balloon by the partial vacuum inside it.

Answer: (A) the air pressure inside the balloon's opening is the same as the air pressure outside that opening.

Why: The open bottom of the hot air balloon isn't a problem because there is no pressure imbalance across it. The hot air inside the opening is at atmospheric pressure, just like the air outside. The difference between the hot air inside and the cold air outside is in their densities. Hot air is less dense than cold air because it takes fewer hot molecules to occupy a particular volume and maintain the pressure in that volume than it would take cold molecules.

Problem 10:

You can tell how much cargo a ship has on board by looking at how it floats. When the ship is full, it floats low in the water because the cargo increases the ship's

(A) average density so that it must displace more water to stay afloat.

(B) volume so that it takes up more room in the water.

(C) momentum so that more water is needed to balance that momentum.

(D) moment of inertia so that the water needs more kinetic energy to keep the ship afloat.

Answer: (A) average density so that it must displace more water to stay afloat.

Why: When you fill a boat with cargo, the boat's volume doesn't change but its mass and weight increase. Since density is mass per volume, the boat's density increases. Density is what determines buoyancy. Since the boat is now more dense than before, it must displace more water before the upward buoyant force is large enough to support it.

Problem 11:

The city water pipes enter your home on the ground floor. Pipes inside your home then carry water up to the second and third floors and down to the basement. The water pressure in your home is highest

(A) in the basement.

(B) on the ground floor.

(C) on the second floor.

(D) on the third floor.

Answer: (A) in the basement.

Why: Water pressure increases with depth because the water at the bottom of a pipe must support the water above it. In the basement, the water's pressure is extra high because it must support the water in the pipes leading upward.

Problem 12:

You are cleaning a wall by spraying water at it from a hose. At the center of the stream of water, right where it hits the wall, the water is coming to a complete stop. If you were to measure the water pressure at that point, you would find that it is

(A) higher than atmospheric pressure.

(B) lower than atmospheric pressure, but more than zero.

(C) equal to atmospheric pressure.

(D) exactly zero.

Answer: (A) higher than atmospheric pressure.

Why: When the water is spraying through the air, its pressure is simply atmospheric pressure. Its energy is in the form of kinetic energy, the energy of motion. But when it hits the wall and slows down, its energy becomes pressure potential energy. The pressure rises upward to well above atmospheric pressure. This explains why you can push things over with a jet of water. The water's pressure rises as it comes to a stop and it exerts extra pressure on the object it hits.

Problem 13:

When you pour honey into a bowl, it flows smoothly. If you did the same with water, it would splash. These different behaviors occur because

(A) honey's high viscosity keeps it flowing smoothly while water's low viscosity allows inertia to break its flow into many separate pieces.

(B) honey's high momentum keeps it moving in a straight line while water's low momentum allows it to turn abruptly in many different directions.

(C) honey's high mass keeps it flowing smoothly while water's low mass allows it to acquire lots of angular momentum.

(D) honey's high density keeps it flowing smoothly while water's low density allows it to float upward and splash about.

Answer: (A) honey's high viscosity keeps it flowing smoothly while water's low viscosity allows inertia to break its flow into many separate pieces.

Why: A fluid will flow without turbulence (splashing) as long as the fluid's viscosity is able to keep it flowing smoothly. Since honey's viscosity is much larger than that of water, honey tends to flow without turbulence.

Problem 14:

When you close a water faucet, the water that was about to flow out of the faucet

(A) remains pressed against the faucet's inlet by the high water pressure in the pipe.

(B) falls back down the pipe leading to the faucet and remains there until you reopen the faucet.

(C) remains at the faucet's inlet, but the water pressure in the pipe drops to zero.

(D) remains at the faucet's inlet, but the water pressure in the pipe drops to atmospheric pressure.

Answer: (A) remains pressed against the faucet's inlet by the high water pressure in the pipe.

Why: When you close a faucet, you are simply blocking the fluid's passage. It comes to a stop and all of its kinetic energy becomes pressure potential energy. It remains in the pipe, pushing strongly against the valve in the faucet, until you reopen the faucet. It then accelerates and begins to flow out of the faucet once again.

Problem 15:

You're having trouble loosening a rusty nut with a small wrench, so you borrow a large wrench from your neighbor. Exerting only a modest force on the handle of this new wrench easily unscrews the nut. The large wrench helps because

(A) it allows you to exert your force far from the center of rotation, so that you produce a large torque on the nut.

(B) it has a large moment of inertia so that it develops a great deal of angular momentum when you exert a force on it.

(C) it has a large mass so that its inertia allows you to overcome the nut's velocity and accelerate it around in a circle.

(D) it has a large acceleration and a large mass, so the force it produces is large, according to the equation F=ma.

Answer: (A) it allows you to exert your force far from the center of rotation, so that you produce a large torque on the nut.

Why: The torque that you produce with a particular force depends on how far from the axis of rotation you exert that force. The greater this "lever arm," the more torque you create. Using a long wrench allows you to exert more torque with the same force because it provides a longer lever arm.

Problem 16:

You reach out to push on a car as it passes by and manage to exert a forward force of 10 N on it. When you do this, the car exerts

(A) a backward force of 10 N on you, because forces always come in equal but oppositely directed pairs.

(B) a backward force of somewhat less than 10 N on you, because the car's forward velocity reduces the force it needs to accelerate forward.

(C) no backward force on you at all, because the force of its velocity is already enough to keep it moving forward.

(D) a backward force of somewhat more than 10 N on you, because, in addition to the reaction force, it must accelerate your hand backward.

Answer: (A) a backward force of 10 N on you, because forces always come in equal but oppositely directed pairs.

Why: Forces really do come in equal but oppositely directed pairs. No matter how you exert a 10 N force on an object and no matter how that object is moving, it will exert a 10 N force back on you in the opposite direction.

Problem 17:

You are out in space, so far from any star or planet that gravity is insignificant. You throw two rubber balls so that they drift forward as a pair. These balls continue to touch one another with one ball directly in front of the other. Which of the balls is pushing on the other?

(A) Neither ball is pushing on the other.

(B) Only the ball in front is pushing on the ball behind.

(C) Only the ball behind is pushing on the ball in front.

(D) They are both pushing on one another.

Answer: (A) Neither ball is pushing on the other.

Why: The two balls are drifting as a pair. Since nothing outside is pushing on them, they must be traveling at constant velocity. Each ball individual must thus be experiencing zero net force. It can't be experiencing any force from the other ball, so the ball's must not be pushing on one another. If the two balls were pushing on one another, they would accelerate in opposite directions and would soon drift apart.

Problem 18:

The pressure in an upright bottle of water, resting on a table, is

(A) highest near the bottom, because the water there must support the weight of the water above it.

(B) highest near the top, because that's the water that leaves the bottle first.

(C) the same throughout (not zero), because the water would accelerate if it were subjected to a pressure imbalance.

(D) zero, because water accelerates whenever it's subjected to pressure.

Answer: (A) highest near the bottom, because the water there must support the weight of the water above it.

Why: Water pressure increases with depth. The same is true for air, which is why the air pressure at sea level is higher than the air pressure on a mountain top.

Problem 19:

When you roll down the first big hill on a roller coaster, you feel particularly weightless because

(A) your acceleration is downward.

(B) your velocity is downward.

(C) your mass is downward.

(D) your momentum is downward.

Answer: (A) your acceleration is downward.

Why: The weightless feeling comes from the upward fictitious force that you experience whenever you accelerate downward. As you accelerate down the first hill of the roller coaster, your acceleration is (mostly) downward and you feel an upward ficitititous force. That upward feeling of "gravity" makes you feel "weightless."

Problem 20:

A book slides slowly off a tilted table. Its speed remains constant until it finally falls off the edge. While it's sliding down the table, the book doesn't accelerate because

(A) sliding friction is exerting an uphill force on it that exactly balances the downhill force due to gravity.

(B) the table's support force exactly balances gravity and there are no other forces on the book.

(C) momentum is a conserved quantity, so the book's momentum can't change.

(D) angular momentum is a conserved quantity, so the book's angular momentum can't change.

Answer: (A) sliding friction is exerting an uphill force on it that exactly balances the downhill force due to gravity.

Why: Like anything on the side of a ramp, the book experiences a downhill force. This downhill force is the residual left when the ramp's support force acts to keep the book from falling through it. The book slides down the ramp but it doesn't accelerate because it experiences one more force: the uphill force of sliding friction. This friction balances the downhill ramp force so that the book travels at constant velocity.

Problem 21:

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: As you turn around at the end of each swing, you come to a complete stop. Your speed and kinetic energy are both zero. All of your energy is gravitational potential energy. It's as you pass through the bottom of the swing that you are moving fastest and have the most kinetic energy.

Problem 22:

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) momentum.

(C) angular velocity.

(D) velocity.

Answer: (A) angular momentum.

Why: In flight, she experiences no torque. She does experience a downward force: her weight. Because she is free of torques, she can't exchange angular momentum with anything so her angular momentum is constant. Her momentum changes because of the force of gravity on her.

Problem 23:

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: Once your feet stop sliding along the track, you stop making thermal energy. Static friction never produces thermal energy.

Problem 24:

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 the ball stops bouncing (which it will do very quickly), it will be stationary in the bottom of the box. It won't have any kinetic or gravitational potential energy. Instead, all of its energy will have turned into thermal energy.

Problem 25:

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 balls travel downward side-by-side because gravity gives them identical

(A) downward accelerations.

(B) weights.

(C) downward momenta.

(D) masses.

Answer: (A) downward accelerations.

Why: Since the force of gravity on an object is proportional to that object's mass, increasing the mass increases the force of gravity on it. The result is that all objects experience the same downward acceleration due to gravity, regardless of their mass. The two ball accelerate downward together.

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:

In the game of pool, the first shot or "break" is very important. The fifteen pool balls are arranged in a triangle and the player rolls another ball, the cue ball, into the triangle to separate the balls.

(A) The break starts when the player pushes the cue stick forward so that it strikes the stationary cue ball. This impact transfers energy to the cue ball. Show that the cue stick has done work on the cue ball. The cue stick pushes the cue ball forward and the cue ball moves forward, so the cue stick does work on the cue ball.

Why: Work involves a force exerted on an object as that object moves in the direction of the force. Here the cue stick pushes the ball forward, so work is done.

(B) Just before it hits the stationary triangle of balls, the cue ball has 16 units of momentum in the forward direction. After the collision, the sixteen balls travel in all directions. If there were no friction or air resistance, what would be the total momentum of all the balls on the table just after the cue ball hit the triangle? 16 units of momentum in the forward direction.

Why: Since momentum is a conserved quantity, the cue ball's momentum can't disappear. Instead, it is transferred to the other balls. Together, these balls still have all of the momentum that the cue ball had before it hit.

(C) Just before it hits the stationary triangle of balls, the cue ball has 1 joule of kinetic energy. After the collision, the balls have a total of only 0.7 joules of kinetic energy. What happened to the remaining 0.3 joules? It has become thermal energy.

Why: When a ball doesn't return all of the collision energy as it rebounds, the missing energy has become thermal energy. The ball becomes hotter.

(D) When one pool ball collides directly with a second stationary ball, the first ball stops and the second ball continues the first ball's motion. The transfer of energy and momentum is almost perfect. This trick works because pool balls are extremely lively (they bounce well when dropped on the floor). If pool balls were perfectly dead (they didn't bounce at all when dropped on the floor), what would happen to the first ball after it collided with the second stationary ball? It would continue to roll forward (slowly).

Why: When a very lively ball hits an identical stationary ball, it pushes the stationary ball forward for a particularly long time. It pushes once as the two balls dent into one another and it pushes again as they spring back apart. It is this second pushing that causes the first ball to slow completely to stop. If the two balls aren't lively and they don't spring apart, then the first ball won't stop completely. Instead, the two balls will roll forward together at half the speed that the first ball had initially. (This is a difficult question, so I don't expect everyone to get it right.)

Problem 2:

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? Your weight and the height of the platform.

Why: Work is force times distance in the direction of that force. As your leg lifts you upward, the force it exerts upward is your weight and the distance it moves you upward is the height of the platform.

(B) How much work is your leg doing on your body as it lowers you gently back down to the ground? It is doing negative work with the same magnitude as in part (A) (your weight times the height of the platform).

Why: As your leg lowers you down, the force it exerts on you is in the opposite direction from the distance you move. It does negative work on you, of the same magnitude as it did lifting you up.

(C) If you let yourself drop back down to the ground, rather than lowering yourself gently, you may injure the leg you land on. Why does wearing padded shoes reduce your risk of injury? The padded shoes allow you to accelerate upward more slowly, with smaller forces.

Why: Large forces can injure you. When you pound your feet on the hard ground, they must accelerate quickly so the forces that the ground exerts on your feet must be large. By inserting padding between you and the ground, you are slowing the deceleration process and allowing it to proceed with smaller forces.

(D) The platforms are all identical and are made of a sturdy plastic that acts like a stiff spring. When you step up onto yours, it distorts downward by about 4 millimeters. 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 6 millimeters. How much does that person weigh? 1.5 times as much as you do.

Why: The other person's platform distorts 1.5 times as much as yours. Since platforms are spring-like, their distortions are proportional to the forces involved. Thus the other person must be exerting 1.5 times as much force on the platform.

Problem 3:

It's a hot summer day and you and your friends are having a water fight. You've visited the local toy store and brought home several fancy water guns and bags of water balloons.

(A) The water guns store energy in compressed air. As you push a handle back and forth, a pump squeezes more and more air molecules into a plastic container that's partly filled with water. Why does the air pressure inside this container increase as you pack the molecules into it? The air molecules bounce more often from surfaces when there are more of them in the same volume.

Why: Air pressure depends on density and temperature. Since the temperature isn't changing here, it's only density that matters. The more air molecules you pack into a certain volume, the more they hit the walls and the more pressure they exert.

(B) The compressed air pressurizes the water, which flows slowly through a tube and then squirts out a narrow nozzle at high speed. How does the water's pressure change as it flows out this nozzle? The water's pressure drops (to atmospheric pressure).

Why: As the water accelerates out the nozzle, it is converting its pressure potential energy into kinetic energy. Its speed is increasing but its pressure is decreasing.

(C) One of your friends begins to squirt water down at you from the second floor balcony. You begin to squirt water up at her but it comes to a stop before it reaches her. You pump some more air into the container and then you're able to squirt her. Why did increasing the water pressure help? The more water pressure, the more energy the water has to convert to gravitational potential energy. It can thus rise higher.

Why: To reach the balcony, the water needs extra energy. You can add this energy in one of three ways: you can increase its gravitational potential energy by climbing up to the balcony yourself, or you can increase its kinetic energy by leaping upward as you spray it, or you can increase its pressure potential energy by pumping extra air into the container. The latter choice is the easiest.

(D) Another friend begins to lob water balloons at you. His aim is poor and one of the balloons hits the window behind you and breaks it. Water can only use pressure to push on a surface and the pressure in the water balloon was roughly atmospheric pressure while it was flying through the air. So how was the balloon able to push the window hard enough to break it? When the water stopped moving, its pressure rose (it converted its kinetic energy into pressure potential energy) (Alternatively: water hammer occurred as the moving water had to accelerate backward).

Why: When the water strikes the surface of the window, the window pushes on it to keep it from passing into the glass. The glass and water exert pressures on one another. The pressure at the interface between the two becomes very high and there is a pressure imbalance across the glass. With more pressure on one side than the other, the glass begins to bend backward and ultimately breaks.