Midterm Examination 1 Solutions

Problem 1:

Two coins slide horizontally off a tabletop side-by-side at the same instant and begin to fall. The US quarter was moving twice as fast as the US dime when the two coins left the tabletop. Where and when do the coins hit the level floor beneath the table? [neglect any effects due to the air.]

(A) The dime hits the ground before the quarter, but the quarter lands about twice as far from the table as does the dime. [43.6% picked]

(B) The two coins hit the ground at the same time and land about the same distance from the table. [2.5% picked]

(C) The quarter hits the ground before the dime, but the two coins land about the same distance from the table. [5.1% picked]

(D) The two coins hit the ground at the same time, but the quarter lands about twice as far from the table as does the dime. [48.7% picked]

Answer: (D) The two coins hit the ground at the same time, but the quarter lands about twice as far from the table as does the dime. [48.7% picked]

Why: TBA

Problem 2:

A hammer's weight acts in the downward direction, yet you can use the steel hammer to pound a nail into the ceiling. Why?

(A) The nail's downward weight is so much smaller than that of the hammer that the overall force due to gravity on the nail is upward and the nail moves upward into the ceiling. [48.5% picked]

(B) Your downward weight is so much greater than that of the nail that you dominate the hammer's motion. [6.3% picked]

(C) The upward-moving hammer transfers its upward momentum to the nail by way of a huge upward force exerted on the nail for a short period of time. [42.6% picked]

(D) Your downward weight is so much greater than that of the hammer that the net force on the hammer is upward as it strikes the nail. [2.5% picked]

Answer: (C) The upward-moving hammer transfers its upward momentum to the nail by way of a huge upward force exerted on the nail for a short period of time. [42.6% picked]

Why: TBA

Problem 3:

You pole vault over the bar and drop onto the giant mattress below. After bouncing a few times, you settle motionless at equilibrium on the mattress. When during your initial descent from the bar into the mattress did you reach your greatest upward acceleration?

(A) When you reached the lowest point in the descent and were denting the mattress most deeply. [76.8% picked]

(B) When you were about to touch the mattress, but not actually touching it. [3.0% picked]

(C) When you were at equilibrium and moving downward. [1.7% picked]

(D) When you first touched the mattress. [18.6% picked]

Answer: (A) When you reached the lowest point in the descent and were denting the mattress most deeply. [76.8% picked]

Why: TBA

Problem 4:

A small airplane is anchored to the ground by a cement block. Although it's windy, friction between the block and the ground manage to prevent any movement of the block for an entire week. Finally, a huge gust of wind causes the plane to drag the block 1 meter across the parking area. During what period(s) does friction produce thermal energy and cause wear to the block?

(A) Only while the block was being dragged across the parking area. [72.2% picked]

(B) At no time during this story was friction producing thermal energy or causing wear to the block. [5.9% picked]

(C) During both the week when the block wasn't moving and while the block was being dragged across the parking area. [20.3% picked]

(D) Only during the week when the block wasn't moving. [1.7% picked]

Answer: (A) Only while the block was being dragged across the parking area. [72.2% picked]

Why: TBA

Problem 5:

A tractor is dragging a log across the ground in a straight line at a steady speed. Compare the force the tractor exerts on the log to the frictional force the ground exerts on the log.

(A) The two forces are equal in amount but opposite in direction, as they must be because they are a Newton's third law pair. [4.2% picked]

(B) The force the tractor exerts on the log is smaller than the frictional force the ground exerts on the log. [5.1% picked]

(C) The force the tractor exerts on the log is larger than the frictional force the ground exerts on the log. [2.1% picked]

(D) The two forces are equal in amount but opposite in direction, so they cancel. [88.6% picked]

Answer: (D) The two forces are equal in amount but opposite in direction, so they cancel. [88.6% picked]

Why: TBA

Problem 6:

To win a prize at the county fair, you must knock a massive block off a shelf. You throw two 1-kilogram balls at the block. Both balls have the same initial velocity, but one ball is "dead" and stops moving after hitting the block, while the other ball is "lively" and bounces back at the same speed it had before the bounce. Which ball transfers the largest amount of momentum to the block?

(A) Both balls transfer equal amounts of momentum. [14.8% picked]

(B) Neither ball transfers any momentum to the block. [2.5% picked]

(C) The lively ball transfers the largest amount of momentum. [64.4% picked]

(D) The dead ball transfers the largest amount of momentum. [18.2% picked]

Answer: (C) The lively ball transfers the largest amount of momentum. [64.4% picked]

Why: TBA

Problem 7:

To win a prize at the county fair, you have toss a US quarter over a barrier and have it come to rest on a small glass plate. Unfortunately, the fast-moving quarter bounces repeatedly on the plate until it misses and falls to the ground. What physics issue makes it almost impossible for the quarter to stay on the plate?

(A) The quarter has so much force in its momentum and so much power in its energy that it can't stop bouncing. [0.0% picked]

(B) The quarter can't transfer energy or momentum to the rigid, immovable plate. Its excess energy and momentum keep it bouncing. [4.6% picked]

(C) The quarter can transfer momentum but not energy to the rigid, immovable plate. Its excess energy keeps it bouncing. [94.1% picked]

(D) The quarter can transfer energy but not momentum to the rigid, immovable plate. Its excess momentum keeps it bouncing. [1.3% picked]

Answer: (C) The quarter can transfer momentum but not energy to the rigid, immovable plate. Its excess energy keeps it bouncing. [94.1% picked]

Why: TBA

Problem 8:

Two astronauts are motionless together in deep, gravity-free space. Suddenly, the green astronaut pushes hard on the purple astronaut. While the green astronaut is pushing, which astronaut(s) is/are accelerating?

(A) Only the purple astronaut is accelerating. [0.8% picked]

(B) Both astronauts are accelerating, but in opposite directions. [73.0% picked]

(C) Neither astronaut is accelerating. [3.8% picked]

(D) Only the green astronaut is accelerating. [22.4% picked]

Answer: (B) Both astronauts are accelerating, but in opposite directions. [73.0% picked]

Why: TBA

Problem 9:

Two astronauts are motionless together in deep, gravity-free space. Suddenly, the green astronaut pushes hard on the purple astronaut. After the push, when the two astronauts are no longer touching, which astronaut(s) is/are accelerating?

(A) Only the purple astronaut is accelerating. [5.9% picked]

(B) Neither astronaut is accelerating. [72.2% picked]

(C) Both astronauts are accelerating, but in opposite directions. [3.8% picked]

(D) Only the green astronaut is accelerating. [18.1% picked]

Answer: (B) Neither astronaut is accelerating. [72.2% picked]

Why: TBA

Problem 10:

A tourist is riding down Main Street in a horse-drawn wagon. The wagon is traveling in a straight line at a constant speed. What is the net force acting on the wagon? The net force is

(A) equal to the tourist's weight plus the force that the horse exerts on the wagon. [1.7% picked]

(B) equal to the tourist's weight. [9.7% picked]

(C) equal to the force that the horse exerts on the wagon. [10.5% picked]

(D) zero. [78.1% picked]

Answer: (D) zero. [78.1% picked]

Why: TBA

Problem 11:

Two puppies are fighting over a toy. Each puppy grips one end of that toy in its mouth and pulls. Suddenly, the puppy on the left pulls especially hard on the toy and moves its end of the toy to the left. The other puppy manages to keep its end of the toy from moving. Alas, the toy breaks and the game ends. Breaking the toy required energy and that energy was provided

(A) only by the puppy on the right. [5.5% picked]

(B) by both puppies, but most was provided by the puppy on the left. [10.1% picked]

(C) only by the puppy on the left. [81.0% picked]

(D) in equal amounts by the two puppies. [3.4% picked]

Answer: (C) only by the puppy on the left. [81.0% picked]

Why: TBA

Problem 12:

Someone has filled two basketballs with water. In one ball, the water is pure so the water's rotation is almost independent of the ball's rotation. In the other ball, the water is gelled so that it must rotate with the ball. The two balls look identical and have equal weights, so how can you tell which ball contains gelled water?

(A) Twist the two balls back and forth rotationally about their centers. The one that exhibits the most resistance to angular acceleration contains the gelled water. [58.2% picked]

(B) Drop the two balls from the same height at the same time. The ball that hits the ground first contains the gelled water. [24.9% picked]

(C) Drop the two balls from the same height at the same time. The ball that hits the ground first contains the pure water. [1.7% picked]

(D) Shake the two balls back and forth. The one that exhibits the most resistance to acceleration contains the gelled water. [15.2% picked]

Answer: (A) Twist the two balls back and forth rotationally about their centers. The one that exhibits the most resistance to angular acceleration contains the gelled water. [58.2% picked]

Why: TBA

Problem 13:

When you walk onto a springboard at the diving center and settle motionless, the board will have bent downward 4 inches. You do some gentle bouncing and soon it is bent downward 8 inches (twice as far as when you were motionless). What is your acceleration when the board is bent downward 8 inches?

(A) About 4.9 meters/second^{2} in the upward direction. [3.8% picked]

(B) Zero. [14.8% picked]

(C) About 4.9 meters/second^{2} in the downward direction. [0.4% picked]

(D) About 9.8 meters/second^{2} in the upward direction. [81.0% picked]

Answer: (D) About 9.8 meters/second^{2} in the upward direction. [81.0% picked]

Why: TBA

Problem 14:

In which of the following four situations are you accelerating? When you are

(A) bicycling around a circular path at a constant speed. [11.4% picked]

(B) riding an escalator and are moving at constant velocity toward the second-floor exit. [1.3% picked]

(C) sliding down a straight vertical pole at a steady speed. [76.8% picked]

(D) traveling in an elevator that is moving upward at constant speed toward the top floor. [10.5% picked]

Answer: (A) bicycling around a circular path at a constant speed. [11.4% picked]

Why: TBA

Problem 15:

You are pulling some children in a wagon and are about to climb a hill. There are two paths up the hill, each of which has a constant slope as it winds around the hill to the top. The steeper path is half as long as the less steep path. Compare the work you would do pulling the wagon up each path to the top of the hill. [neglect friction and any effects due to the air.]

(A) You would do twice as much work pulling the wagon up the steeper path. [18.6% picked]

(B) You would do half as much work pulling the wagon up the steeper path. [2.5% picked]

(C) You would do the same work pulling the wagon up either path. [78.9% picked]

(D) You would do positive work pulling the wagon up the steeper path, but negative work pulling the wagon up the less steep path. [0.0% picked]

Answer: (C) You would do the same work pulling the wagon up either path. [78.9% picked]

Why: TBA

Problem 16:

The lid of a honey jar is stuck and you can't unscrew it by hand. You find a kitchen gadget that grips the lid tightly and provides with you with a long handle on which to push. Why does the gadget's long handle make it relatively easy to unscrew the lid?

(A) The handle exerts a force equal to the force you exert on it, so the lid experiences twice as much force as without the gadget. [6.3% picked]

(B) The handle has more energy than your hand, so the lid's rotational mass is smaller when using the kitchen gadget. [0.0% picked]

(C) The handle provides you with a long lever arm. A modest force exerted perpendicular to that lever arm produces the large torque required to unscrew the lid. [92.4% picked]

(D) The handle has more angular momentum than your hand, so the lid accelerates more rapidly when using the kitchen gadget. [1.3% picked]

Answer: (C) The handle provides you with a long lever arm. A modest force exerted perpendicular to that lever arm produces the large torque required to unscrew the lid. [92.4% picked]

Why: TBA

Problem 17:

You are the elevator operator in a retro-designed luxury high-rise apartment building. When during your vertical travels do you feel less than your normal weight? In other words, when do you feel partly weightless?

(A) Whenever the elevator is starting a trip up or finishing a trip down. [1.7% picked]

(B) Whenever the elevator is starting a trip up or starting a trip down. [1.3% picked]

(C) Whenever the elevator is stopping a trip up or finishing a trip down. [57.0% picked]

(D) Whenever the elevator is finishing a trip up or starting a trip down. [40.1% picked]

Answer: (D) Whenever the elevator is finishing a trip up or starting a trip down. [40.1% picked]

Why: TBA

Problem 18:

You are pulling some children in a wagon and are about to climb a hill. There are two paths up the hill, each of which has a constant slope as it winds around the hill to the top. The steeper path is half as long as the less steep path. Compare the uphill force you must exert on the wagon to keep it moving at a steady pace up each path. [neglect friction and any effects due to the air.]

(A) You must exert the same amount of uphill force on the wagon when going up either path. [0.0% picked]

(B) You must exert twice as much uphill force on the wagon when going up the steeper path. [53.6% picked]

(C) You must exert four times as much uphill force on the wagon when going up the steeper path. [46.0% picked]

(D) You must exert half as much uphill force on the wagon when going up the steeper path. [0.4% picked]

Answer: (B) You must exert twice as much uphill force on the wagon when going up the steeper path. [53.6% picked]

Why: TBA

Problem 19:

Two children jump off the edge of a porch and soon land on the level ground below the porch. They jumped simultaneously and were moving at the same speed when the left the porch. However, the girl jumped horizontally forward while the boy jumped vertically upward. When and where do they land on the ground?

(A) The girl lands first and the two children land at about the same distance from the porch. [1.7% picked]

(B) The girl lands first and the girl lands farther from the porch than does the boy. [88.2% picked]

(C) The two children land at about the same time and the girl lands farther from the porch than does the boy. [2.5% picked]

(D) The boy lands first and the girl lands farther from the porch than does the boy. [7.6% picked]

Answer: (B) The girl lands first and the girl lands farther from the porch than does the boy. [88.2% picked]

Why: TBA

Problem 20:

You are exercising on a stair machine. That machine resembles a small down escalator; it presents you with an endless series of stairs that move steadily downhill. You climb the steps but they move downward, so your altitude above the ground doesn't change much. When are you doing work on the downward-moving steps?

(A) You do work on the steps only when your altitude above the ground is increasing. [27.4% picked]

(B) You do work on the steps only when your altitude above the ground is constant. [0.0% picked]

(C) You do work on the steps whenever you push downward on them. [65.8% picked]

(D) You do work on the steps only when your altitude above the ground is decreasing. [6.8% picked]

Answer: (C) You do work on the steps whenever you push downward on them. [65.8% picked]

Why: TBA

Problem 21:

You are watching people step off a 20-meter cliff and fall into a deep lake. It takes a person 2 seconds of falling to reach the water. After only 1 second of falling, how high above the water is the person? [Values are approximate, so choose the closest value.]

(A) 9.8 meters above the water. [7.2% picked]

(B) 15 meters above the water. [88.2% picked]

(C) 10.2 meters above the water. [4.2% picked]

(D) 10 meters above the water. [0.4% picked]

Answer: (B) 15 meters above the water. [88.2% picked]

Why: TBA

Problem 22:

A player kicks the soccer ball almost the entire length of the field. While the ball is traveling in an arc and touching nothing, what horizontal force does the ball experience? [neglect any effects due to the air.]

(A) The ball experiences a horizontal force that pushes it forward. The force is constant. [1.7% picked]

(B) The ball experiences a horizontal force that is pushes it forward. The force decreases steadily to zero just as the ball hits the ground. [5.1% picked]

(C) The ball experiences no horizontal force. [68.8% picked]

(D) The ball experiences a horizontal force that pushes it forward. The force is constant until the ball reaches peak height, then decreases steadily to zero just as the ball hits the ground. [24.5% picked]

Answer: (C) The ball experiences no horizontal force. [68.8% picked]

Why: TBA

Problem 23:

A player kicks the soccer ball almost the entire length of the field. The ball travels in an arc; it rises to peak height and then descends. Is there a time during its travel when the ball is moving fastest along the horizontal direction? In other words, is there a time when its horizontal component of velocity is greatest? [neglect any effects due to the air.]

(A) It moves fastest along the horizontal direction when it is exactly at peak height. [0.8% picked]

(B) It moves fastest along the horizontal direction while it is descending (after reaching peak height). [4.2% picked]

(C) It moves steadily along the horizontal direction because its horizontal component of velocity is constant. [91.6% picked]

(D) It moves fastest along the horizontal direction while it is rising (before reaching peak height). [3.4% picked]

Answer: (C) It moves steadily along the horizontal direction because its horizontal component of velocity is constant. [91.6% picked]

Why: TBA

Problem 24:

You pole vault over the bar and drop onto the giant mattress below. After bouncing a few times, you settle motionless at equilibrium on the mattress. When during your initial descent from the bar into the mattress did you reach your greatest downward velocity?

(A) When you were about to touch the mattress, but not actually touching it. [20.7% picked]

(B) When you first touched the mattress. [13.9% picked]

(C) When you were at equilibrium and moving downward. [60.3% picked]

(D) When you reached the lowest point in the descent and were denting the mattress most deeply. [5.1% picked]

Answer: (C) When you were at equilibrium and moving downward. [60.3% picked]

Why: TBA

Problem 25:

You are roller-skating in silence with friends on a totally dark night. You are holding hands with someone, but you're not sure who it is. Fortunately, your friends have different masses. How can determine the mass of the person with whom you are holding hands?

(A) Give that person a gentle upward push and measure that person's upward velocity. [6.3% picked]

(B) Give that person a gentle horizontal push and measure how rapidly they accelerate. [89.0% picked]

(C) Trip that person and measure how long it takes them to fall to the ground. [1.3% picked]

(D) Hold on tight and measure that person's horizontal velocity. [3.4% picked]

Answer: (B) Give that person a gentle horizontal push and measure how rapidly they accelerate. [89.0% picked]

Why: TBA

Problem 26:

You drop a baseball 3 feet onto three different rigid horizontal surfaces. One surface is motionless, the second surface is moving steadily upward, and the third surface is moving downward but is accelerating steadily upward. From which surface does the ball bounce upward highest?

(A) It bounces to the same height from all three surfaces. [11.0% picked]

(B) From the upward moving surface. [65.7% picked]

(C) From the downward moving surface that is accelerating upward. [11.0% picked]

(D) From the motionless surface. [12.3% picked]

Answer: (B) From the upward moving surface. [65.7% picked]

Why: TBA

Problem 27:

A bicyclist is pedaling hard and the bicycle is accelerating forward along level ground. What force is causing the bicycle to accelerate forward?

(A) The force the bicyclist's foot exerts on the pedal of the bicycle. [3.8% picked]

(B) The frictional force the bicycle's powered wheel exerts on the ground. [11.4% picked]

(C) The force of the bicyclist's momentum. [6.4% picked]

(D) The frictional force the ground exerts on the bottom of the bicycle's powered wheel. [78.4% picked]

Answer: (D) The frictional force the ground exerts on the bottom of the bicycle's powered wheel. [78.4% picked]

Why: TBA

Problem 28:

You are riding a carousel and are moving in a circular path at a constant speed. Just as you reach the northern-most point on the circular path and are heading toward the east, you accidently let go of your keys. In which direction do your keys move?

(A) The keys move toward the east as they fall. [79.7% picked]

(B) The keys move toward the north (away from the center of the carousel) as they fall. [4.6% picked]

(C) The keys move toward the south (toward the center of the carousel) as they fall. [2.1% picked]

(D) The keys fall directly downward. They have no horizontal component of velocity. [13.5% picked]

Answer: (A) The keys move toward the east as they fall. [79.7% picked]

Why: TBA

Problem 29:

At the grocery store, you select a melon with a mass of 2 kilograms and weigh it on a spring scale. The scale reports a weight of about 20 newtons. You then take the melon and scale to Planet X, where the acceleration due to gravity is only half the Earth's acceleration due to gravity. After setting up the spring scale, you again weigh the melon. What are the melon's mass and weight on Planet X?

(A) The melon's mass is 1 kilogram and its weight is about 20 newtons. [26.2% picked]

(B) The melon's mass is 2 kilograms and its weight is about 20 newtons. [9.3% picked]

(C) The melon's mass is 2 kilograms and its weight is about 10 newtons. [46.0% picked]

(D) The melon's mass is 1 kilogram and its weight is about 10 newtons. [18.6% picked]

Answer: (C) The melon's mass is 2 kilograms and its weight is about 10 newtons. [46.0% picked]

Why: TBA

Problem 30:

You are riding a roller coaster with a loop-the-loop. At this moment, you are located exactly at the top of the loop-the-loop. Although you and your car are inverted, you feel pressed into your seat. At this moment, what are your velocity and acceleration?

(A) Your velocity is downward. Your acceleration is horizontal in the backward direction. [38.8% picked]

(B) Your velocity is upward. Your acceleration is zero. [1.7% picked]

(C) Your velocity is horizontal. Your acceleration is downward and larger than the acceleration due to gravity. [59.1% picked]

(D) Your velocity is downward. Your acceleration is the acceleration due to gravity. [0.4% picked]

Answer: (C) Your velocity is horizontal. Your acceleration is downward and larger than the acceleration due to gravity. [59.1% picked]

Why: TBA