Midterm Examination 1 Solutions

Problem 1:

It is difficult to cut thick cardboard with a pair of scissors. The farther the cardboard is from the scissors' pivot, the harder it becomes for you to rotate the scissors closed because the cardboard then

(A) has more momentum to stop the scissors from moving and to prevent them from cutting through the cardboard. [1.7% picked]

(B) exerts larger forces on the scissors and keeps them from accelerating. [14.6% picked]

(C) exerts larger forces on the scissors and causes them to accelerate. [0.0% picked]

(D) has longer lever arms with which to produce larger torques on the scissors to oppose the scissors rotating closed. [83.7% picked]

Answer: (D) has longer lever arms with which to produce larger torques on the scissors to oppose the scissors rotating closed. [83.7% picked]

Why: TBA

Problem 2:

Which of these vehicles is accelerating?

(A) An elevator moving downward and experiencing a net force of zero. [11.6% picked]

(B) An elevator that is motionless and experiencing a net force of zero. [0.9% picked]

(C) A train that is moving at a steady speed around a curved track. [85.8% picked]

(D) A wagon moving up a smooth, straight ramp at a steady speed. [1.7% picked]

Answer: (C) A train that is moving at a steady speed around a curved track. [85.8% picked]

Why: TBA

Problem 3:

You are weighing a pineapple on a spring scale. The scale reports the pineapple's correct weight only when

(A) the pineapple is in equilibrium (zero net force). [74.2% picked]

(B) the pineapple is motionless. [7.7% picked]

(C) the force the pineapple exerts on the scale is equal in amount to the force the scale exerts on the pineapple. [16.3% picked]

(D) the pineapple is accelerating at the acceleration due to gravity. [1.7% picked]

Answer: (A) the pineapple is in equilibrium (zero net force). [74.2% picked]

Why: TBA

Problem 4:

As you accelerate forward at the start of a marathon (a long-distance running race), what force or forces is the level ground exerting on you?

(A) A horizontal support force that is directed forward. [0.0% picked]

(B) An upward support force. [16.3% picked]

(C) An upward support force and a horizontal frictional force that is directed forward. [74.7% picked]

(D) A horizontal frictional force that is directed forward. [9.0% picked]

Answer: (C) An upward support force and a horizontal frictional force that is directed forward. [74.7% picked]

Why: TBA

Problem 5:

You are pulling a toy wagon up a ramp that rises vertically 1 meter for every 8 meters you travel uphill along its surface (see figure). If you let go of the wagon, how will it move? [neglect friction and effects due to the air]

(A) It will accelerate downhill at 1/8^{th} the acceleration due to gravity. [76.4% picked]

(B) It will move downhill at a constant velocity. [13.7% picked]

(C) It will accelerate downhill at 1/4^{th} the acceleration due to gravity. [6.9% picked]

(D) It will accelerate downhill at 1/2^{th} the acceleration due to gravity. [3.0% picked]

Answer: (A) It will accelerate downhill at 1/8^{th} the acceleration due to gravity. [76.4% picked]

Why: TBA

Problem 6:

When you drop a beanbag on cement, the bag doesn't bounce. Suppose you are playing tennis with a beanbag instead of a tennis ball. How should you adjust your tennis racket to make the beanbag travel as fast as possible after you hit it with the racket?

(A) You should tighten the strings so that the racket surface is like a firm trampoline. [12.9% picked]

(B) You should loosen the strings so that the racket surface is like a soft trampoline. [85.4% picked]

(C) You should replace the strings with a rigid carbon-fiber plate so that the racket surface acts like cement. [0.4% picked]

(D) You should add mass to the racket so that it carries more momentum. [1.3% picked]

Answer: (B) You should loosen the strings so that the racket surface is like a soft trampoline. [85.4% picked]

Why: TBA

Problem 7:

A box is touching the top of a table. The downward force the box exerts on the table

(A) is equal to the box's weight. [24.0% picked]

(B) can be greater than, less than, or equal to the box's weight. [75.1% picked]

(C) is less than the box's weight. [0.4% picked]

(D) is greater than the box's weight. [0.4% picked]

Answer: (B) can be greater than, less than, or equal to the box's weight. [75.1% picked]

Why: TBA

Problem 8:

You are watching two puppies fight over a rubber toy. The puppy on the right pulls its end of the toy toward the right while the puppy on the left pulls its end of the toy toward the left. Suddenly, the puppy on the right pulls its end of the toy violently toward the right while the puppy on the left keeps its end of the toy from moving. The toy breaks into two pieces. Breaking the toy required energy and that energy was provided by

(A) the puppy on the left. [0.0% picked]

(B) both puppies. [3.4% picked]

(C) neither puppy. It was instead provided by chemical potential energy in the toy itself. [0.0% picked]

(D) the puppy on the right. [96.6% picked]

Answer: (D) the puppy on the right. [96.6% picked]

Why: TBA

Problem 9:

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. [9.4% picked]

(B) When you first touched the mattress. [4.3% picked]

(C) When you reached the lowest point in the descent and were denting the mattress most deeply. [10.7% picked]

(D) When you were at equilibrium and moving downward. [75.5% picked]

Answer: (D) When you were at equilibrium and moving downward. [75.5% picked]

Why: TBA

Problem 10:

Highway work trucks often have large crushable yellow "impact attenuator" boxes mounted on their rear bumpers. Suppose your forward-moving car collides with the rear end of a motionless truck and that the massive truck doesn't move at all during the impact. Compared to hitting the truck's immovable bumper, how does hitting the crushable box "attenuate" the impact? [Assume your car comes to a complete stop in either case. Neglect effects due to friction and the air.]

(A) Your car transfers more forward momentum to the attenuator box than it would to the truck bumper and less force remains in the car. [2.1% picked]

(B) Your car transfers all of its forward momentum to the attenuator box, but with a smaller force over a longer time. Your car transfers most of its energy to the truck in either case. [33.0% picked]

(C) Your car transfers less forward momentum to the attenuator box than it would to the truck bumper and more force remains in the car. [0.4% picked]

(D) Your car transfers all of its forward momentum to the attenuator box, but with a smaller force over a longer time. Your car transfers much of its energy to the attenuator box, whereas it cannot transfer energy to the truck bumper. [64.4% picked]

Answer: (D) Your car transfers all of its forward momentum to the attenuator box, but with a smaller force over a longer time. Your car transfers much of its energy to the attenuator box, whereas it cannot transfer energy to the truck bumper. [64.4% picked]

Why: TBA

Problem 11:

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 north (away from the center of the carousel) as they fall. [10.7% picked]

(B) The keys move toward the south (toward the center of the carousel) as they fall. [1.7% picked]

(C) The keys move toward the east as they fall. [83.3% picked]

(D) The keys fall directly downward. They have no horizontal component of velocity. [4.3% picked]

Answer: (C) The keys move toward the east as they fall. [83.3% picked]

Why: TBA

Problem 12:

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) 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. [1.3% picked]

(B) 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. [1.7% 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. [97.0% picked]

(D) Your downward weight is so much greater than that of the nail that you dominate the hammer's motion. [0.0% 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. [97.0% picked]

Why: TBA

Problem 13:

Running on soft dry sand is exhausting, so you switch to running on hard wet sand. The hard wet sand removes less energy from you because

(A) it stops the downward motion of your foot faster and thus absorbs less of your momentum. [20.3% picked]

(B) it barely moves downward as you push downward on it, so you do almost zero work on it. [66.4% picked]

(C) it pushes up on your foot just as hard as your foot pushes on it, unlike the soft dry sand. [10.8% picked]

(D) its water content gives it more mass and that prevents it from absorbing energy. [2.6% picked]

Answer: (B) it barely moves downward as you push downward on it, so you do almost zero work on it. [66.4% picked]

Why: TBA

Problem 14:

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 10 newtons. [0.9% picked]

(B) The melon's mass is 2 kilograms and its weight is about 10 newtons. [96.6% picked]

(C) The melon's mass is 2 kilograms and its weight is about 20 newtons. [0.4% picked]

(D) The melon's mass is 1 kilogram and its weight is about 20 newtons. [2.1% picked]

Answer: (B) The melon's mass is 2 kilograms and its weight is about 10 newtons. [96.6% picked]

Why: TBA

Problem 15:

You can open a swinging door (see figure) by pushing it in the middle (Point A, located 1 foot from the hinges) or at the edge farthest from the hinges (Point B, located 2 feet from the hinges). If you exert a 10-newton force on the door, perpendicular to its surface, how will your choice of Point A or Point B affect the door's motion?

(A) Pushing on Point B will cause twice the angular acceleration as compared to pushing on Point A. [70.4% picked]

(B) Pushing on Point B will cause half the angular velocity as pushing on Point A. [8.6% picked]

(C) Pushing on Point B will cause half the angular acceleration as pushing on Point A. [7.3% picked]

(D) Pushing on Point B will cause twice the angular velocity as compared to pushing on Point A. [13.7% picked]

Answer: (A) Pushing on Point B will cause twice the angular acceleration as compared to pushing on Point A. [70.4% picked]

Why: TBA

Problem 16:

You throw your water bottle straight up and it rises for 2 seconds before reaching its peak height of about 20 meters (66 feet) above the ground. After only 1 second of rising, what was the water bottle's approximate height?

(A) About 10 meters above the ground. [9.0% picked]

(B) About 15 meters above the ground. [82.0% picked]

(C) About 5 meters above the ground. [6.0% picked]

(D) About 7.5 meters above the ground. [3.0% picked]

Answer: (B) About 15 meters above the ground. [82.0% picked]

Why: TBA

Problem 17:

You place a stiff ruler on a pencil and then stack coins on the two ends of the ruler until it is balanced. The ruler and its coins are then able to remain motionless on the pencil pivot. What did you have to do to achieve this balanced condition?

(A) The overall center of gravity of the ruler and its coins had to be directly above the pencil pivot. [62.2% picked]

(B) The forces that the coins on each side of the ruler exerted on the ruler had to be equal. [12.9% picked]

(C) The weights of the coins on each side of the ruler had to be equal. [3.0% picked]

(D) The overall center of gravity of the ruler and its coins had to coincide with the overall center of mass of the ruler and its coins. [21.9% picked]

Answer: (A) The overall center of gravity of the ruler and its coins had to be directly above the pencil pivot. [62.2% picked]

Why: TBA

Problem 18:

A plastic step used in an exercise class consists of a plastic board supported at each end by a plastic block. When you step on the board and stand motionless, the board bends downward 1 millimeter. Your friend weighs twice as much as you do. When your friend steps on the board and stands motionless, the board bends downward

(A) 2 millimeters [95.7% picked]

(B) 1 millimeter [0.4% picked]

(C) 4 millimeters [3.4% picked]

(D) 8 millimeters [0.4% picked]

Answer: (A) 2 millimeters [95.7% picked]

Why: TBA

Problem 19:

You're at the lake and watch two children jump off a dock. They jump at the same time and at the same speed, but the girl jumps mostly upward while the boy jumps mostly forward. After they leave the dock,

(A) the two children reach the water at the same moment and at the same distance from the dock. [0.4% picked]

(B) the two children reach the water at the same moment and but the boy travels farther from the dock than does the girl. [7.7% picked]

(C) the boy reaches the water before the girl. [90.6% picked]

(D) the girl reaches the water before the boy. [1.3% picked]

Answer: (C) the boy reaches the water before the girl. [90.6% picked]

Why: TBA

Problem 20:

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 twice 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 twice as much uphill force on the wagon when going up the steeper path. [0.0% picked]

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

(C) You must exert half as much uphill force on the wagon when going up the steeper path. [0.0% picked]

(D) You must exert four times as much uphill force on the wagon when going up the steeper path. [0.0% picked]

Answer: (A) You must exert twice as much uphill force on the wagon when going up the steeper path. [Problem was dropped because of the typo marked above as "twice HALF"]

Why: TBA

Problem 21:

You are swinging a bucket full of water around you in a big horizontal circle at a constant speed. You are at the center of its circular path. The net force on the bucket points directly

(A) away from you. [16.0% picked]

(B) downward. [13.0% picked]

(C) along the bucket's velocity (along its direction of travel). [17.3% picked]

(D) toward you. [53.7% picked]

Answer: (D) toward you. [53.7% picked]

Why: TBA

Problem 22:

You are bicycling up a hill at constant velocity. Neglecting any effects due to the air, in which direction is the hill's overall force on the bicycle (i.e., the total force that the hill exerts on the bicycle)?

(A) Upward [68.7% picked]

(B) Downhill [20.2% picked]

(C) Forward horizontally [1.3% picked]

(D) Uphill [9.9% picked]

Answer: (A) Upward [68.7% picked]

Why: TBA

Problem 23:

You are a passenger in a fast-moving car that is turning toward the left. You find yourself pressed against the door on your right. What force (if any) is pushing you toward the right?

(A) The force of your inertia is pushing you toward the right. [10.3% picked]

(B) A centrifugal force is pushing you toward the right. [1.3% picked]

(C) There is no force pushing you toward the right. [87.6% picked]

(D) The force of your momentum is pushing you toward the right. [0.9% picked]

Answer: (C) There is no force pushing you toward the right. [87.6% picked]

Why: TBA

Problem 24:

When a person falls onto the ground, that person does not bounce. When the person instead falls onto a trampoline, the person bounces upward. Why does the trampoline allow the person to bounce?

(A) The soft trampoline dents during the collision, stores momentum as it dents, and returns that momentum to the person during the rebound. [27.5% picked]

(B) The soft trampoline dents during the collision, stores energy as it dents, and returns that energy to the person during the rebound. [71.2% picked]

(C) The elastic trampoline contains stored energy that was put into it by the manufacturer. Some of that stored energy is released during the collision and causes the person to bounce. [1.3% picked]

(D) The elastic trampoline contains stored force that was put into it by the manufacturer. Some of that stored force is released during the collision and causes the person to bounce. [0.0% picked]

Answer: (B) The soft trampoline dents during the collision, stores energy as it dents, and returns that energy to the person during the rebound. [71.2% picked]

Why: TBA

Problem 25:

You are pushing a table across the floor. As the table moves forward at constant velocity, compare the horizontal force you exert on the table to the horizontal frictional force the floor exerts on the table. [Neglect any effects due to the air]

(A) Your horizontal force on the table is equal in amount but opposite in direction to the floor's horizontal frictional force on the table. [86.3% picked]

(B) Your horizontal force on the table is less in amount than the floor's horizontal frictional force on the table. [0.0% picked]

(C) Your horizontal force on the table is greater in amount than the floor's horizontal frictional force on the table. [6.9% picked]

(D) Your horizontal force on the table is equal to the floor's horizontal frictional force on the table. [6.9% picked]

Answer: (A) Your horizontal force on the table is equal in amount but opposite in direction to the floor's horizontal frictional force on the table. [86.3% picked]

Why: TBA

Problem 26:

Your friends have made a huge batch of lemonade and they need a huge ice cube to chill it. After buying the ice cube, they tie the cube in the middle of a pickup truck's horizontal bed and begin driving home. While the truck and its contents are all moving forward horizontally at constant velocity, the ropes break so is nothing holding the ultra-slippery ice cube in place. The ice cube

(A) remains in the middle of the pickup truck's horizontal bed. [78.1% picked]

(B) slides forward to the front of the pickup truck's horizontal bed. [2.6% picked]

(C) slides to the side of the pickup truck's horizontal bed. [0.4% picked]

(D) slides backward to the back of the pickup truck's horizontal bed. [18.9% picked]

Answer: (A) remains in the middle of the pickup truck's horizontal bed. [78.1% picked]

Why: TBA

Problem 27:

While searching for your keys, you place your cup of coffee on the roof of your parked car. Unfortunately, you forget about the coffee and climb into the car without it. As you start driving the car forward, you hear the coffee hit the ground behind the car. Why didn't the coffee stay on the roof of the car?

(A) The coffee pushed itself backward as the car pushed itself forward. [0.4% picked]

(B) The car's roof pushed the coffee backward, in the direction opposite the car's acceleration. [2.6% picked]

(C) The car's roof pushed the coffee backward, in the direction opposite the car's velocity. [0.0% picked]

(D) The coffee's inertia kept it essentially motionless as the car accelerated forward and left the coffee behind. [97.0% picked]

Answer: (D) The coffee's inertia kept it essentially motionless as the car accelerated forward and left the coffee behind. [97.0% picked]

Why: TBA

Problem 28:

When the batter in a baseball game hits the baseball with the middle part of the baseball bat, the bat vibrates loudly and may even shatter. Why does the ball bounce relatively weakly off the bat in this situation?

(A) Much of the ball's force goes into the bat's vibration and is not available to the rebounding baseball. [1.3% picked]

(B) Much of the ball's angular momentum goes into the bat's vibration and is not available to the rebounding baseball. [2.6% picked]

(C) Much of the ball's momentum goes into the bat's vibration and is not available to the rebounding baseball. [21.5% picked]

(D) Much of the collision energy goes into the bat's vibration and is not available to the rebounding baseball. [74.7% picked]

Answer: (D) Much of the collision energy goes into the bat's vibration and is not available to the rebounding baseball. [74.7% picked]

Why: TBA

Problem 29:

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 is pushes it forward. The force decreases steadily to zero just as the ball hits the ground. [1.7% picked]

(B) The ball experiences no horizontal force. [89.3% picked]

(C) The ball experiences a horizontal force that pushes it forward. The force is constant. [3.4% 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. [5.6% picked]

Answer: (B) The ball experiences no horizontal force. [89.3% picked]

Why: TBA

Problem 30:

You are arm-wrestling a friend. While you are gradually winning the competition, compare the torque that your arm exerts on your friend's arm to the torque your friend's arm exerts on your arm.

(A) The two torques are equal. [6.9% picked]

(B) The torque you exert on your friend is greater in amount than the torque your friend exerts on you. [42.5% picked]

(C) The torque you exert on your friend is less in amount than the torque your friend exerts on you. [0.9% picked]

(D) Those two torques are equal in amount but opposite in direction. [49.8% picked]

Answer: (D) Those two torques are equal in amount but opposite in direction. [49.8% picked]

Why: TBA