Physics 105 - How Things Work - Fall, 2004

Midterm Examination - Solutions

Given Friday, October 15, 2004 from 1:00pm to 1:50pm

Should be complete -- Please report typos or mistakes to me so I can fix them -- Lou Bloomfield 7:20am Tuesday, Oct 19

Please mark the correct answer for each question on the bubble sheet. Fill in the dot completely with a #2 pencil.

Problem 1 :

You are riding your bicycle fast on a level road. A deer crosses in front of you and you slam on the brakes, locking your wheels so that you skid to a stop. During this skidding stop, the kinetic energy you had while you were moving forward

Answer: (C) becomes mostly thermal energy. [93.6% picked]

Why: The wheels are experiencing sliding friction and work done against sliding friction ends up mostly as thermal energy.

Problem 2 :

When you drop a bouncy ball on a concrete floor, it bounces for a long time because it has difficulty getting rid of which conserved quantity?

Answer: (B) Energy [73.4% picked]

Why: The ball easily transfers energy to the floor via an impulse, but it is unable to do work on the floor. Thus the ball's energy remains in the ball and until that energy is converted into thermal energy, the ball continues to bounce.

Problem 3 :

For tomorrow's scuba diving trip, you pick up a full tank of air at the dive shop. You leave the tank in the hot sun and its temperature increases substantially. As a result of this temperature increase,

Answer: (C) the pressure inside the tank increases, but the tank's weight remains unchanged. [88.2% picked]

Why: As the air heats up, its particles move faster and therefore experience a rise in pressure. However, the weight of that air depends only on how many molecules are in the tank and that doesn't change.

Problem 4 :

To save space, you hang some shelves from the back of your door and fill them with objects. Neglecting friction or air resistance, these objects make it harder

Answer: (B) to start your door swinging, but have no effect on its ability to continue swinging once started. [66.5% picked]

Why: Increasing the door's angular mass makes it harder to start and stop swinging (that is, experience angular acceleration), but has no effect on its ability to coast at constant angular velocity.

Problem 5 :

You take your eyes off the road to read a text message on your cell phone and drive into a car stopped at the intersection. Neither car has its brakes on, so both cars coast into the intersection after the collision. The total momentum of the two cars after the collision is

Answer: (D) the same as the total momentum of the two cars before the collision. [82.3% picked]

Why: With their brakes off, neither car can exchange momentum with the roadway. Thus the total momentum they had before the collision is the same as they have after the collision.

Problem 6 :

As you fill your hanging birdfeeder with seed, you notice that its supports bend downward slightly. When you add 1 pound of seed, it bends downward 1 inch. When you add 1 more pound of seed, it bends downward a total of

Answer: (D) 2 inches. [96.1% picked]

Why: It bends downward 1 inch per pound because it's a spring. To support the first pound of seed, it must bend downward 1 inch. To support the second pound of seed as well, it must bend downward another 1 inch, for a total of 2 inches.

Problem 7 :

A toy helium balloon is full when it arrives, but deflates steadily over the next several days. This deflation occurs because the number of helium atoms in the balloon

Answer: (D) decreases as they diffuse through the walls of the balloon. [72.4% picked]

Why: Helium atoms are so tiny and move so quickly that they can and do diffuse right through materials. They escape from the balloon by traveling through its skin.

Problem 8 :

You are standing on the tip of a pointed fence post, trying not to fall off. Each time you start to tip, some wild arm motions return you to your precarious position. Your upright position on the post is

Answer: (B) an unstable equilibrium and your arm waving serves to return you to that unstable equilibrium. [82.8% picked]

Why: When you are balanced so precariously, any tip threatens to get worse. That's because you are at a maximum of total potential energy and a tip reduces that potential energy. To keep from falling over, you have to get yourself back to the unstable equilibrium any way you can and your arm waving serves that purpose.

Problem 9 :

You are at the county fair and are trying to knock over a stack of heavy blocks by throwing something at it. You have a choice of various 1 kilogram projectiles, which you can throw at 80 kilometers/hour. To have the best chance of knocking the stack over, you should chose the projectile that

Answer: (D) has the largest coefficient of restitution (is most lively). [59.6% picked]

Why: Knocking over the blocks requires that you transfer momentum to them. To transfer as much momentum as possible, the projectile should do more than just come to a stop--it should also leap backward or "rebound." In that act of rebounding, the projectile transfers another dose of forward momentum to the blocks and helps to knock them over.

Problem 10 :

If you hold a properly filled glass bottle of soda or beer upright in your hand and strike the cap hard with a rubber mallet, the

Answer: (B) bottom of the bottle will be knocked off by a pressure surge there. [94.6% picked]

Why: Pounding down on the bottle causes it to accelerate downward rapidly. The water is inertial and gets left behind as the bottle plummets. Soon the water has pulled away from the bottom of the bottle and is up in the bottle's neck. Once the bottle stops accelerating downward, the water has a chance to catch up to and is propelled downward by the high pressure air in the bottle's neck. When the water finally returns to the bottom of the bottle, it hits hard and knocks the bottom out of the bottle.

Problem 11 :

A child is riding in a wagon tied to the family dog with a string. As the dog walks steadily forward on the level sidewalk, the wagon follows perfectly. Suddenly the dog leaps forward to chase a squirrel and the string snaps. The loaded wagon breaks the string because the loaded wagon has such a large

Answer: (B) mass. [78.3% picked]

Why: The string breaks because the force needed to accelerate the massive wagon is too great for it.

Problem 12 :

Many high-rise buildings have water tanks on their roofs. Water stored in such a tank ensures good water pressure throughout the building because it has more than enough

Answer: (C) energy per liter. [84.7% picked]

Why: Height increases the energy per liter of the water, but leaves everything else (mass per liter, weight per liter, and density) unchanged.

Problem 13 :

The silvery Mylar bags used for long-lasting helium balloons barely stretch at all. Once you have filled such a balloon to the point where it is taut, it becomes counterproductive to add any more helium atoms. If you add more helium to a taut Mylar balloon, its weight will

Answer: (B) increase while the buoyant force it experiences will remain unchanged. [90.1% picked]

Why: Each helium atom has a weight, so adding more to the contents of the balloon increases the balloon's total weight. However, the buoyant force that the balloon experience depends only on its volume, not on its contents. Thus as you fill the balloon without changing its volume, you increase its weight but not the buoyant force it experiences.

Problem 14 :

The tumble dryer in the laundry room spins its drum about a horizontal axis. The clothes in this drum rise part way up the side of the drum as it turns and then fall back toward the bottom of the drum, over and over again. If the drum turned too fast, this tumbling effect wouldn't work because the

Answer: (C) clothes' inertia would keep them pressed against the drum as it spun. [80.3% picked]

Why: If the dryer spins too quickly, the clothes own tendency to travel inertially (i.e. in a straight line) will keep them pressed against the drum. Even at the top of their trip around in a circle, they'll then be accelerating downward so quickly that gravity will need help from the drum to push them downward. The clothes will never lose contact with the drum and will simply spin around and around with it.

Problem 15 :

At equilibrium, the surface of a lake is smooth and level. That's because bumps or dips in the water's surface would

Answer: (A) increase the water's total potential energy and the water would accelerate so as to reduce that total potential energy. [74.4% picked]

Why: Any bump in the lake involves water that is higher than it needs to be and therefore has more gravitational potential energy than it needs to have. Whenever there is excess total potential energy, a system will accelerate so as to reduce that excess energy. In this case, the lake will accelerate toward flatness.

Problem 16 :

You are living in an old house with aged plumbing. The pressure in the water main outside the house is good and steady, but the shower spray is surprisingly weak. And when other people are running water at the same time, the shower barely sprays at all. The reason that the shower spray is so weak while other people are running water is that

Answer: (C) speeding up the water flow in the pipes causes it to turn an even larger fraction of its total energy into thermal energy through viscous effects. [17.2% picked]

Why: The more water that has to go through the pipes, the faster it has to flow and the more it rubs on the pipe walls. Like water flowing too quickly through a garden hose, the water in this house loses so much energy en route to you that it barely sprays at all.

Problem 17 :

You have just added sugar to your coffee and are about to mix the two together with 10 swirls of a teaspoon. If you move the spoon very slowly during these swirls, it won't be nearly as effective as if you move the spoon fast. Rapid motion is important because you want the coffee to experience

Answer: (A) turbulent flow around the spoon and high speeds help inertia produce turbulence. [63.5% picked]

Why: Turbulence is important when mixing chemicals because you need to separate that various pure chemicals from one another. Laminar flow won't do that separating, so you deliberately create turbulence. Inertia is the key to achieving turbulence: the fluid's inertia is what allows it to rip itself apart as it flows through or around obstacles, such as the spoon.

Problem 18 :

During the spin-dry cycle, the drum of a standard, top-loading washing machine spins rapidly about a vertical axis and flings water out of the wet clothes. This water flows out of the spinning drum through holes and goes into the air. Ignoring gravity, this water then travels at constant

Answer: (C) velocity in the direction it was traveling just before leaving the drum. [64.5% picked]

Why: As soon as the water leaves the drum, it becomes inertial (we're neglecting gravity, so it is free of forces). It travels in a straight line path at the velocity it had just before it lost contact with the drum. Its path takes it tangent to the drum.

Problem 19 :

When a skater pulls in her arms while spinning on the tip of her skate, she begins spinning faster. That's because pulling in her arms decreases her

Answer: (B) angular mass or moment of inertia, and her angular velocity must increase so as to keep her angular momentum constant. [99.5% picked]

Why: Because the skater is not exerting torques on the ground, the ground isn't exerting torques on her and she spins with constant angular momentum. As she pulls in her arms and moves her mass closer to the axis of rotation, her angular mass decreases. To compensate for that decrease, while preserving her constant angular momentum, she has to spin faster.

Problem 20 :

You are building a decorative mobile and the first thing you do is hang a long stiff rod from a string attached to the ceiling. When you have properly centered the string on the rod, the rod experiences zero torque about its center of mass. With zero net torque acting on it, the rod

Answer: (C) experiences zero angular acceleration. [50.2% picked]

Why: This observation is basically Newton's first law for rotation. An object that isn't experiencing any torque spins at constant angular velocity (i.e. is experiencing zero angular acceleration).

Problem 21 :

You have joined the rodeo and are in the midst of riding an angry bull. Amazingly enough, you remain in the saddle as the bull leaps up and down, and you feel alternately very heavy and very light. You feel heaviest when the bull is

Answer: (B) accelerating upward the fastest. [77.3% picked]

Why: Your experience of acceleration is a fictitious "pull" in the direction opposite your acceleration. Thus when you accelerate upward, you feel that "pull" in the downward direction

Problem 22 :

You and a friend are having a tug-of-war: you are pulling on opposite ends of a rope, each trying to pull the other one into a mud puddle that lies between you. You successfully pull your friend into the puddle and win. In doing so, you do

Answer: (B) positive work on the rope and your friend does negative work on the rope. [83.3% picked]

Why: You pull the rope toward you and it moves toward you, so you do positive work on it. However, your friend pulls the rope toward her and the rope moves away from her, so she does negative work on it; her pull on the rope and its movement are in opposite directions, so the work she does on the rope is negative.

Problem 23 :

You are rearranging the furniture and are moving your desk to the other side of the room. To keep your desk sliding across the level floor at constant velocity, you have to keep pushing it forward. The net force on the desk is

Answer: (A) zero, even though the ground is exerting a backward frictional force on the desk. [45.8% picked]

Why: The desk is moving at constant velocity, so it is not accelerating and must be experiencing zero net force. Nonetheless, the floor is pushing it backward with a frictional force and you're having to balance that frictional force to keep it sliding forward.

Problem 24 :

You're watching a decorative fountain spray water straight up. As the water rises from its source, the water's velocity is

Answer: (C) upward but its acceleration is downward. [94.1% picked]

Why: Once it leaves the nozzle or other source, the water is in free fall. Like a ball that has been thrown upward and is no longer begin supported, the water is accelerating downward at the acceleration due to gravity. So while it is heading upward (its velocity is upward), it is accelerating downward.

Problem 25 :

You are lying motionless in a hammock at its equilibrium point when a friend gives you a strong push sideways. Now you are swinging back and forth about that equilibrium. As you swing, your acceleration is greatest when you

Answer: (D) reach the end of a swing and your speed is greatest when you coast through equilibrium. [75.4% picked]

Why: Although the curved nature of your motion makes the problem a little more complicated than if it were straight, you are basically "bouncing" back and forth through a stable equilibrium. The restoring force increases with distance from that equilibrium, so your acceleration is strongest when you are farthest from equilibrium. And as you coast through equilibrium in either direction, your kinetic energy and speed are greatest.

Problem 26 :

A rubber bouncy ball won't bounce on loose sand, but a beach ball will. The difference is that only the

Answer: (C) soft beach ball dents during the impact, stores energy efficiently, and rebounds effectively. [81.8% picked]

Why: Sand doesn't store energy when you dent it, so anything that tries to bounce off it will either have to store its own energy or fail to bounce. The beach ball is so soft that it does virtually all the denting when it hits the sand and is therefore responsible for almost all the collision energy. Since it's pretty lively, it rebounds well.

Problem 27 :

A rocking chair recovers automatically from any tip. When it is upright, the chair is clearly in a stable equilibrium. As you tip this chair away from this equilibrium, you can be sure that its center of gravity

Answer: (B) rises and its total potential energy increases. [81.3% picked]

Why: Objects in stable equilibrium are always at points of lowest total potential energy. If you move them away from equilibrium, they experience a rise in total potential energy and naturally accelerate back toward the stable equilibrium point. The rocking chair is a case in point: its at a low in the potential energy and any tip raises that potential energy by lifting its center of gravity.

Problem 28 :

You're riding in a horse-drawn carriage in New York City . As each of the cart's wheels turns against the pavement without slipping, the ground exerts a static frictional force on that wheel. This frictional force does

Answer: (B) zero work on the wheel. [39.9% picked]

Why: Since the wheel touches the pavement and then lifts off, its contact point with the ground doesn't move horizontally. Although there may be frictional forces between the wheel and ground, no distance is ever traveled in the directions of those forces so no work is done.

Problem 29 :

You are stocking shelves in the grocery store. You can lift 12 containers of milk onto a high shelf either all together or one at a time. If you lift them all together, the work you do in raising them onto the shelf will be

Answer: (C) the same as if you lift them all one at a time. [89.7% picked]

Why: The work you do raising an object from one height to another does not depend on any of the details involved in that raising process. Whether you lift the object alone or as part of a collection, you do a certain amount of work in raising it. Thus you do the same work lifting the 12 milk cartons together as if you do lifting all 12 of them separately.

Problem 30 :

Your shampoo bottle is almost empty, so you tighten its cap and swing it rapidly in a circle with its cap end pointing outward. The remaining shampoo collects just inside the cap and you are able to squeeze out one more dollop. This technique works because

Answer: (C) the bottle's rapid inward acceleration leaves the shampoo behind so that it drifts toward the cap end of the bottle. [52.2% picked]

Why: There is never any real force pushing the shampoo toward the cap -- it's just an inertial effect. When you whip the container around in a circle, you are making it accelerate inward at a furious pace and the shampoo can't follow. Instead, the shampoo gets left behind and ends up in the cap area of the shampoo container.

Problem 31 :

You have just leapt off the high diving board and are falling. Neglecting any effects due to air, which of the following quantities can't change while you are above the water?

Answer: (C) Your angular momentum. [31.5% picked]

Why: Only your angular momentum remain constant; everything else changes. You are falling, converting gravitational potential energy into kinetic energy. Furthermore, you are being pull downward by gravity and are accumulating downward momentum. But without any torques acting on you, you are not experiencing any angular impulses and therefore not changing your angular momentum.

Problem 32 :

You kick a stationary soccer ball and it flies off into the distance. At the moment the ball stops touching your foot, it is traveling

Answer: (C) faster than your foot. [27.6% picked]

Why: The soccer ball bounces off your foot and thus heads away from you at least somewhat faster than your foot is heading forward. Only if it had exactly zero coefficient of resolution (like a bean bag) would it head away from you at exactly the speed of your foot. Since its coefficient of restitution is greater than zero, it out paces your foot.

Problem 33 :

A 4-story apartment building is fed by a single water pipe that runs up one corner of the building. The pipe has a constant diameter all the way up. As water rises in this pipe toward the upper floors,

Answer: (B) its pressure potential energy becomes gravitational potential energy, but its speed remains constant. [80.3% picked]

Why: Water rising in a pipe of constant diameter can neither speed up nor slow down -- if it did, either a gap would form or a traffic jam would take place. Instead, the water can only turn its pressure potential energy gradually into gravitational potential energy.

Problem 34 :

An arrow is heading toward its target after leaving the archer's bow. Neglecting any effects due to air, the net force on the arrow

Answer: (B) points directly downward. [35.0% picked]

Why: The arrow is simply a falling object and it is accelerating straight down due to its weight. It is experiencing no forward force; it is merely coasting forward.

Problem 35 :

A log floats motionless at the surface of a still lake. The log's weight is exactly equal to the weight of

Answer: (B) the mixture of water and air that the log is displacing. [37.4% picked]

Why: Even in this context, Archimedes' principle works perfectly. The log is displacing a mixture of water and air and it experiences a buoyant force equal to the weight of that mixture.

Problem 36 :

Your friend is wearing roller-skates on a bus that is stopped at a traffic light. The light turns green. He is standing motionless in the aisle as the bus starts forward and he finds himself moving rapidly toward the back of the bus. He is heading toward the back of the bus because

Answer: (C) his inertia is keeping him motionless as the bus moves forward around him. [89.2% picked]

Why: The bus is trying to drive out from under your friend. Your friend is inertial and remains in place as the bus heads forward without him. It isn't until he encounters the rear wall of the bus that he experiences the forward force he needs to accelerate along with the bus. Ouch!

Problem 37 :

You roll a ball directly up a ramp. It travels up the ramp, comes to a stop, and rolls back to its starting point. Neglecting friction or air resistance, the ball accelerates

Answer: (A) steadily downhill (along the ramp) the whole time. [53.2% picked]

Why: An object on a ramp experiences a downhill net force -- the result of an imperfect cancellation between its weight down and the ramp's support force up and to the side. Since there are no other forces on the ball it experiences only this downhill force and therefore accelerates steadily downhill (even when it's moving uphill).

Problem 38 :

Your friend is running in a long race and you are watching from the sidewalk. To encourage her as she runs swiftly past you, you reach out and pat her on the back. During that pat, you push her forward with a force of 10 newtons (about 2 pounds). She pushes back on you with a force of

Answer: (B) 10 newtons. [96.6% picked]

Why: Newton's third law always works. No matter what your friend is doing as she runs, she pushes back on you with a force equal to but oppositely directed from the force you exert on her.

Problem 39 :

Two identical balls roll off a horizontal desk at exactly the same moment. One ball is traveling horizontally twice as fast as the other at the moment the two leave the desk. Compared to the slower ball, the faster ball hits the ground

Answer: (C) at the same time, but at twice the horizontal distance from the desk. [71.9% picked]

Why: The two balls fall perfectly together and therefore hit the ground together. But the faster moving ball travels twice as fast horizontally and is twice as far from the desk by the time the two hit.

Problem 40 :

You are pounding nails into the floor with a steel hammer. To reduce the noise, you wrap a thick layer of rubber around the hammer. Although you swing the hammer at just the same speed as before, it's unable to push the nails into the wood. That's because the wrapped hammer transfers

Answer: (D) momentum to each nail over a longer time. [68.0% picked]

Why: Whether or not its wrapped in rubber, the hammer will transfer all of its momentum to the nail. But the rubber wrapping will slow down that transfer so that it involves a smaller force exerted over a longer time. This smaller force is less effective at pushing the nail into the wood.