Physics 106 - How Things Work - Spring, 1995

Sample Midterm Examination - Problems and Solutions

Actual Exam Will Be Given Wednesday, March 8, 1995, at 1:00 PM

Actual Exam will have 25 Multiple Choice Questions and 3 Short Answer Questions

PART I: MULTIPLE CHOICE QUESTIONS

Please mark the correct answer for each question on the bubble sheet. Fill in the dot completely with #2 pencil. Part I is worth 67% of the grade on the midterm examination.

Problem 1:

A speedboat is pulling a water-skier with a rope, exerting a large forward force on her. The skier is traveling forward in a straight line path at a constant speed. The net force experienced by the skier is

(A) in the backward direction.

(B) in the forward direction.

(C) zero.

(D) in the upward direction.

Answer: (C) zero.

Why: Since the skier is traveling forward in a straight line path at a constant speed, she is traveling at constant velocity and is not accelerating. For her acceleration to be zero, she must be experiencing zero net force.

Problem 2:

A television set uses a magnetic field to deflect its electron beam horizontally. This magnetic field is able to steer the electron beam because

(A) a moving charged particle can experience a force when it passes through a magnetic field.

(B) an electron always travels in the direction of the magnetic field.

(C) an electron always travels at right angles to the direction of the magnetic field.

(D) a stationary charged particle can experience a force in a magnetic field.

Answer: (A) a moving charged particle can experience a force when it passes through a magnetic field.

Why: When a charged particle such as an electron moves through a magnetic field, it experiences a force perpendicular to its direction of travel.

Problem 3:

Ball bearings permit a wheel to turn freely on an axle without creating any heat because they form a mechanical system that involves

(A) no static friction.

(B) no sliding friction.

(C) no friction of either type.

(D) no electricity.

Answer: (B) no sliding friction.

Why: As the balls turn, they touch the wheel hub and the axle but do not slide across either one. The static friction that occurs as these objects touch one another does not waste energy as heat but sliding friction does. Since there is no sliding in a ball bearing, there is essentially no heat production.

Problem 4:

If you measure the force experienced by an electrically-charged bead placed inside an operating microwave oven, you will find that the force

(A) reverses directions several billion times per second.

(B) is proportional to the mass of the bead.

(C) is proportional to the velocity of the bead.

(D) is proportional to the amount of air inside the microwave oven.

Answer: (A) reverses directions several billion times per second.

Why: The microwaves themselves have electric and magnetic fields, both of which reverse directions at any point in space several billion times each second. An electrically-charged particle located at one point in space will experience a fluctuating force. That force will push the particle back and forth, reversing directions several billion times per second.

Problem 5:

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) velocity.

(D) angular velocity.

Answer: (A) angular momentum.

Why: While the gymnast is in the air, the only force she experiences is gravity. Gravity changes her velocity and momentum (she travels up then down) but it cannot exert any torque on her about her center of mass. That is because gravity acts at her center of gravity, which is coincident with her center of mass. With no lever arm over which to act, the force of gravity produces no torque. Since she experiences no torque, her angular momentum cannot change. Her angular velocity may vary if she changes her shape.

Problem 6:

If the local radio station WXYZ at 1020 on the AM dial wants to increase the strength of its radio signal so that it can reach a wider audience, it should

(A) increase the average amount of electrical charge that oscillates up and down its antenna but keep the frequency of oscillation the same.

(B) increase the frequency of oscillation of the electrical charge that travels up and down its antenna but keep the average amount of charge constant.

(C) increase the average amount of electrical charge that oscillates up and down its antenna and increase the frequency of oscillation.

(D) increase the temperature of the antenna by running more current through the heater coil.

Answer: (A) increase the average amount of electrical charge that oscillates up and down its antenna but keep the frequency of oscillation the same.

Why: The strength of the radio wave emitted by an antenna depends on how much charge runs up and down it. By increasing the average amount of charge moving on the antenna, WXYZ boosts its radio wave strength and widens its audience. Since WXYZ has been allocated the frequency 1020 (kilohertz), it cannot change the frequency with which those charges move up and down the antenna.

Problem 7:

Even when you are driving at a constant 60 miles-per-hour along a straight, level road, your car's engine must be running. As the engine turns the car's wheels, friction between the ground and the tires exerts a forward force on the car. The car needs this forward force from the ground because

(A) an object that is moving requires a net force to keep it moving. In the absence of any net force, objects are motionless.

(B) air drag (air resistance) exerts a backward force on the car.

(C) an object's velocity points in the direction of the net force on that object.

(D) the car has a velocity and is thus accelerating. In order to accelerate, the car must be experiencing a net force.

Answer: (B) air drag (air resistance) exerts a backward force on the car.

Why: As an object moves through the air, the air pushes backward on that object with a drag force. Drag forces always oppose relative motion and thus resemble frictional forces between surfaces. To keep a car moving forward against the backward force of air resistance, the ground must push the car forward.

Problem 8:

A small current of high-voltage electrons can carry the same amount of power as a large current of low-voltage electrons. Cross-country power transmission systems operate with a small current of very high-voltage electrons because this arrangement

(A) minimizes the fraction of total electrical power wasted as heat in the transmission wires.

(B) eliminates the need for transformers at either end of the cross-country transmission system.

(C) makes it possible to deliver electrical energy to the consumer continuously without requiring a complete electrical circuit. Only a single wire is needed to carry the power.

(D) is less likely to give anyone a shock than a system in which a large current of low-voltage electrons carries the power.

Answer: (A) minimizes the fraction of total electrical power wasted as heat in the transmission wires.

Why: The power wasted in the power lines is proportional to the square of the current passing through them. By sending a smaller current of higher energy charges through these power lines, the amount of power they waste can be dramatically reduced.

Problem 9:

At the end of the power cord of a table lamp is a plug. A typical plug has two metal prongs that you insert into the two slots of an electrical outlet. The plug has two separate metal prongs because

(A) electrons flow toward the lamp through one prong and return from the lamp through the other prong.

(B) alternating current means that only one wire is actively transporting electrons at any given time. For half the cycle electrons flow toward the lamp through one prong and the other prong has no current through it. For the next half cycle, the roles reverse.

(C) a single prong offers the potential of a bad connection, which would cause it to overheat and possibly start a fire. Electric current flows toward the lamp through both prongs simultaneously, reducing the risk of fire.

(D) one prong carries the electric current and the other prong serves as a grounding wire, enhancing the safety of the lamp.

Answer: (A) electrons flow toward the lamp through one prong and return from the lamp through the other prong.

Why: The table lamp cannot accumulate charges indefinitely. Instead, it must accept charges briefly, extract energy from them, and then return them to the power company to pick up more energy. These charges arrive at the lamp through one wire and return to the power company through the other wire.

Problem 10:

In some motors, the spinning rotor is made of nonmagnetic aluminum and has no electrical connections. This rotor becomes magnetic as the motor operates on alternating current because

(A) the changing magnetic environment around the rotor induces electrical currents in the rotor.

(B) the positive and negative charges in the rotor separate as the rotor spins.

(C) alternating current is inherently magnetic while direct current is not.

(D) aluminum is easily magnetized when exposed to a nearby magnetic pole.

Answer: (A) the changing magnetic environment around the rotor induces electrical currents in the rotor.

Why: An induction motor is an AC motor that uses an aluminum rotor inside a moving magnetic field. As the magnetic field moves in a circle around the rotor, it induces currents and magnetic poles in that rotor. Since the magnetic field is moving in a circle, it drags the rotor around in a circle with it.

PART II: SHORT ANSWER QUESTIONS

Please give a brief answer in the space provided. Part II is worth 33% of the grade on the midterm examination.

Problem 1:

Many doors are equipped with simple mechanical devices that close them automatically when no one is holding the door open. One of the simplest automatic door closers is a spring that connects the top corner of the door to the door frame. As you open the door, the spring stretches beyond its equilibrium length. The system now contains stored mechanical energy.

(A) When you hold this spring-equipped door open and stationary, what is the net torque on the door? zero.

Why: Since the door is stationary, its angular acceleration is zero so the net torque on it must be zero.

(B) Use words like "force" and "distance" to show that, when you let go of the door and it begins to close, work is done by one object on the other: The spring exerts an inward force on the door and the door moves inward. Thus the spring does work on the door.

Why: You do work when you exert a force on an object and that object moves in the direction of your force. Since the spring exerts a closing force on the door and the door closes, the spring is doing work on the door.

(C) What object contains most of the system's original energy in the moments just before the door shuts completely and latches? The door (as kinetic energy)

Why: Just before the door shuts, it is moving very rapidly and the spring is almost out of elastic potential energy. The spring has transferred most of its energy to the door, which now holds that energy as kinetic energy.

(D) More sophisticated door closers bring the door closed very gently and quietly. This type of door closer still contains a spring, but it also contains a damping device that always oppose the door's motion. What kind of force must the damping device use and what becomes of the system's original mechanical energy? A frictional or other disappative force that turns work into heat.

Why: To get rid of the energy in the spring without making noise or damaging anything, the door closer must turn it into heat. It uses sliding friction, drag, or another force that turns work done against it into heat.

Problem 2:

A blender is a common kitchen appliance. It consists of a glass or plastic pitcher with a rotating blade at the bottom. The pitcher sits in a base containing an electric motor. When you push the on button, the motor spins very rapidly and turns the blade. The spinning blade stirs and liquefies the contents of the pitcher.

(A) If you put an ice cube into the pitcher and push the on button, the blade spins and chops the ice cube into small fragments. The bottom of the pitcher is smooth and the ice cube is slippery, so no outside forces keep the ice cube from moving and staying ahead of the spinning blade. Still the ice cube stays put and the blade slices through it. What holds the ice cube in place? The ice cube's inertia.

Why: It takes a force and some time to get the ice cube moving. If the blade approaches the ice cube quickly enough, the ice cube will not have time to accelerate enough to avoid having the blade cut through it. Although the blade exerts a huge force on the ice cube, the ice cube's inertia prevents it from getting out of the blade's way quickly enough. Thus the blade slices through the ice cube despite the ice cube's apparent freedom to move.

(B) The blender plugs into an electrical outlet. When you push the on button, the blender mixes. At a particular moment during its operation, which way is electrical current flowing through each of the two wires in the blender's power cord? It is flowing toward the blender through one wire and returning from the blender through the other wire.

Why: The blender cannot accumulate charge so it must accept charge through one wire and return it through the other wire. Although the direction of current flow through the circuit reverses many times each second, at any given moment, the current is flowing in through one wire and out through the other.

(C) The blender contains a universal motor and can actually run on either AC or DC electrical power. If you reverse the blender's plug, so that the two prongs trade places in the outlet, will the motor and blade continue turning in the same direction or will they now turn in the opposite direction? The motor and blade will continue turning in the same direction.

Why: A universal motor is designed to turn in one direction even though it is operating on AC current. It is used to having the current reverse directions every 1/120th of a second. When you reverse the electrical connections between it and the power company, you are merely adding one more current reversal. It doesn't respond and continues to turn in its usual direction.

(D) You leave a beverage mixing in the blender while you answer the telephone. When you return, you find that the beverage has become quite warm. How did the spinning blade heat up the liquid? The spinning blade is doing work on the beverage and that work is being converted into heat.

Why: Work done against a disappative force such as sliding friction or drag is converted into heat. As the blade pushes through the beverage, it does work on that beverage (force times distance) and the beverage becomes hotter and hotter.