Physics Ii Exam 1

Front 1

An object-spring system undergoes simple harmonic motion with an amplitude A. Does the total energy change if the mass is doubled but the amplitude isn’t changed? Are the kinetic and potential energies at a given point in its motion affected by the change in mass? Explain.

Back 1

No. Because the total energy is E = $kA2, changing the mass of the object while keeping A constant has no effect on the total energy. When the object is at a displacement xfrom equilibrium, the potential energy is \kx2, independent of the mass, and the kinetic energy is KE = E - \kx2, also indepen­ dent of the mass.

Front 2

If an object-spring system is hung vertically and set into oscillation, why does the motion eventually stop? Friction. This includes both air resistance and damping within the spring.

Back 2

When the spring with two objects on opposite ends is set into oscillation in space, the coil at the exact center of the spring does not move. Thus, we can imagine clamping the center coil in place without affecting the motion. If we do this, we have two separate oscillating systems, one on each side of the clamp. The half-spring on each side of the clamp has twice the spring constant of the full spring, as shown by the follow­ ing argument: The force exerted by a spring is proportional to the separation of the coils as the spring is extended. Imag­ ine that we extend a spring by a given distance and measure the distance between coils. We then cut the spring in half. If one of the half-springs is now extended by the same distance, the coils will be twice as far apart as they were in the com­ plete spring. Thus, it takes twice as much force to stretch the half-spring, from which we conclude that the half-spring has a spring constant which is twice that of the complete spring. Hence, our clamped system of objects on two half-springs will vibrate with a frequency that is higher than /b y a factor of the square root of two.

Front 3

An object is hung on a spring, and the frequency of oscil­ lation of the system,/, is measured. The object, a second identical object, and the spring are carried to space in the space shuttle. The two objects are attached to the ends of the spring, and the system is taken out into space on a space walk. The spring is extended, and the system is released to oscillate while floating in space. The coils of the spring don’t bump into one another. What is the frequency of oscillation for this system in terms of/?

Back 3

We assume that the buoyant force acting on the sphere is negligible in comparison to its weight, even when the sphere is empty. We also assume that the bob is small compared with the pendulum length. Then, the frequency of the pen­ dulum is/= 1/7’= (1/27r)Vg/L, which is independent of mass. Thus, the frequency will not change as the water leaks out.

Front 4

If a spring is cut in half, what happens to its spring constant?

Back 4

Each half-spring will have twice the spring constant of the full spring, as shown by the follow­ ing argument. The force exerted by a spring is proportional to the separation of the coils as the spring is extended. Imagine that we extend a spring by a given distance and measure the distance between coils. We then cut the spring in half. If one of the half-springs is now extended by the same distance, the coils will be twice as far apart as they were for the complete spring. Thus, it takes twice as much force to stretch the half-spring, from which we conclude that the half-spring has a spring constant which is twice that of the complete spring.

Front 5

A pendulum bob is made from a sphere filled with water. What would happen to the frequency of vibra­ tion of this pendulum if the sphere had a hole in it that allowed the water to leak out slowly?

Back 5

We assume that the buoyant force acting on the sphere is negligible in comparison to its weight, even when the sphere is empty. We also assume that the bob is small compared with the pendulum length. Then, the frequency of the pen­ dulum is/= 1/7’= (1/27r)Vg/L, which is independent of mass. Thus, the frequency will not change as the water leaks out.

Front 6

If a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when it is moved to the top of the mountain? Explain.

Back 6

No. The period of vibration is T = 2k y[tfg and g is smaller at high altitude. Therefore, the period is longer on the mountain top and the clock will run slower.

Front 7

(a) Is a bouncing ball an example of simple harmonic motion? (b) Is the daily movement of a student from home to school and back simple harmonic motion?

Back 7

(a) The bouncing ball is not an example of simple harmonic motion. The ball does not follow a sinusoidal function for its position as a function of time, (b) The daily movement of a student is also not simple harmonic motion, because the stu­ dent stays at a fixed location, school, for a long time. If this motion were sinusoidal, the student would move more and more slowly as she approached her desk, and as soon as she sat down at the desk, she wotdd start to move back toward home again.

Front 8

If a grandfather clock were running slow, how could we adjust the length of the pendulum to correct the time?

Back 8

Shorten the pendulum to decrease the period between ticks.

Front 9

What happens to the speed of a wave on a string when the frequency is doubled? Assume the tension in the string remains the same.

Back 9

The speed of a wave on a string is given byv= V7//L This says the speed is independent of the frequency of the wave. Thus, doubling the frequency leaves the speed unaffected.

Front 10

If you stretch a rubber hose and pluck it, you can observe a pulse traveling up and down the hose. What happens to the speed ofthe pulse ifyou stretch the hose more tightly? W hat happens to the speed if you fill the hose with water?

Back 10

The speed of the pulse is v = yjF/u, so increasing the tension F in the hose increases the speed of the pulse. Filling the hose with water increases the mass per unit length //, and will decrease the speed of the pulse.

Front 11

Explain why the kinetic and potential energies of an object-spring system can never be negative.

Back 11

The kinetic energy is proportional to the square of the speed, and the potential energy is proportional to the
square of the displacement. Therefore, both must be positive quantities.

Front 12

A grandfather clock depends on the period of a pen­ dulum to keep correct time. Suppose such a clock is calibrated correctly and then the temperature of the room in which it resides increases. Does the clock run slow, fast, or correctly? Hint: A material expands when its tem perature increases.

Back 12

As the temperature increases, the length of the pendulum will increase due to thermal expansion, and with a greater length, the period of the pendulum increases. Thus, it takes longer to execute each swing, so that each second according to the clock will take longer than an actual second. Consequently, the clock will run slow.

Front 13

(a) You are driving down the highway in your car when a police car sounding its siren overtakes you and passes you. If its frequency at rest is f 0, is the frequency you hear while the car is catching up to you higher or lower than (b) What about the frequency you hear after the car has passed you?

Back 13

(a) higher (b) lower


Front 14

A crude model of the human throat is that of a pipe open at both ends with a vibrating source to introduce the sound into the pipe at one end. Assuming the vibrating source produces a range of frequencies, dis­ cuss the effect of changing the pipe’s length.

Back 14

The resonant frequency depends on the length of the pipe. Thus, changing tire length of the pipe will cause different frequencies to be emphasized in the resulting sound. The shorter the pipe, the higher the fundamental resonance frequency.

Front 15

Older auto-focus cameras sent out a pulse of sound and measured the time interval required for the pulse to reach an object, reflect off of it, and return to be detected. Can air temperature affect the cam­ era’s focus? New cameras tise a more reliable infrared system.

Back 15

Yes. The speed of sound in air is proportional to the square root of the absolute temperature, VT. The speed of sound
is greater in warmer air, so the pulse from the camera would return sooner than it would on a cooler day from an object at the same distance. The camera would interpret an object as being closer than it actually is on a hot day.

Front 16

Explain how the distance to a lightning bolt (Fig. CQ14.4) can be determined by counting the seconds between the flash and the sound of thunder.

Back 16

The speed of light is so high that the arrival of the flash is practically simultaneous with the lightning discharge. Thus, the delay between the flash and the arrival of the sound of thunder is the time sound takes to travel the distance separating the lightning from you. By counting the seconds between the flash and thunder and knowing the approximate speed of sound in air, you have a rough measure of the distance to the lightning bolt.

Front 17

Secret agents in the movies always want to get to a secure phone with a voice scrambler. How do these devices work?

Back 17

Sophisticated electronic devices break the frequency range used in telephone conversations into several frequency bands and then mix them in a predetermined pattern so that they become unintelligible. The descrambler moves the bands back into their proper order.

Front 18

Why does a vibrating guitar string sound louder when placed on the instrument than it would if allowed to vibrate in the air while off the instrument?

Back 18

A vibrating string is not able to set very much air into motion when vibrated alone. Thus it will not be very loud. If it is placed on the instrument, however, the string’s vibration sets the sound­ ing board of the guitar into vibration. A vibrating piece of wood is able to move a lot of air, and the note is louder.

Front 19

You are driving toward the base of a cliff and you honk your horn, (a) Is there a Doppler shift of the sound when you hear the echo? If so, is it like a moving source or moving observer? (b) What if the reflection occurs not from a cliff, but from the for­ ward edge of a huge alien spacecraft moving toward you as you drive?

Back 19

(a) The echo is Doppler shifted, and the shift is like both
a moving source and a moving observer. The sound that leaves your horn in the forward direction is Doppler shifted to a higher frequency, because it is coming from a moving source. As the sound reflects back and comes toward you, you are a moving observer, so there is a second Doppler shift to an even higher frequency, (b) If the sound reflects from the spacecraft coming toward you, there is a different mov­ ing-source shift to an even higher frequency. The reflecting surface of the spacecraft acts as a moving source.

Front 20

The radar systems used by police to detect speeders are sensitive to the Doppler shift of a pulse of radio waves. Discuss how this sensitivity can be used to measure the speed of a car.

Back 20

A beam of electromagnetic waves of known frequency is sent toward a speeding car, which reflects the beam back to a detector in the police car. The amount the returning frequency has been shifted depends on the velocity of the oncoming car.

Front 21

An archer shoots an arrow from a bow. Does the string of the bow exhibit standing waves after the arrow leaves? If so, and if the bow is perfectly symmetric so that the arrow leaves from the center of the string, what harmonics are excited?

Back 21

The bowstring is pulled away from equilibrium and released, in a manner similar to the way a guitar string is pulled and released when it is plucked. Thus, standing waves will be excited in the bowstring. If the arrow leaves from the exact center of the string, then a series of odd harmonics will be excited. Even harmonics will not be excited, because they have a node at the point where the string exhibits its maxi­ mum displacement.

Front 22

A soft drink bottle resonates as air is blown across its top. What happens to the resonant frequency as the level of fluid in the bottle decreases?

Back 22

Consider the level of fluid in the bottle to be adjusted so that the air column above it resonates at the first harmonic. This is given by / = v/AL. This equation indicates that as the length L of the column increases (fluid level decreases), the resonant frequency decreases.

Front 23

An airplane mechanic notices that the sound from a twin-engine aircraft varies rapidly in loudness when both engines are running. What could be causing this variation from loud to soft?

Back 23

The two engines are running at slightly different frequencies, thus producing a beat frequency between them.

Front 24

A glass object receives a positive charge of +3 nC by rub­ bing it with a silk cloth. In the rubbing process, have protons been added to the object or have electrons been removed from it?

Back 24

Electrons have been removed from the glass object. Nega­ tive charge has been removed from the initially neutral rod, resulting in a net positive charge on the rod. The protons cannot be removed from the rod; protons are not mobile because they are within the nuclei of the atoms of the rod.

Front 25

Explain from an atomic viewpoint why charge is usually transferred by electrons.

Back 25

Electrons are more mobile than protons and are more easily freed from atoms than the protons which are tightly bound within the nuclei of the atoms.

Front 26

A person is placed in a large, hollow metallic sphere that is insulated from ground. If a large charge is placed on the sphere, will the person be harmed upon touching the inside of the sphere?

Back 26

No. The charge on the metallic sphere resides on its outer surface, so the person is able to touch the surface without causing any charge transfer.

Front 27

Why must hospital personnel wear special conducting shoes while working around oxygen in an operating room? What might happen if the personnel wore shoes with rubber soles?

Back 27

Conducting shoes are worn to avoid the build up of a static charge on them as the wearer walks. Rubber-soled shoes acquire a charge by friction with the floor and could discharge with a spark, possibly causing an explosive burning situation, where the burning is enhanced by the oxygen.

Front 28

(a) Would life be different if the electron were posi­ tively charged and the proton were negatively charged? (b) Does the choice of signs have any bearing on physi­ cal and chemical interactions? Explain your answers.

Back 28

No. Life would be no different if electrons were + charged and protons were —charged. Opposite charges would still attract, and like charges would repel. The naming of + and —charge is merely a convention.

Front 29

If a suspended object A is attracted to a charged object B, can we conclude that A is charged? Explain.

Back 29

No. Object A might have a charge opposite in sign to that
of B, but it also might be neutral. In this latter case, object
B causes object A to be polarized, pulling charge of the sign opposite the change on B toward the near face of A and pushing an equal amount of charge of the same sign as that on B toward the far face. Then, due to difference in distances, the force of attraction exerted by B on the induced charge
of opposite sign is slightly larger than the repulsive force exerted by B on the induced charge of like sign. Therefore, the net force on A is toward B.

Front 30

Explain how a positively charged object can be used to leave another metallic object with a net negative charge. Discuss the motion of charges during the process.

Back 30

Move an object A with a net positive charge so it is near, but not touching, a neutral metallic object B that is insulated from the ground. The presence of A will polarize B, caus­ ing an excess negative charge to exist on the side nearest A and an excess positive charge of equal magnitude to exist on the side farthest from A. While A is still near B, touch B with your hand. Additional electrons will then flow from ground, through your body, and onto B. With A continuing to be near but not in contact with B, remove your hand from B, thus trapping the excess electrons on B. When A is now removed, B is left with excess electrons, or a net negative charge. By means of mutual repulsion, this negative charge will now spread uniformly over the entire surface of B.

Front 31

Consider point A located an arbitrary distance from two point charges in oth­erwise empty space, (a) Is it possible for an electric field to exist at point A in empty space? (b) Does charge exist at this point? (c) Does a force exist at this point?

Back 31

(a) Yes. The positive charges create electric fields that extend in all directions from those charges. The total field at point A is the vector sum of the individual fields produced by the charges at that point. (b) No, because there are no field lines emanating from or converging on point A. (c) No. There must be a charged object present to experience a force.

Front 32

A student stands on a thick piece of insulating mate­ rial, places her hand on top of a Van de Graaff genera­ tor, and then turns on the generator. Does she receive a shock?

Back 32

She is not shocked. She becomes part of the dome of the Van de Graaff, and charges flow onto her body. They do not jump to her body via a spark, however, so she is not shocked.

Front 33

In fair weather, there is an electric field at the surface of the Earth, pointing down into the ground. What is the sign of the electric charge on the ground in this situation?

Back 33

Electric field lines start on positive charges and end on negative charges. Thus, if the fair-weather field is directed into the ground, the ground must have a negative charge.

Front 34

A charged comb often attracts small bits of dry paper that then fly away when they touch the comb. Explain why that occurs.

Back 34

The dry paper is initially neutral. The comb attracts the paper because its electric field causes the molecules of the paper to become polarized—the paper as a whole cannot be polarized because it is an insulator. Each molecule is polar­ ized so that its unlike-charged side is closer to the charged comb than its like-charged side, so the molecule experiences a net attractive force toward the comb. Once the paper comes in contact with the comb, like charge can be trans­ ferred from the comb to the paper, and if enough of this charge is transferred, the like-charged paper is then repelled by the like-charged comb.

Front 35

Why should a ground wire be connected to the metal support rod for a television antenna?

Back 35

To some extent, a television antenna will act as a lightning rod on the house. If the antenna is connected to the Earth by a heavy wire, a lightning discharge striking the house may pass through the metal support rod and be safely carried to the Earth by the ground wire.

Front 36

There are great similarities between electric and gravi­ tational fields. A room can be electrically shielded so that there are no electric fields in the room by sur­ rounding it with a conductor. Can a room be gravita­ tionally shielded? Explain.

Back 36

The electric shielding effect of conductors depends on the fact that there are two kinds of charge: positive and negative. As a result, charges can move within the conductor so that the combination of positive and negative charges establishes an electric field that exactly cancels the external field within the conductor and any cavities inside the conductor. There is only one type of gravitation charge, however, because there is no negative mass. As a result, gravitational shielding is not possible. A room cannot be gravitationally shielded because mass is always positive or zero, never negative.

Front 37

A spherical surface surrounds a point charge q. Describe what happens to the total flux through the surface if (a) the charge is tripled, (b) the volume of the sphere is doubled, (c) the surface is changed to a cube, (d) the charge is moved to another location inside the surface, and (e) the charge is moved outside the surface.

Back 37

(a) If the charge is tripled, the flux through the surface is also tripled because the net flux is proportional to the charge inside the surface. (b) The flux remains constant when the volume changes because the surface surrounds the same amount of charge, regardless of its volume. 
(c) The flux does not change when the shape of the closed surface changes. (d) The flux through the closed surface remains unchanged as the charge inside the surface is moved to another location inside that surface. (e) The flux is zero because the charge inside the surface is zero. All of these conclusions are arrived at through an understanding of Gauss’s law.

Front 38

If more electric field lines leave a Gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?

Back 38

You can only conclude that the net charge inside the Gauss­ ian surface is positive.

Front 39

A student who grew up in a tropical country and is studying in the United States may have no experience with static electricity sparks and shocks until his or her first American winter. Explain.

Back 39

All of the constituents of air are nonpolar except for water. The polar water molecules in the
air quite readily “steal" charge from a charged object, as any physics teacher trying to perform electrostatics demonstrations in the summer well knows. As a result, it is difficult to accumulate large amounts of excess charge on an object in a humid climate. During a North American winter, the cold, dry air allows accumulation of significant excess charge, giving the possibility for shocks caused by static electricity sparks.

Front 40

What happens when a charged insulator is placed near an uncharged metallic object? (a) They repel each other, (b) They attract each other, (c) They may attract or repel each other, depending on whether the charge on the insulator is positive or negative, (d) They exert no electrostatic force on each other, (e) The charged insulator always spontaneously discharges.

Back 40

B

Front 41

(a) Describe the motion of a proton after it is released from rest in a uniform electric field, (b) Describe the changes (if any) in its kinetic energy and the electric potential energy associated with the proton.

Back 41

(a) The proton moves in a straight line with constant accel­ eration in the direction of the electric field, (b) As its veloc­ ity increases, its kinetic energy increases, and the electric potential energy associated with the proton decreases.

Front 42

Rank the potential energies of the four systems of par ticles shown in Figure CQ16.2 from largest to smallest. Include equalities if appropriate.

Back 42

The potential energy between a pair of point charges separated by distance R is PE = keq{q2/R. Therefore, the correct ranking from largest to smallest is (a) > (b) = (d) > (c).

Front 43

A parallel-plate capacitor is charged by a battery, and the battery is then disconnected from the capacitor. Because the charges on the capacitor plates are oppo site in sign, they attract each other. Hence, it takes posi tive work to increase the plate separation. Show that the external work done when the plate separation is increased leads to an increase in the energy stored in the capacitor.

Back 43

The work done in pulling the capacitor plates farther apart is transferred into additional electric energy stored in the capacitor. The charge is constant, and the capacitance decreases, but the potential difference between the plates increases, which results in an increase in the stored electric energy.

Front 44

When charged particles are separated by an infinite distance, the electric potential energy of the pair is zero. When the particles are brought close, the electric potential energy of a pair with the same sign is posi tive, whereas the electric potential energy of a pair with opposite signs is negative. Explain.

Back 44

To move like charges together from an infinite separation, at which the potential energy of the system of two charges is /.ero, requires work to be done on the system by an outside agent. Ilence energy is stored, and potential energy is positive. As charges with opposite signs move together from an infinite separation, energy is released, and the potential energy of the set of charges becomes negative.

Front 45

Suppose you are sitting in a car and a 20-kV power line drops across the car. Should you stay in the car or get out? The power line potential is 20 kV compared to the potential of the ground.

Back 45

If the power line makes electrical contact with the metal of thecar,itwillraisethepotentialofthecarto20kV.Itwill also raise the potential of your body to 20 kV, because you are in contact with the car. In itself, this is not a problem. If you step out of the car,however,yourbodyat20kVwillmake contact with the ground, which is at zero volts. As a result, a current will pass through your body, and you will likely be injured. Thus, it is best to stay in the car until help arrives.

Front 46

Why is it important to avoid sharp edges or points on conductors used in high-voltage equipment?

Back 46

A sharp point on a charged conductor would produce a large electric field in the region near the point. An electric discharge could most easily take place at the point.

Front 47

Explain why, under static conditions, all points in a conductor must be at the same electric potential. 


Back 47

If two points on a conducting object were at different poten­ tials, then free charges in the object would move, and we would not have static conditions, in contradiction to the initial assumption. (Free positive charges would migrate from locations of higher to locations of lower potential. Free electrons would rapidly move from locations of lower to locations of higher potential.) All of the charges would continue to move until the potential became equal everywhere in the conductor.

Front 48

If you are given three different capacitors Q, C2, and C3, how many different combinations of capacitance can you produce, using all capacitors in your circuits? 


Back 48

There are eight different combinations that use all three capacitors in the circuit.

Front 49

(a) Why is it dangerous to touch the terminals of a high- voltage capacitor even after the voltage source that charged the battery is disconnected from the capaci tor? (b) What can be done to make the capacitor safe to handle after the voltage source has been removed?


Back 49

(a)The capacitor often remains charged long after the voltage source is disconnected. This residual charge can
be lethal, (b) The capacitor can be safely handled after discharging the plates by short-circuiting the device with a conductor, such as a screwdriver with an insulating handle.

Front 50

The plates of a capacitor are connected to a battery, (a) What happens to the charge on the plates if the connecting wires are removed from the battery? (b) What happens to the charge if the wires are removed from the battery and connected to each other?

Back 50

(a) If the wires are disconnected from the battery and not allowed to touch each other or another object, the charge on the plates is unchanged. (b) If, after being disconnected from the battery, the wires are connected to each other, electrons will rapidly flow from the negatively charged plate to the positively charged plate to leave the capacitor uncharged with both plates neutral.

Front 51

Rank the electric potentials at the four points shown in Figure CQ16.11 from largest to smallest.

Back 51

D>C>B>A


Front 52

If you were asked to design a capacitor in which small size and large capacitance were required, what would be the two most important factors in your design?

Back 52

The primary choice would be the dielectric. You would want to choose a dielectric that has a large dielectric constant and dielectric strength, such as strontium titanate, where k ~ 233. A convenient choice could be thick plastic or Mylar. Secondly, geometry would be a factor. To maximize capacitance, one would want the individual plates as close as possible, since the capacitance is proportional to the inverse of the plate separation—hence the need for a dielectric with a high dielectric strength. Also, one would want to build, instead of a single parallel-plate capacitor, several capacitors in parallel. This could be achieved through “stacking” the plates of the capacitor.

Front 53

Is it always possible to reduce a combination of capacitors to one equivalent capacitor with the rules developed in this chapter? Explain.

Back 53

Not all connections are simple combinations of series sand parallel circuits. This combination cannot be reduced to a simple equivalent by the techniques of combining series and parallel capacitors.

Front 54

Explain why a dielectric increases the maximum operating voltage of a capacitor even though the physical size of the capacitor doesn’t change.

Back 54

The material of the dielectric may be able to withstand a larger electric field than air can with­ stand before breaking down to pass a spark between the capacitor plates.