Posted solutions to Hewitt 9^th/10^th problems for PHYS 101— Prof. Livelybrooks

Chapter 2:

Review Questions:

5/5 What did Galileo discover in his legendary experiment at the Leaning Tower?

Galileo found that, except for variations in air resistance, all objects fall at the same acceleration (change in velocity over time). This refuted thinking attributed to Aristotle that said that heavier (more massive) objects would fall faster. Specifically, Galileo found that objects with different masses, when dropped side-by-side at the same time, would both hit the ground at the same time.

11/11 Why do we say that force is a vector quantity?

Vectors have both a magnitude (strength) and direction. Force has both. Applying a force in a particular direction causes changes in motion (accelerations) only in that direction. The amount of change in motion scales as the magnitude of the force.

18/18 When you stand at rest on a bathroom scale, how does your weight compare with the support force by the scale.

Your weight, which is the force of gravity pulling you towards the center of the Earth, is equal in magnitude to the support force offered by the scale in a direction away from the Earth’s center. The directions of the two forces (weight and support) are opposite.

24/24 Stand next to a wall that travels at 30 km/s relative to the sun. With your feet on the ground you also travel the same 30km/s. Do you keep this speed when your feet leave the ground? What concept supports your answer?

You do keep this speed when you leave the ground. Your inertia helps you keep this speed. The wall’s inertia does the same for it.

Exercises:

4/4 What Aristotelian idea did Galileo demolish with his inclined planes experiments?

Aristotle thought that, in order for an object to remain in (constant) motion, a force was needed. Galileo showed that, when no forces act on an object its motion doesn’t change. He did this using inclined planes, where a ball would speed up rolling down a plane, travel at a constant speed along a horizontal part of the plane, and then slow down in climbing up a ramp. He reasoned that, minus friction, the ball would roll up to its original height on the ramp before stopping. He then reasoned that a ball rolling down a plane and along the level would never reach its starting height and would, therefore, roll forever along the level.

12/12 In tearing a paper towel or plastic bag from a roll, why is a sharp jerk more effective that a slow pull?

Rolls of towels and plastic bags have inertia, which makes them stay in a non-spinning state if they are already still. Jerking sharply on the end of the roll exerts a large and brief force on the roll. Because of the roll’s inertia, it resists spinning, which briefly causes greater tension in the paper/bags, so they tear off. Have you ever noticed that this trick is more difficult to pull off when the towel/bag roll is smaller (more depleted)?

27/27 The rope supports a lantern that weights 50N. Is the tension in the rope less than, equal to, or more than 50N. Defend your answer.

The tension in the rope is 25N, as we saw in lab. Each side of the rope is supporting 1/2 the weight of the lantern.

Chapter 3:

Review Questions:

4/4 Distinguish between instantaneous speed and average speed. Give an example.

Instantaneous speed describes how fast something is moving for a brief instant in time. For example, when we let go of carts and they rolled down a ramp, we used a motion detector to more precisely measure “instantaneous speed” at the bottom of the ramp, and thus calculate Kinetic Energy. When we, instead, timed how long it took for the cart to travel 0.75m at the bottom of the track we estimated, instead, the carts average speed over that distance. It most likely was moving faster (instantaneous speed higher than average speed) than that at the start of the0.75m and more slowly at the end.

9/9 If a car is moving at 90 km/h and it rounds a corner, also at 90 km/h, does it maintain a constant speed? A constant velocity? Defend your answer.

It does maintain a constant speed of 90 km/h. Speed doesn’t depend on direction. It does not maintain a constant velocity. Velocity does depend on direction as well as speed. Since acceleration is the change in velocity over time, the car undergoes an acceleration when rounding a corner. This means a net force was applied to the car to change its direction. The force comes from the road pushing (somewhat) sideways on the car in response to turned wheels.

13/13 When are you most aware of motion in a moving vehicle—when it is moving steadily in a straight line or when it is accelerating? If a car moved with absolutely constant velocity (no bumps at all), would you be aware of motion?

Personally, I am most aware of motion when the car is accelerating. In my home town there used to be this sharply curved bridge over the railroad tracks, and traveling over that bridge with some speed was a great way to be aware of motion. If a car moves at absolutely constant velocity, and you were inside and couldn’t see out, you couldn’t tell it was moving.

19/NA What is the gain in speed per second for a freely falling object?

The acceleration of gravity at the Earth’s surface specifies this: 9.8 m/s/s. In one second speed changes by the amount 9.8 m/s.

21/21 The acceleration of free fall is about 10 m/s/s. Why does the seconds unit appear twice?

The acceleration tells us about change in velocity over time. Velocity tells us about change in position over time. Position is measured in m (meters), velocity in m/s, and acceleration tells us about change in velocity (m/s) per second (m/s/s).

Exercises:

8/10 You are driving north on a highway. Then, without changing speed, you round a curve and drive east. a) Does your velocity change? b) Do you accelerate? Explain.

a) velocity depends on speed and direction, so by changing direction you change your velocity. You go from having some constant speed in the north direction to having no speed in the north direction. Vice versa for the east direction. b) acceleration is a change in velocity (not just speed), so you do accelerate. That’s good, because a force is required to turn a car, so observing an acceleration is consistent with Newton’s second law.

14/17 (a) Can an object be moving when its acceleration is zero? If so, give an example. (b) Can an object be accelerating when its speed is zero? If so, give an example.

a) Yes, if an object is moving with a constant velocity (constant speed and direction), its acceleration (change in velocity over time) is zero. A car moving up I5 towards Portland with cruise control on is moving with a zero acceleration (except when it hits bumps, of course!). b) If an objects speed is zero, then even if it is changing directions, it has zero velocity. If its velocity stays zero, it is not accelerating.

22/XX (N/A) Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its speed reading increase with each second of fall?

If it is freely falling, it is subject only to the force of gravity, which causes it to accelerate at –9.8 m/s/s (with the direction up defined as positive). This causes a change of speed of 9.8 m/s for each second of fall. Starting from zero speed, it would be traveling at 9.8 m/s downwards. After 2 seconds, 19.6 m/s, etc.

23/XX (N/A) Suppose that the freely falling object in the preceding exercise were also equipped with an odometer. Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds?

Distance traveled under constant acceleration is 1/2 a t t. So (starting from zero) after one second the distance fallen (a = g = 9.8 m/s/s) is 4.9 m. After 2 seconds it is 19.6 m, and the difference in positions between 1 and 2 seconds is 19.6 – 4.9 m = 14.7 m. So the distance fallen each second is increasing.

25/28 If air resistance can be neglected, how does the acceleration of a ball that has been tossed straight upwards compare with its acceleration if simply dropped?

They are the same. When tossed upwards, the ball slows down, stops for an instant, and then speeds up traveling downwards. The change in velocity each second for the ball tossed upwards is the same as that for the ball that is dropped.

33/36 If it were not for air resistance, why would it be dangerous to go outdoors on rainy days?

Without air resistance, rain drops would continue to gain velocity as they fall downwards. After falling for 10 seconds their velocity would be 10 x 9.8 m/s, or 98 m/s (about 350 km/hour!). They would hurt when they hit you!

Chapter 4:

Review Questions:

10/10 What relationship does mass have with inertia?

An object’s inertia, it’s resistance to change in motion, is directly related to its mass. An object with twice as much mass has twice the inertia of a smaller object.

12/12 Which is more fundamental, mass or weight? Which varies with location?

Mass is more fundamental. It doesn’t vary with location. A kg of cheese has the same mass on the moon as it does on Earth. A lb of cheese doesn’t have the weight on the moon.

20/20 Is acceleration directly proportional to mass, or is it inversely proportional to mass? Give an example.

For a constant applied net force, an object’s acceleration is inversely proportional to its mass. If one doubles the mass, the acceleration of the object (its change in velocity over time) is halved.

23/23 If the net force acting on a sliding block is somehow tripled, by how much does the acceleration increase?

The acceleration is then tripled. Acceleration is directly proportional to net force when mass is held constant.

24/29 If the mass of a sliding block is tripled while a constant net force is applied, by how much does the acceleration increase?

The acceleration is decreased so that is 1/3 of its original value.

Exercises:

6/3 Is it possible to go around a curve in the absence of a force? Defend your answer.

An object can move in a curve only when a force acts. With no force its path would be a straight line.

11/9 In the orbiting space shuttle you are handed two identical boxes, one filled with sand and the other with feathers. How can you tell which is which without opening the boxes?

Shake the boxes. The box that offers the greater resistance to acceleration is the more massive box, the one containing the sand.

43/52 How does the terminal speed of a parachutist before opening a parachute compare to terminal speed after? Why is there a difference?

There are usually two terminal speeds, one before the parachute opens, which is faster, and one after, which is slower. The difference has mainly to do with the different areas presented to the air in falling. The large area presented by the open chute results in a slower terminal speed, slow enough for a safe landing.

45/54 Why is it that a cat that accidentally falls from the top of a 50-story building hits the ground no faster than if it fell from the 20^th story?

The terminal speed attained by the falling cat is the same whether it falls from 50 stories or 20 stories. Once terminal speed is reached, falling extra distance does not affect the speed. (The low terminal velocities of small creatures enables them to fall without harm from heights that would kill larger creatures.)

Chapter 7:

Review Questions:

5/4 Which requires more work—lifting a 50-kg sack a vertical distance of 2 m or lifting a 25-kg sack a vertical distance of 4 m?

Both require the same work. A force of 50 kg x 9.8 m/s/s is applied over 2m, giving 980 N-m of work to lift the 50-kg sack. A force of 25 kg x 9.8 m/s/s is applied over 4m, giving 980 N-m of work to lift the 25-kg sack twice as high.

8/6 Exactly what is it that a body having energy is capable of doing?

The body is capable of doing work or having work done on it. If it is moving and has kinetic energy, it can run into another object, exert a force over a distance on that object, and do work on that other object. If it has potential energy, work can be done on it to convert its energy into kinetic energy, as when a ball is dropped.

14/10 A moving car has kinetic energy. If it speeds up until it is going four times as fast, how much kinetic energy does it have in comparison?

Its speed will increase by 4. The kinetic energy is proportional to speed x speed, so its kinetic energy will increase by a factor of 16.

22/17 Can a machine multiply input force? Input distance? Input energy?

Yes, yes and no. Machines are intended to multiply input force (e.g., a car jack). They multiply input distance in the process. But input force times input distance is input work, and this can not be multiplied (or you could multiply energy and “create” it in the process).

Exercises:

5/13 You and a flight attendant toss a ball back and forth in an airplane in flight. Does the KE of the ball depend on the speed of the airplane? Explain carefully.

The KE of the tossed ball relative to occupants in the airplane does not depend on the speed of the airplane. The KE of the ball relative to observers on the ground below, however, is a different matter. KE, like velocity, is relative. See the answer to the Check Yourself question 2 in the textbook.

13/19 At what point in its motion is the KE of a pendulum bob a maximum? At what point is its PE a minimum? When its KE is half its maximum value, how much PE does it have?

The KE of a pendulum bob is maximum where it moves fastest, at the lowest point; PE is maximum at the uppermost points; When the pendulum bob swings by the point that marks half its maximum height, it has half its maximum KE, and its PE is half way between its minimum and maximum values. If we define PE = 0 at the bottom of the swing, the place where KE is half its maximum value is also the place where PE is half its maximum value, and KE = PE at this point. (In accordance with energy conservation: total energy = KE + PE).

28/36 If a golf ball and a Ping-Pong ball both move with the same kinetic energy, can you say which has the greater speed? Explain in terms of the definition of KE. Similarly, in a gaseous mixture of massive molecules and light molecules with the same average KE, can you say which have the greater average speed?

If KEs are the same but masses differ, then the ball with smaller mass has the greater speed. That is, 1/2 Mv² = 1/2 mV². Likewise with molecules, where lighter ones move faster on the average than more massive ones. (We will see in Chapter 14 that temperature is a measure of average molecular KE – lighter molecules in a gas move faster than same-temperature heavier molecules.)

34/44 Your friend is confused about ideas discussed in Chapter 4 that seem to contradict ideas discussed in this chapter. For example, in Chapter 4 we learned that the net force is zero for a car traveling along a level road at constant velocity, and in this chapter we learned that work is done in such a case. your friend asks, “How can work be done when the net force equals zero?” What is your explanation?

When we speak of work done, we must understand work done on what, by what. Work is done on the car by an applied force that originates in the engine. The work done by the engine in moving the car is equal to the product of the applied force and the distance moved, not the net force that involves air resistance and other friction forces. When doing work, we think of applied force; when considering acceleration, we think of net force. Actually, the frictional forces of the road and the air are doing negative work on the car. The zero total work explains why the car’s speed doesn’t change.

Chapter 8:

Review Questions:

5/3 What is the relationship between tangential speed and distance from the center of the rotational axis? Give an example.

Tangential speed is directly proportional to the distance from the axis (for a given rotational speed). Move twice as far from the axis and your tangential speed doubles.

12/10 Which is easier to get swinging, a baseball bat held at the end, or one held close to the massive end (choked up)?

Held closer to the massive end means less rotational inertia, which means greater ease in making it rotate.

17/15 How do clockwise and counterclockwise torques compare when a system is balanced?

Balance is achieved when the net torque is zero–when clockwise and counterclockwise torques have the same magnitude

27/24 Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of an automatic washer?

It is an inward force, a centripetal force. Without this force, the clothes would (somehow) go flying out of the washer.

32/28 How can gravity be simulated in an orbiting space station?

A wheel-type design for the station would help. Set the wheel spinning at the proper angular velocity and inhabitants would feel a centrifugal force pushing them towards the outside edge of the wheel. This would simulate the feeling of gravity.

33/NA Why will orbiting space stations that simulate gravity likely be large structures?

If they are small, the change in centrifugal force from near the center to near the outside edge would be noticeable (and unpleasant!). Also, if a large structure is used, it doesn’t have to spin as fast to simulate Earth-like gravity.

Exercises:

3/3 An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If larger wheels, such as those of snow tires, are used, will the speedometer reading be high or low—or no different?

Large diameter tires mean you travel farther with each revolution of the tire. So you'll be moving faster than your speedometer indicates. (A speedometer actually measures the RPM of the wheels and displays this as mi/h or km/h. The conversion from RPM to the mi/h or km/h reading assumes the wheels are a certain size.) Oversize wheels give too low a reading, because they really travel farther per revolution than the speedometer indicates; and undersize wheels give too high a reading because the wheels do not go as far per revolution.

6/NA Unlike a phonograph record that has a constant angular speed, a CD scans information at a constant linear speed (130 cm/s). Does a CD therefore rotate at a constant angular speed, or a varying angular speed?

Unlike a phonograph record, a CD rotates at a variable angular speed so that the linear speed if constant.

NA/4.

14/12 Which will have the greater acceleration rolling down an incline—a bowling ball or a volleyball? Defend your answer.

The bowling ball wins. A solid sphere of any mass and size beats both a solid cylinder and a hollow ball of any mass and size. That's because a solid sphere has less rotational inertia per mass than the other shapes. A solid sphere has the bulk of its mass nearer the rotational axis that extends through its center of mass, whereas a cylinder or hollow ball has more of its mass farther from the axis. The object with the least rotational inertia per mass is the "least lazy" and will win races.

22/26 Explain why a long pole is more beneficial to a tightrope walker if the pole droops.

The long drooping pole lowers the CG of the balanced system – the tightrope walker and the pole. The rotational inertia of the pole contributes to the stability of the system also.

31/34 Why is it dangerous to roll open the top drawers of a fully loaded file cabinet that is not secured to the floor?

It is dangerous to pull open the upper drawers of a fully-loaded file cabinet that is not secured to the floor because the CG of the cabinet can easily be shifted beyond the support base of the cabinet. When this happens, the torque that is produced causes the cabinet to topple over.

34/37 A long track balanced like a seesaw supports a golf ball and a more massive billiard ball with a compressed spring between the two. When the spring is released, the balls move away from each other. Does the track tip clockwise, tip counterclockwise, or remain in balance as the balls roll outward? What principles do you use for your explanation?

The track will remain in equilibrium as the balls roll outward. This is because the CG of the system remains over the fulcrum. For example, suppose the billiard ball has twice the mass of the golf ball. By conservation of momentum, the twice-as-massive ball will roll outward at half the speed of the lighter ball, and at any time be half as far from the starting point as the lighter ball. So there is no CG change in the system of the two balls. We can see also that the torques produced by the weights of the balls multiplied by their relative distances from the fulcrum are equal at all points – because at any time the less massive ball has a correspondingly larger lever arm.

Chapter 9:

Review Questions:

3/3 In what sense does the moon "fall?"

It falls beneath the straight-line path it would follow if there were no gravity.

10/10 How does the thickness of paint sprayed on a surface change when the sprayer is held twice as far away?

The paint is 1/4 as thick, in accord with the inverse-square law.

14/13 Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Downward?

More compressed; less compressed.

15/14 Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that moved upward at constant velocity? Downward at constant velocity?

Oops, almost a trick question: The scale readings would be unchanged. They change only with changes in velocity–acceleration.

Chapter 10:

Review Questions:

3. Why does the vertical component of velocity for a projectile change with time, whereas the horizontal component of velocity doesn't?

The force of gravity on a projectile acts only vertically, hence only the vertical component of a projectile changes with time. There is no component of gravity in the horizontal direction, hence horizontal motion is constant.

12. Why will a projectile that moves horizontally at 8 km/s follow a curve that matches the curvature of the earth?

Because 8 km/s tangential speed is sufficient for the 5-m vertical drop at the end of the first second to match the corresponding 5-m drop of Earth's curvature.

15. Why doesn't the force of gravity change the speed of a satellite in circular orbit?

In circular orbit the force of gravity is everywhere perpendicular to the satellite's path (like the radius of a circle is perpendicular to the circumference). There's simply no component of force along the path to change speed.

25. Why is kinetic energy a constant for a satellite in circular orbit?

In terms of energy, the PE is a constant because of the constant radial distance. In terms of work, there is no component of force along the satellite's path to do work on it. No work means no change in energy.

26. Why is kinetic energy a variable for a satellite in an elliptical orbit?

In terms of energy, PE varies because the radial distance varies. So KE must vary, also. In terms of work, there is a component of force along the satellite's path to do work on it. This work changes its KE.

Chapter 22:

Review Questions:

3/2 What part of an atom is positively charged and what part is negatively charged?

Protons are positively charged, and electrons are negatively charged.

11/11 How is Coulomb's law similar to Newton's law of gravitation? How is it different?

Both are products of fundamental quantities (mass for gravitation and charge for electric) and obey the inverse-square law. The greatest difference is that whereas gravitational forces are only attractive, electrical forces may be repulsive as well as attractive.

12/12 Why are metals good conductors of both heat and electricity?

Electrons in the outer atomic shell of metals are "loose" and easily migrate–conducting heat and/or electric charge.

17/17 What happens to electrons in any charging process?

Electrons are transferred from one place to another.

26/25 How is the magnitude of an electric field defined?

The magnitude of an electric field is the force per unit of charge; E = F/q.

27/26 How is the direction of an electric field defined?

The same direction in which a small positive test charge at rest would be moved.

31/30 How much energy is given to each coulomb of charge that flows through a 1.5-volt battery?

A1.5-volt battery gives 1.5 joules of energy to each coulomb of charge that flows thought it.

Exercises:

2/NA Charge and mass are alike in that both determine the strength of a force between objects. Both appear in an inverse-square law of force. They differ in that charge can be positive or negative while mass is always positive. They differ also in the strength of force they determine.

NA/3

1014 It is not necessary for the charged body to touch the ball of an electroscope. If a negative charge is simply brought near, some electrons in the ball are repelled and driven to the gold leaves, leaving the ball positively charged. Or if a positive charge is brought near the ball, some electrons will be attracted and move up to the ball to make it negative and leave the leaves positively charged. This is charge separation due to induction. (If by small chance you are attempting an answer to this question without having witnessed this, pity, pity, pity! Better that your time is spent studying the physics of familiar things.)

16/20 Electrons are easily dislodged from the outer regions of atoms, but protons are held tightly within the nucleus.

25/35 Planet Earth is negatively charged. If it were positive, the field would point outward.

Chapter 23:

Review Questions:

3/3 Why are electrons, rather than protons, the principal charge carriers in metal wires?

Because electrons in the metal are free to move throughout the atomic lattice. Protons, however, are locked in the atomic lattice.

11/11 If the voltage impressed across a circuit is held constant while the resistance doubles, what change occurs in the current?

Current will be half.

23/23 Why does a wire that carries electric current become hot?

Electrons bump into anchored atoms and transfer kinetic energy to them, making the material hot.

27/27 When you pay your household electric bill at the end of the month, which of the following are you paying for: voltage, current, power, energy?

Energy!

Exercises:

5/7 The net charge in a wire, whether carrying current or not, is normally zero. The number of electrons is ordinarily offset by an equal number of protons in the atomic lattice. Thus current and charge are not the same thing: Many people think that saying a wire carries current is the same thing as saying a wire is charged. But a wire that is charged carries no current at all unless the charge moves in some uniform direction. And a wire that carries a current is typically not electrically charged and won't affect an electroscope. (If the current consists of a beam of electrons in a vacuum, then the beam would be charged. Current is not charge itself: current is the flow of charge.)

14/16 Before it heats up, the filament is cooler and more conducting.

33/38 If the parallel wires are closer than the wing span of birds, a bird could short circuit the wires by contact with its wings, be killed in the process, and possibly interrupt the delivery of power.

35/40 How quickly a lamp glows after an electrical switch is closed does not depend on the drift velocity of the conduction electrons, but depends on the speed at which the electric field propagates through the circuit – about the speed of light.

Chapter 24:

Review Questions:

6. An electric field surrounds an electric charge. What additional field surrounds it when it moves?

A magnetic field.

11/11 Why will dropping an iron magnet on a hard floor make it a weaker magnet?

Some of the domains are jostled out of alignment, which makes the magnet weaker.11.

17/NA Both gravitational and electrical forces act along the direction of the force fields. How does the direction of the magnetic force on a moving charged particle differ?

The direction of the magnetic force is always perpendicular to both the magnetic field lines and the velocity of the charged particle.

NA/17

27/NA What is a likely cause of the earth's magnetic field?

Electric currents, produced by convection or by some other means.

NA/26

Exercises:

5/7 The poles of the magnet attract each other and will cause the magnet to bend, even enough for the poles to touch if the material is flexible enough.

13/15 The needle is not pulled toward the north side of the bowl because the south pole of the magnet is equally attracted southward. The net force on the needle is zero. (The net torque, on the other hand, will be zero only when the needle is aligned with the Earth's magnetic field.)

24/26 Newton's 3rd law again: Yes, the paper clip, as part of the interaction, certainly does exert a force on the magnet – just as much as the magnet pulls on it. The magnet and paper clip pull equally on each other to comprise the single interaction between them.

Chapter 25:

Review Questions:

3/2 What must change in order for electromagnetic induction to occur?

The magnetic field must change to induce electromagnetic induction.

6/5 How does the frequency of induced voltage compare to how frequently a magnet is plunged in and out of a coil of wire?

The same, for the frequency of the alternating voltage induced equals the frequency of the changing magnetic field.

22/20 When the magnetic field changes in a coil of wire, voltage in each loop of the coil is induced. Will voltage be induced in a loop if the source of the magnetic field is the coil itself?

Yes, this is self-induction.

23/21 Why is power transmitted at high voltages over long distances?

The high voltages allow lower currents in the wires, which lose less energy due to heating.

Exercises:

6/8 Part of the Earth's magnetic field is enclosed in the wide loop of wire imbedded in the road. If this enclosed field is somehow changed, then in accord with the law of electromagnetic induction, a pulse of current will be produced in the loop. Such a change is produced when the iron parts of a car pass over it, momentarily increasing the strength of the field. A practical application is triggering automobile traffic lights. (When small ac voltages are used in such loops, small "eddy currents" are induced in metal of any kind that passes over the loop. The magnetic fields so induced are then detected by the circuit.)

10/12 When the ground shakes, inertia of the suspended massive magnet tends to resist such shaking. But the coils of wire are fixed to the Earth and shake relative to the magnet. Motion of the magnet within conducting loops induces a current, which depends on the strength of the Earthquake. So the law of inertia and the law of electromagnetic induction underlie the operation of this device.

18/22 Since all the electric resistance in this case is merely that of the wire itself (no other external load), twice the wire length means twice the resistance. So although twice the number of loops means twice the voltage, twice-as-much resistance results in the same current.