Solutions to Homework Assignment #2 - Santa Barbara...

Ron Ferril SBCC Solutions 2017Summer2 HW #02 2017Jul06A of 15

Solutions to Homework Assignment #2

Correct answers shown in bold type.

These questions and exercises are similar to problems and questions that can appear on exams.

1. Suppose a thin shaft along a line is to be turned using a torque τ about this shaft because a straight wrench is perpendicular to the shaft and a force of magnitude F = 4 N is applied, perpendicular to both the shaft and the wrench, at a distance r = 0.2 m from the shaft. What is the magnitude τ of the torque about this shaft? (Hint: Consider the description of torque given in my Chapter 03.)

a) 20 N m

b) 4.2 N m

c) 0.8 N m

d) 0.2 N m

Since the displacement r and force F are perpendicular, the situation is simple compared to the diagram shown in Chapter 03. For this situation with displacement and force perpendicular, the magnitude of the torque τ is the product of the magnitudes of r and F. That product is 0.2 m x 4 N = 0.8 N m.

2. Suppose the angular momentum L of a spinning body is changing at a rate of ΔL/Δt = 20 kg m2 rad/s2 upward. What is the net torque τ on this body? (Hints: 1 N m = 1 kg m2/s2. The units in this problem are metric units so the constant K' in τ = K' ΔL/Δt is 1. This is one of those problems in which radians disappear so m2 rad/s2 = m2/s2.)

a) Zero.

b) Cannot be determined without knowing either the moment of inertia or the net force.

c) 10 N m upward.

d) 20 N m upward.

3. Suppose the direction of the total torque τ on a closed system is North and the direction of the total angular momentum L of the system is East. What is the direction of the rate of change of angular momentum ΔL/Δt?

a) North


b) East

c) Northeast

d) Cannot be determined without knowing the magnitudes of the torque and angular momentum.

τ = K' ΔL/Δt. Thus the direction of the torque is the direction of ΔL/Δt.

4. Suppose the total torque τ on a closed system is zero. If the moment of inertia of the system about a point is I = 20 kg m2 and is constant, then what is the rate ΔL/Δt at which the angular momentum changes?

a) Zero.

b) 20 kg m2 rad/s2.

c) Cannot be determined without knowing the angular velocities.

d) Cannot be determined without knowing the angular accelerations.

τ = K' ΔL/Δt and the torque is zero. Thus the (total) angular momentum does not change. Notice that the value of the moment of inertia was not really needed for this problem.

5. Suppose a car of mass m = 8000 kg is traveling at constant speed on a circular track and the centripetal force FR on the car is 2000 N toward the center of the circle. Passengers inside the car experience an inertial force which is the centrifugal force. What is this centrifugal force FC?

a) 2000 N toward the center of the circle.

b) 2000 N away from the center of the circle.

c) 8000 N toward the center of the circle.

d) 8000 N away from the center of the circle.

FC = -FR. The centrifugal force and the centripetal force are in opposite directions. We

did not need to know the value of the mass.

6. Suppose a body has a mass m = 10 kg. What is the weight of the body (including the direction since weight is a force)?

a) 10 N downward

b) 10 N upward.

c) 98 N downward.

d) 98 N upward.

Weight of a body is mg = 10 kg x 9.8 m/s2 downward = 98 N downward.


7. Two tiny bodies are separated by a distance r. What happens to the magnitude FG of the gravitational force FG of one body on the other if the mass M1 or M2 of either body is doubled?

a) The magnitude of the gravitational force quadruples.

b) The magnitude of the gravitational force doubles.

c) The magnitude of the gravitational force becomes half of what it was.

d) The magnitude of the gravitational force becomes one quarter of what it was.

The magnitude FG of the gravitational force FG is FG = G M1 M2 / r2. Thus, doubling the mass of either body doubles the magnitude of the force.

8. Two tiny bodies are separated by a distance r. What happens to the magnitude of the gravitational force of one body on the other if the distance r between the bodies doubles?

a) The magnitude of the gravitational force quadruples.

b) The magnitude of the gravitational force doubles.

c) The magnitude of the gravitational force becomes half of what it was.

d) The magnitude of the gravitational force becomes one quarter of what it was.

The magnitude FG of the gravitational force FG is FG = G M1 M2 / r2. Thus, doubling the distance between the tiny bodies causes the magnitude of the force to change by a factor ofone quarter.

9. Suppose an astronaut explores areas around a planet which is a uniform solid sphere. Where is the gravitational field of the planet zero?

a) At the surface of the planet.

b) At a distance of at least a thousand miles from the surface.

c) In the center of the planet.

d) Nowhere.

The formula FG = G M1 M2 / r2 holds everywhere outside the planet. The formula has the gravitational force as nonzero everywhere outside the planet. My Chapter 03 mentions the situation inside the planet. The branch of mathematics called “calculus” can be used to show that the gravitational force is zero at the center of a uniform spherical planet.

10. Consider two balls that are released to fall at the same time from the same height above level ground and without any vertical component of initial velocity, but one of the balls, only


one, has a nonzero horizontal component of initial velocity. Thus, one ball falls straight down but the other falls in a curved path. Which ball will hit the ground first?

a) The ball that falls straight down with zero horizontal component of initial velocity because the path of that ball was shorter.

b) The ball that has nonzero horizontal component of initial velocity since the horizontal component increases the magnitude of the initial velocity.

c) Both balls will strike the ground at the same time since the horizontal component does not affect the result.

d) We cannot know which will hit first because we don't know the direction of the horizontal component.

This was actually demonstrated in class. My Chapter 03 mentions that the vertical andhorizontal motions are independent.

11.NASA considered plans for lowering the magnitude of the escape velocity for spacecraft leaving the Earth by launching rocket spacecraft from high altitudes rather than from the surfaceof the Earth. One plan involved assembling spacecraft in high orbit around the Earth. Spacecraftlaunched from the surface of the Earth are launched from one Earth radius from the center of the Earth. If a spacecraft were launched from four times that radius from the center of the Earth,what would the magnitude of the new escape velocity be?

a) The same as at the surface of the Earth.

b) Half what it is from the surface of the Earth.

c) A quarter of what it is from the surface of the Earth.

d) Twice what it is from the surface of the Earth.

The formula vE = √[2GM/r] given in Chapter 03 shows the magnitude of the escape velocity is inversely proportional to the square root of the distance r from the center of the Earth. Thus, quadrupling this distance causes the magnitude of the escape velocity to become half of what it was.

12. Suppose two satellites orbit the Earth with the second satellite at a radius from the centerof the Earth that is nine times the radius from the center for the first satellite. What would be theratio of the magnitudes the tangential velocities for the two satellites?

a) The first satellite (the one closer to Earth) would have nine times the magnitude of tangential velocity as the second satellite (the one further from Earth).

b) The first satellite (the one closer to Earth) would have three times the magnitude of tangential velocity as the second satellite (the one further from Earth).


c) The first satellite (the one closer to Earth) would have one third the magnitude of tangential velocity as the second satellite (the one further from Earth).

d) The first satellite (the one closer to Earth) would have one ninth the magnitude of tangential velocity as the second satellite (the one further from Earth).

The formula vT = √[GM/r] given in Chapter 03 shows that the magnitude of the tangential velocity for the orbit is inversely proportional to the square root of the distance r from center of the Earth. Thus, the satellite that is farther from the Darth has a magnitude of tangential velocity that is one third of that of the satellite closer to Earth.

13. 1.204 x 1024 atoms is approximately how many moles of atoms?

a) 0.5 mole

b) 1 mole

c) 2 moles

d) 3 moles

One mole is approximately 6.022 x 1023. Thus, two moles of atoms or molecules is approximately 1.204 x 1024 atoms. [1.204 x 1024 atoms] x [1 mole / (6.022 x 1023 atoms)] is approximately 2 moles.

14. Approximately how many moles of carbon 12 are in 36 grams of carbon 12?

a) 1 mole

b) 2 moles

c) 3 moles

d) 4 moles

The “mole” has been defined (although there is a current effort to change this definition) as the number of atoms of carbon 12 that has a mass of exactly 12 grams. Thus, 36 grams is 3 moles.

15. Lithium (the common isotope of Lithium) has an atomic number of 3, and atomic weightor atomic mass of approximately 7 amu. Approximately how much mass is in a mole of Lithium?

a) 3 grams

b) 4 grams

c) 7 grams


d) 10 grams

16. The element magnesium (Mg) is in the second column of the Periodic Table of Elements. How many electrons does a magnesium atom tend to lose easily in chemical reactions?

a) None. It resists losing any electrons.

b) One.

c) Two.

d) Three.

17. Consider an incompressible fluid flowing with streamline flow (on heat generated and no turbulence) in a pipe with varying cross-sectional area. Assume there are no chemical reactions. If the fluid is flowing at a speed of 10 m/s at a point where the cross-sectional area is 0.4 m2, but at another point downstream the cross-sectional area is constricted to 0.1 m2. What is the new flow speed at this constriction?

a) 2.5 m/s

b) 5 m/s

c) 20 m/s

d) 40 m/s

v2 / v1 = A1 / A2 = ¼ and v2 = (10 m/s) / (¼) = 40 m/s.

18. If a particle and its antiparticle annihilate each other so that only gamma rays remain, what happens to the linear and angular momenta of the two particles? In other words, what carries the linear momentum and angular momentum after annihilation?

a) The linear and angular momenta are destroyed in the annihilation.

b) The linear and angular momenta are both carried by the gamma rays.

c) The linear and angular momenta are converted to heat.

d) The linear and angular momenta were zero because the annihilation would not happen unless the momenta are both zero.

19. Which of the following is not a difference between dark matter and dark energy?

a) Dark matter attracts matter by gravitational attraction and dark energy accelerates parts of the universe away from each other.

b) Dark matter is believed to be matter because it has a gravitational attraction but dark energy is suspected of being due to a “cosmological constant” or “vacuum energy.”


c) Dark matter can accelerate matter but dark energy causes the space or spacetime (containingthe matter) to expand.

d) Dark matter is more black than dark energy.

20. If the mass density of a body is ρ then what is the weight density?

a) ρ2

b) 2 ρ

c) ρg

d) ρ

21. A spring that obeys Hooke's Law is stretched 0.1 m from its relaxed position when a force with magnitude 2.0 newtons is applied. How far from its relaxed position will it extend if a force with magnitude 3.0 newtons is applied? (Hint: Use Hooke's Law twice, once to find the value of the constant k in Hooke's Law and then the second time to find the elongation of the spring due to the 3.0 N force. )

a) 0.1 m

b) 0.15 m

c) 0.2 m

d) 0.3 m

Hooke's Law has F=kΔx.

22. Suppose a spring is stretched by 0.2 meter and held at this elongation by a force of 2 newtons. What is the Hooke's Law constant (spring constant) k and the potential energy EP gained by the spring by this elongation?

a) k =10 N/m and EP = 0.2 J

b) k =10 N/m and EP = 0.4 J

c) k =20 N/m and EP = 0.2 J

d) k =20 N/m and EP = 0.4 J

F=kΔx and the change in elastic potential energy is EP=½ k(Δx)2.

23. Consider two situations: one with you standing on two feet and one with you lying downon your back. To avoid confusion, it must be understood that the area of your body touching theground is greater when you lie down than when you are standing. Which position, if any, causesthe pressure you apply to the ground to be greater?


a) Lying down.

b) Standing on two feet.

c) Both positions provide the same pressure because the weight is the same for both.

d) Which is greater cannot be determined because we don't know how you are leaning when you stand or which side is on the ground when you are lying on the ground.

P=F/A

24. A small device that measures pressure in a liquid by detecting the total force on a circular plate on the device. It is immersed into a liquid and is kept at a constant depth. The device is turned so the plate faces downward and then turned so it face upward. Which of those two orientations, if any, with the plate facing upward and the plate facing downward, should result in the higher pressure reading?

a) The pressure will be greater when the plate faces upward.

b) The pressure will be greater when the plate faces downward.

c) The pressure will be the same regardless of orientation.

d) There is no pressure on the plate but only in the liquid.

25. Suppose the pressure at a certain depth D in a liquid is P. What will the pressure be at depth D if the volume of the liquid is doubled?

a) P/2

b) P

c) 2P

d) 4P

As mentioned in class, the pressure P=ρgD. The volume does not matter. (Some students confused this problem with the case of a gas in a closed container and try to use Boyle's Law.)

26. A spherical ball made of a material with a certain weight density and is placed in a liquidwith twice the weight density as the ball. Which of the following is correct? (Hint: drawing a diagram of each of the choices given here may help. There is a useful principle for this problem.Consider which principle applies.)

a) The ball will sink.

b) The ball will float with only a quarter of its volume submerged.

c) The ball will float with only half its volume submerged.


d) The ball will float with three quarters of its volume submerged.

The ball will be at rest when the sum of the forces—gravitational and buoyant force—is zero. Archimedes' Principle tells us the buoyant force on the ball has magnitude equal to the weight of fluid displaced. Since the density of the liquid is twice that of the ball, the ball displaces half its own volume for the forces to sum to zero.

27. A thick metal plate with faces of area 1 m2 is placed horizontally in a liquid. The pressure in the liquid at the top surface of the plate is 2 Pa and the pressure at the bottom surface is 3 Pa. What is the buoyant force on the thick metal plate? (1 Pa = 1 N/m2.)

a) [2 Pa + 3 Pa] x 1 m2 = 5 N

b) [3 Pa – 2 Pa] x 1 m2 = 1 N

c) [2 Pa x 3 Pa] x 1 m2 = 6 N

d) Zero

The buoyant force on a body is the difference of the forces on the bottom and on the top. The forces are the products of pressures and area.

28. Water has a mass density of 1000 kg/m3. Neglecting effects of the atmospheric pressure on the top of the water, what is the pressure at depth 10 m below the surface of the water? (1 Pa = 1 N/m2.)

a) 9.8 x 104 Pa

b) 10000 Pa

c) 1000 Pa

d) 9.8 x 103 Pa

P = PA + ρgD but PA is zero since we are neglecting it. Thus, P = ρgD.

29. The pressure in a liquid changes by 2 pascals at depth 1 meter, what is the change in pressure at depth 2 meters? (Warning: I am asking about pressure change not about pressure alone. I am not asking you to calculate the pressure at depth of 2 meters but the change in pressure at that depth.)

a) 1 pascal

b) 2 pascals

c) 4 pascals

d) 8 pascals

Pascal's Principle tells us the pressure change is the same throughout the fluid.


30. Consider the hydraulic lift mentioned in Chapter 04. Suppose the masses of the pistons are negligible. If a force of F1 = 1 newton downward is exerted on the little piston, this little piston has an area of A1 = 0.01 m2, and the larger piston has an area of A12 = 1 m2, then what is the magnitude of force F2 exerted by the liquid on the wide piston?

a) 1 newton

b) 10 newtons

c) 100 newtons

d) 1000 newtons

Since Pascal's Principle tells us the pressure change is the same at all points in the fluid, the pressure will be the same on each piston. The piston with larger area will have more magnitude of force on it. F2 = F1A2 / A1.

31. In which of the following is surface tension not significantly involved?

a) A slender pin is made of a metal with a higher mass density than the mass density of water, but the pin rests on the surface of the water rather than sinking.

b) Air blown into water causes bubbles to form and be blown off the water into the air.

c) Water rises by capillarity in a narrow tube.

d) Water is in streamline flow through a wide pipe.

Our textbook and Chapter 04 tell how surface tension is involved with the pin on the surface of a liquid, bubbles and capillary action. Streamline flow is not directly relatedto surface tension.

32. A common physics demonstration involves blowing air from an opening below on a ballso the ball rises. The ball remains over the opening as the air blows on it from the opening below. The ball may move sideways back and forth, but does not leave the stream of air and continues to return to near the center of the stream. There must be some force or pressure on thesides that makes the ball return to near the center of the stream of air. What principle or law tellswhat this force or pressure difference is?

a) Hooke's Law

b) Archimedes' Principle

c) Pascal's Principle

d) Bernoulli's Principle


33. Consider the atoms or molecules of which a body is composed. If the average translational kinetic energy of the atoms or molecules doubles, what happens to the absolute temperature of the body?

a) The absolute temperature remains the same.

b) The absolute temperature doubles.

c) The absolute temperature quadruples.

d) The absolute temperature becomes a quarter of what it was.

34. Convert from Celsius to Kelvin. What is 7 Celsius in Kelvin?

a) 7 Kelvin

b) 273.15 Kelvin

c) 266.15 Kelvin

d) 280.15 Kelvin

35. Which of the following statements about heat is false?

a) Heat is energy.

b) Heat is a macroscopic quantity, not a microscopic quantity.

c) Heat is a relative quantity.

d) The total amount of heat in a body can be measured and is called the “heat capacity.”

36. Suppose 20 J of heat flows into a closed system and no other heat flows into or out of the system, but the energy of the system remains constant. Which of the following must be true?

a) The system did 20 J of work.

b) The system has a high specific heat capacity.

c) The system has a low specific heat capacity.

d) The system is cooler after the heat flow into it.

The Work-Energy Theorem for the macroscopic view has ΔE = ΔW + ΔQ.

37. Suppose zero work is done on a body of mass 5 kg and specific heat capacity 0.2 J/[kg K], but the temperature still rises by 2 K. How much heat flowed into the body to cause this temperature change?

a) Zero

b) 1 J


c) 2 J

d) 4 J

ΔQ = mcΔT.

38. The Sun, Earth and Moon are all losing heat by transferring the heat out into space. The heat is flowing away. Which of the three ways, in which heat flow can automatically happen, is at work here?

a) Conduction

b) Convection

c) Radiation

d) Destruction

39. A man lays his hand on a woman's shoulder and she feels the heat of his hand, which of the three ways heat transfer automatically happens is at work here?

a) Conduction

b) Convection

c) Radiation

d) Destruction

40. Old multi-story buildings had a fireplace on the lowest floor that could heat the entire interior of the building. By which of the three ways heat transfer automatically causes the heat to reach the upper floors?

a) Conduction

b) Convection

c) Radiation

d) Destruction

41. In Chapter 05, I described the kitchen refrigerator as a type of heat pump. Why do I fail to cool my house by leaving the refrigerator door open? (Hint: Consider how a heat pump works and what it does with the heat.)

a) A house is too large for a single refrigerator to cool. Even if the refrigerator were 100% efficient, over 100 refrigerators would be needed to cool a three-bedroom house.

b) The refrigerator merely pumps heat from inside to the outside of the refrigerator and, thus, is not removing any heat from the house.


c) The refrigerator fails to pump heat if the door is left open.

d) The refrigerator was a cheap one and should be returned so I can get my money back.

42. Is a mirror a good emitter of radiation that emits radiation at a high rate? Why?

a) Yes it is a good emitter because it is shiny and being shiny is an indication that much radiation is emitted from its surface.

b) No it is not a good emitter because a good emitter must also be a good absorber and a mirror reflects well rather than being a good absorber.

c) Yes it is a good emitter because all substances are good emitters regardless of their reflectivity.

d) No it is not a good emitter because it breaks too easily.

43. Which of the following is not a method of cooling?

a) Converting heat energy to chemical potential energy.

b) Transferring heat by use of a heat pump.

c) Transferring heat away from a body by letting a liquid evaporate from the body.

d) Destroying heat by use of cold rays.

44. Suppose a substance is changing from the liquid phase to the gas phase by boiling. Whathappens to the temperature while the phase change is happening?

a) The temperature remains constant.

b) The temperature rises.

c) The temperature lowers.

d) The temperature changes form the Celsius scale to the Kelvin scale.

45. Suppose a liquid is cooled by evaporation and the air above the liquid is very still (not blowing). While the temperature of the liquid starts lowering, what happens to the temperature of the air at the surface of the liquid?

a) It remains constant.

b) It also lowers.

c) It rises slightly.

d) We cannot know because changes in the temperature of the air depend on the chemical composition of the liquid.

The energy released by the cooling liquid is transferred to the vapor.


46. Which of the following happens in the process of sublimation?

a) Parts of a solid melts and changes to a liquid.

b) Parts of a solid melts and then evaporates to become a gas.

c) Parts of a solid change to the gas phase without melting.

d) Parts of a solid change to another type of solid.

47. Which of the following is not the heat of fusion?

a) The energy per mass required to melt some solid to the liquid phase.

b) The energy per mass released when a liquid freezes.

c) The energy per mass needed to raise the temperature of a solid from one temperature to the melting temperature.

d) None of these are the heat of fusion.

48. Which of the following is not directly involved in the statements of the Second Law of Thermodynamics given in this class?

a) Heat flow from a region at one temperature to a region at another temperature.

b) Changes in entropy.

c) The changes in linear momentum during a phase change.

d) None of these are directly involved in the statements of the Second Law of Thermodynamics given in this class or in the Chapter 05.

49. If the temperature of a body is maintained at absolute temperature 300K while 30 J of heat flows into the body, what is the change in entropy of the body?

a) 0.1 J/K

b) 30 J

c) 300 K

d) 9000 J K

ΔS = ΔQ/T

50. Suppose two closed systems can interact with each other, but the systems are otherwise isolated. If the first system causes the entropy of the second system to decrease, then what happens to the first system?

a) The energy of the first system increases by the amount of heat absorbed form the second system.


b) The temperature of the first system decreases to match the rise in temperature of the second system.

c) The entropy of the first system increases at least as much as the entropy of the second system decreased so the combined entropy of the two systems does not decrease.

d) The energy, temperature and entropy of the first system all decrease.

51. If heat flows into a heat engine at a rate of 50 W and the engine performs work at a rate of 5 W, then what is the efficiency of the heat engine?

a) 5%

b) 10%

c) 15%

d) 50%

e = ΔW / ΔQ = power output / power input

52. If a Carnot engine operates between regions of temperatures 600 K and 300 K, then what is the maximum efficiency of the engine?

a) 5%

b) 10%

c) 15%

d) 50%

Maximum e = 1 – Tlow / Thigh.

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