Phy 121 homework, continued. (Reading refers to College Physics by OpenStax.)

Sec. 5: Inclines. Uniform Circular Motion. Reading: Finish sections 4.5 & 5.1. Also, sections 6.2 – 6.4. A. 1. (2 points) What force furnishes the centripetal force in each of the following cases? a. The earth circling the sun. b. A car turning a corner on a level road. 2. (8) A 3.00 kg object hung on a string follows a horizontal circle of radius .839 m. It takes 2.20 seconds to go around the circle once. If the string makes

an angle of 35.0 with the vertical, what is the tension in the string? ans: 35.8 N

B. 1. (1 point) As the board is tipped more and more steeply, the force of static friction pulling uphill on the stationary block ______. (increases? decreases? stays the same?) (The actual force, not the maximum it could reach without the block sliding.) 2. (2 points) Why does an astronaut in a spaceship orbiting the earth experience a feeling of weightlessness?

3. (7) A coin is placed 30.0 cm from the center of a record player turntable. The coin slips when its

speed reaches 50.0 cm/s. What is the coefficient of static friction between the coin and turntable? ans: .0850 C. 1. (2 points) A box is sliding up a frictionless incline. The push which got it moving is no longer acting. Draw a free body diagram of the box, labeling each force with its name. Stop there; don’t do components. 2. (8) The picture shows an incline that has friction. How large is the force P which pulls uphill on the box if it moves up the incline at a constant

speed? Mass of box = 5.00 kg, k = .40 ans: 41.5 N D. A 70 kg box is sitting on a ramp which is 35° from the horizontal. You are pushing this box with a force of 150 N parallel to the ramp, which is just enough to keep it from sliding downhill. How large is the force of friction acting on the box? ans: 243 N E. 1. A car is going around a circular track at a constant speed. When in the position shown, what is the direction of its acceleration? (North, South, East, West, or no acceleration?)

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2. (8) A battery powered 700 g toy car on a 25° incline circles a nail it is tied to. If the car has a certain speed, the weight and normal force are the only forces in the xy plane when the car is at the very top of the circle. There is no tension in the string. (a) What is this speed? (b) How large is the normal force? ans: 1.58 m/s, 6.22 N Sec. 6: Work, Energy and Power. Read: In Ch. 7, sections 7.1 – 7.3, 7.5 & 7.7 Quiz A. 1. (3 points) a. A box is released at the top of a 20° incline 2.0 m long and slides to the bottom. Is the work done by friction positive, negative, or zero? b. Is the work done by the normal force positive, negative or zero? c. Another box is released at the top of a 30° incline 2.0 m long, and slides to the bottom. The friction force is the same as on the first box. Is the work done by friction more, less or the same as on the first box? 2. (7) a. Assuming 100% efficiency, what minimum horsepower motor would be needed to lift a 200 kg load of bricks to the top of a 30.0 m high building in half a minute? b. Assuming 100% efficiency, what minimum horsepower engine would be needed to accelerate a 1400 kg car from rest to 26.8 m/s (60 mi/hr) in 6.00 s? ans: 2.62 hp, 112 hp B. 1. (2 points) When a particle revolves around a circle, a force acts on it directed toward the center of the circle. Why is it that this force does no work on the particle? 2. (8) A 20.0 gram bead slides along a wire in a vertical plane, as shown. It has a speed of .800 m/s as it passes point A, and then coasts to a stop at point E. If the distance along the wire from A to E is 6.00 m, how large is the average friction force? ans: .0272 N C. 1. (2 points) Work equals F cosθ s. For the work done by the 250 N in the next question, what is θ? 2. (8) A 1200 kg car with 540,000 J of kinetic energy runs out of gas at point A. It then coasts up a hill as shown, while experiencing a drag force of 250 N. What is the distance, s, which it coasts before coming to rest at point B? ans: 505 m

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D. A 15 kg block is dragged over a horizontal surface by a 70 N force acting at an angle of 20 above the horizontal. The block is displaced 5.0 m and the coefficient of kinetic friction is 0.3. Find (a) the work done by the 70 N force, and (b) the work done by the force of friction. ans. 329 J, -185 J E. A slide is attached to a swimming pool as shown. A 22 kg child starts at rest at point A, then is launched horizontally from point B.

a. If 35 J is lost to friction along the slide, what is her speed at B? b. How much time is she in the air? c. How far from the point directly under point B does she hit the water?

ans: 6.10 m/s, .484 s, 2.96 m Sec. 7: Newton's Third Law and Momentum/ Rotational Kinematics. Read: Ch. 4, p. 140 – 141; Ch. 6, sec. 6.1; Ch 8, sec. 8.1, 8.5, 8.6 and just skim sec. 8.3 & 8.4; Ch 10, sec. 10.1 & 10.2.

A. 1. (3) State whether each of the following is an example of or a. The label on a motor says “3500 RPM.” b. At a particular moment, a playground swing is 30° from the vertical. c. The earth spins at a rate of one revolution per day. 2. (7) A wheel has an angular acceleration of 1.70 rad/s

2. It starts from rest. How fast is it turning (in

radians per second) after it has completed 20 revolutions? ans: 20.7 rad/s B. 1. (3 points) An old style record player turntable rotates at a constant 45 rev/min. a. What is its angular speed in radians per second? b. What is its angular acceleration? 2. (7) A wheel rotating at 3.00 rev/s turns 45 revolutions while slowing to a stop. Assuming uniform acceleration, (a) How long did it take to stop? (b) What was its angular acceleration? ans: 30.0 s, –.100 rev/s

2

C. 1. (2 points) Newton's third law states that every force has a reaction force which is equal in magnitude and opposite in direction. If this is the case, how can the net force on an object ever add up to anything other than zero? 2. (8) An unstable nucleus of mass 17.0 x 10

-27 kg, initially at rest at the origin, disintegrates into three

particles. One of the particles, mass = 5.00 x 10-27

kg, moves up the y axis with a velocity of 6.00 x 106

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m/s. Another, of mass 8.40 x 10

-27 kg, moves along the positive x axis at 4.00 x 10

6 m/s. Find the x any

y components of the third particle's velocity. ans: –9.33 x 10

6 m/s, – 8.33 x 10

6 m/s

D. A 65.0 kg person on skates, initially going forward at 2.50 m/s, throws a .710 kg snowball forward at 30.0 m/s. (All velocities in this problem are relative to the ground.) A60.0 kg person on skates, initially at rest, catches the snowball. Find the velocity of the thrower and the velocity of the catcher after this exchange. Ignore friction between the skates and ice. ans.: 2.20 m/s, .351 m/s E. 1. (2 points) A ball is dropped. a) What force is exerted on it while it is falling? b) Identify the reaction force. (Neglect air resistance.) 2. (8) A 90 kg fullback running east with a speed of 5.00 m/s is tackled by a 95 kg opponent running north with a speed of 3.00 m/s. They cling to each other after colliding. Calculate the speed and direction of the players just after the tackle.

ans: 2.88 m/s at 32.3 north of east Sec. 8: Rotational and Linear Quantities. Rotational Kinetic Energy. Read: Ch. 10 sec. 10.1, 10.2 & 10.4 A. 1. (2 points) A wheel is rotating about a fixed axis. Do all points on the wheel have the same (a) angular velocity? (b) linear velocity? 2. (8) A pulley with a smaller part and a larger part drives two belts as shown. Both parts are solidly connected; the pulley is a single rigid object. If the belt on the smaller part has a speed of 45 cm/s, find a. the angular speed of the pulley, in rev/min, b. the speed of the belt on the larger part, in cm/s. ans: 85.9 rpm, 99 cm/s B. 1. (2 pts) Two cars are going around two different circular paths at the same angular velocity. The speed of one car is 60 km/hr on a track of radius R. What is the speed of the other car if its track has a radius of .5R? ans: 30 km/hr 2. (8) The four particles shown are connected by rigid rods of negligible mass. They rotate about the z axis, which passes through the page at the center of the rectangle, with an angular speed of 6.00 rad/s. Find the system's a. moment of inertia about the z axis, and

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b. rotational kinetic energy.

ans: 143 kgm2, 2.57 kJ

C. 1. a. (1.5 points) A .30 m radius wheel spins at 5.0 revolutions per second. Someone calculates the speed of the edge of this wheel as v = r ω = (.30)(5.0) = 1.5 m/s. Explain why this is incorrect. b. (1.5 points) A point on the edge of a .30 m radius wheel gains speed at a rate of .40 m/s

2. Someone

calculates the angular acceleration of this wheel as a = r α = (.30)(.40) = .12 rad/s2. Explain why this is

incorrect. 2. (7) A string is wrapped several times around the axle of a wheel, as shown. The wheel is a 600 g disk with a 20.0 cm radius. The axle's mass is negligible. If released from rest, what is its angular velocity after unwinding down 15.0 cm? Friction is very small. Assume the final energy is all rotational kinetic energy. (The center of mass moves very slowly.) ans: 12.1 rad/s D. 1. (2 points) A car is moving on a circular track. a. If there is a way it can have a centripetal acceleration but no tangential acceleration, what is it? b. If there is a way it can have a tangential acceleration but no centripetal acceleration, what is it? 2. (8) A cord is wound on the rim of a 30.0 cm radius wheel. A weight hung from the end of the cord accelerates downward at .800 m/s

2. (a) What is the wheel’s angular acceleration? (b) Through how

many revolutions does the wheel turn as the weight falls 2.00 m from rest? ans: 2.67 rad/s

2, 1.06 rev

E. 1. (1 point) The angular velocity of gear A is _______ (more than? less than? the same as?) the angular velocity of gear B.

2. (2 points) The same object is rotated about two different axes, as shown. Compare the moment of inertia. (More in A, more in B, or the same.) Explain how you know.

3. (7) A quarter you dropped while using a vending machine rolls away. It has a diameter of 2.40 cm, starts out with an angular speed of 18.0 rad/s, and slows with an angular acceleration of magnitude 1.90 rad/s

2. If it rolls in a straight line without slipping, what is the distance across the floor from where it

starts to where it comes to rest? ans: 1.02 m Sec. 9: Torque and Rotational Dynamics. Read: Ch. 9, sec. 9.2; Ch. 10 sec. 10.3. A. 1. (3 points) Consider pulling a nail with a claw hammer, whose weight is small enough to ignore, at the moment the nail begins to move.

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(a) Aside from the force at its pivot point, there are two forces on the hammer. Identify them.

(What two objects pull on the hammer?)

(b) Which of these two forces is larger?

(c) Which of these two forces produces a larger torque?

2. (7) The uniform metal plate is in a vertical plane, and weighs 50

N. Rods A, B and C are being pulled; D is being pushed. FA = 75

N, FB = 150 N, FC = 150 N and FD = 200 N. Find the net torque

about point P.

ans. +105 Nm

B. A 25.0 cm radius wheel has a 10.0 cm radius axle. A string

wound around the wheel pulls with 90.0 N and a string around the

axle pulls with 120 N. The box which makes the 90.0 N force

accelerates downward at a = 5.10 m/s2. What is the system’s

moment of inertia?

ans: .515 kgm2

C. 1. (1 point) If you see an object rotating, is there necessarily a net torque acting on it?

2. (9) A log is floating in a pond. If you pull on a branch as shown, the log begins to

rotate, taking 4.50 s to turn 90°. What are the log's (a) angular acceleration, and (b)

its moment of inertia?

ans: .155 rad/s2, 63.8 kg m

2

D. A 150 g stick 1.1 m long is pivoted at one end. It is held horizontally and released. Find (a) its

angular acceleration in radians per second2 just after its release, and (b) the acceleration of its center of

mass, in meters per second2, at this time.

ans: 13.4 rad/s2, 7.37 m/s

2

E. A wheel 1.00 m in diameter rotates on a fixed, frictionless, axle. Its moment of inertia about this

axis is 5.00 kgm2. A constant tension of 20.0 N is maintained on a rope wrapped around the rim of the

wheel. If the wheel starts from rest at t = 0, find

a. the wheel's angular acceleration, (ans: 2.00 rad/s2)

b. the wheel's angular speed at t = 3.00 s, (ans: 6.00 rad/s)

c. the wheel's kinetic energy at t = 3.00 s, (ans: 90.0 J)

d. the length of rope unwound in the first 3.00 s (ans: 4.50 m)

Sec. 10: Static Equilibrium.

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Read: Ch. 9, sections 9.1, 9.2, 9,4 & 9.6. A. The uniform boom 3.0 m long weighs 80 N and supports a 200 N weight. Find the tension in the tie rope. (ans. 257 N) B. The uniform boom 3.0 m long weighs 80 N, supports a 200 N weight, and the tension in the tie rope is 257 N. Find the horizontal and vertical components of the force exerted by the pin at the lower end. (ans. 197 N, 115 N) C. A bridge of length 50.0 m and weight 784 kN is supported only at its ends, points A and B. A truck weighing 294 kN is located 15.0 m from end A. What are the forces on the bridge at each point of support? ans: FA = 598 kN, FB = 480 kN D. The figure shows a claw hammer pulling a nail out of a board. The force on the hammer from the nail is vertical and the force from the hand is horizontal. The hammer weighs 4.0 N. What are (a) the force from the nail, (b) the x component of the force from the board at the point of contact and (c) the y component of the force at the point of contact. ans: 900 N, – 150 N, 904 N

E. A painter has a ladder against a house at a dangerously steep angle. If he leans back too far, the ladder will tip over. The ladder weighs 135 N, the painter weighs 750 N and the bucket of paint weighs 35.0 N. What is the maximum value of x for which it doesn’t tip? ans: 5.86 cm F. From now on, each assignment will include review questions. You are just as likely to be given the review quiz as any of the others.

A stunt man who can run at 4.50 m/s is to run off the level roof of a building and land in a nearby swimming pool. To avoid landing on the cement in between, he needs to come down at least 5.00 m from the base of the building. At least how high should the building be? ans: 6.05 m Sec. 11: Fluids. The Ideal Gas Law.

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Read: Ch. 11, sec. 11.2, 11.3, 11.5 – 11.7; Ch. 12, sec. 12.1 – 12.3; Ch. 13, Temp. scales on p. 470 & sec. 13.3 A. The water supply enters a building at point A, through a pipe with a 6.30 cm

2 cross sectional area.

All of the water then flows past point B, 6.5 m higher than point A, through a 3.00 cm2 pipe. The

pressure at A is 3.1 x 105 Pa and the pressure at B is 2.3 x 10

5 Pa. Find the speed of flow at each point.

ans: vA = 3.09 m/s, vB = 6.49 m/s B. 1. (2 points) A person in a boat floating in a small pond throws a heavy anchor overboard. Does the level of the pond rise, fall, or remain the same? 2. (8) A small girl at a fair has a balloon filled with .0058 cubic meters of helium. The total mass of balloon plus helium is 3.15 grams. If she lets go of it, what will its upward acceleration be? ans: 13.5 m/s

2

C. 1. (1 point) Water freezes at ________ kelvins. Water boils at ________ kelvins. 2. (1) Air flowing through a carburetor enters a narrow part of the airway. As the cross sectional area of the tube decreases, what happens to the pressure? 3. (8) Some air is in a horizontal cylinder fitted with a piston. The piston’s area is .00170 m

2. At first,

the air in the cylinder is at standard atmospheric pressure. You then push on the piston with a force F, making the air’s volume 1/3 of what it was before. If the temperature did not change, what is F? ans: 344 N

D. 1. (2 points) The pipe has the same diameter at points B and C, and is larger at A. Point A is at the same elevation as B and C is higher. a. List the speeds vA, vB and vC from slowest to fastest. b. List the pressures PA, PB and PC from lowest to highest. 2. (2 points) Lead has a greater density than iron. If submerged in some fluid, is the buoyant force on a lead object greater than, less than, or equal to the buoyant force on an iron object of the same volume? 3. (6) A certain hydraulic press has an output piston of 8.00 cm diameter. The input piston has a diameter of .375 cm. How large a force must be supplied to the input piston to provide an output force of 60 000 N? ans: 132 N E. An open barrel full of water has a hole in it 30.0 cm below the water level and 45.0 cm above the ground. a. With what speed does water shoot out of the hole? (Hint: The

pressure is atmospheric at both the top surface of the water and at the hole.)

b. How far from the bottom of the barrel does the water hit the

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ground? (Think of the water as a stream of projectiles.) ans: 2.42 m/s, .733 m F. 1. (1 point) This calculation using the gas law contains an error. What is wrong?

P2 = P1

V1T2

V2T1 = (1.00 x 10

5 Pa)

(.005 𝑚3)(75°C)

(.007 𝑚3)(30°C) = 1.79 x 10

5 Pa

2. (Review. 9 pts) The 4.00 kg box moves up the incline at a constant speed. Find μk. ans: .306 Sec. 12 – Temperature & Heat Read: Ch. 13, sec. 13.2; Ch. 14, sec. 14.1 – 14.3

A. 1. (2 points) a. The amount of heat needed to raise the temperature of one pound of water by 1F is called a .

b. The amount of heat needed to raise the temperature of one gram of water by 1C is called a .

2. (8) How many grams of steam at 100C must be condensed in 500 grams of water at 20C to raise

its temperature to 30C? ans: 8.21 g

B. 1. (2 pts) Why can you get a more severe burn from steam at 100C than from water at 100C?

2. (8) One kilogram of water at 30C is used to make iced tea. How much ice at 0C must be added to

lower the temperature of the tea to 10C? ans: 223 g C. 1. (2 points) A steel wire and a copper wire are strung between the same two poles. On a hot summer day, they sag the same amount. On a cold winter night, which hangs lower?

2. (8) A 90 g piece of hot iron is dropped into 500 g of oil at 20C. The final temperature of the oil and

the iron is 30C. Find the original temperature of the iron. (c = 2100 J/kgC for the oil.)

ans: 279C D. 1. (2 pts) A lead sphere and a steel sphere are heated in boiling water. Both have a mass of 100 g. Compare the sizes of the holes they will melt in a block of ice onto which they are dropped. 2. (8) Back in the stagecoach era, rims were placed on wooden wheels by shrink-fitting. Suppose the

iron rim has an inside diameter of 99.81 cm at 20C. To what temperature must it be heated to slide it onto the outside of a 100.00 cm diameter wheel?

ans: 179C

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E. 1. (2 points) The specific heat of water is about two times that of ethyl alcohol. Equal masses of alcohol and water in separate beakers are supplied with the same amount of energy. Compare their temperature increases.

2. (8) A 3.00 g lead bullet at 30.0C is fired at a speed of 240 m/s into a large block of ice at 0C, in which it becomes embedded. What quantity of ice melts? ans: .293 g F. (Review) The three 1.80 g cylinders, each with a radius of 3.00 mm, are mounted on a rod as shown below. The mass of the rod is insignificant. If spinning at 10.0 rad/s, what is this system’s kinetic energy a) when rotating about its center of mass like this: (The masses are small enough to be treated as point-particles in this case.) b) when rotating about an axis through the centers of the cylinders like this. ans: .0463 J, 1.21 μJ Sec. 13 – The 1

st & 2

nd Laws of Thermodynamics.

Read: Ch 15, sections 15.1 – 15.3, and just skim 15.4 – 15.6 A. 1. (2 pts) Give an example of each of the following situations: a. Heat is added to an object, its internal energy increases and its temperature increases. (sample answer: Hold a piece of metal over a flame.) b. Heat is added, its internal energy increases, and temperature does not increase. 2. (8) One mole of hydrogen gas is heated from 300 K to 420 K at a constant pressure of 200 kPa. In the process its volume increases from .0125 m

3 to .0175 m

3. Calculate (a) how much heat flows into the

gas, (b) the work done by the gas, and (c) the increase in its internal energy. ans: 3.46 kJ, 1.00 kJ, 2.46 kJ B. 1. (2 pts) Give an example of each of the following situations: a. No heat is added to an object, its internal energy increases, and its temperature increases. b. Work is done on an object, its internal energy does not increase, and its temperature does not increase. 2. (8) One mole of argon (Ar), initially at 300 K and 1.00 atmosphere is compressed adiabatically to one fourth of its initial volume. Find its final pressure and temperature. ans: 10.1 atm, 759 K C. 1. (2 pts) As an ideal gas expands, it does 100 J of work. What is ΔEint (the increase in internal energy) if the expansion is

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a. adiabatic? b. isothermal?

2. (8) A gas expands from point I to F. Calculate the work done by

the gas if the change is made along (a) path IF, (b) path IAF.

ans: 506 J, 203 J

D. 1. (2 points) Is it possible to cool a room by leaving a refrigerator open? Explain.

2. (8) An ideal gas is taken through a Carnot cycle using a hot reservoir at 250C and a cold reservoir at

50C. If the gas absorbs 1200 J of energy from the hot reservoir during each cycle, find (a) the energy

expelled to the cold reservoir in each cycle, and (b) the net work done by the gas in each cycle.

ans: 741 J, 459 J

E. 1. (2 pts) As sunflower grows from a seed, it assembles a very organized structure from scattered,

disorganized molecules. Explain why this does not violate the second law, "entropy doesn't

spontaneously decrease."

2. (8) An engine absorbs 1600 J form from a hot reservoir and expels 1000 J to a cold reservoir in each

cycle. (a) What is the efficiency of the engine? (b) How much work is done in each cycle? (c) What is

the power output of the engine if each cycle lasts for 0.30 s?

ans: 0.375, 600 J, 2.00 kW

F. 1. (2 points) Newton’s first law says that in the absence of a net force, a moving object continues to

move with a constant velocity. Give an example of this, and make it a situation where a significant

amount of friction is present.

2. (8) The rod has negligible weight. How large must F be if

the rod is to be in equilibrium?

ans. 115 N Sec. 14 – Special Relativity. Read: Ch.28, sections 28.1 – 28.3 & 28.6. Also, Binding Energy on p. 1259. A. 1. (2 points) The speed of an electron is calculated from the voltage which accelerated it, using the formula KE = 1/2 mv

2. In each case, state whether the answer is correct to at least three significant

figures: a. What if the answer is 5.00 x 10

8 m/s? ____________

b. What if the answer is 1.00 x 108 m/s? ____________

c. What if the answer is 5.00 x 107 m/s? ____________

d. What if the answer is 1.00 x 107 m/s? ____________

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2. (8) You and a friend get into spaceships which are identical when docked at the space station. You later fly past each other at a high speed. At this moment he measures his ship as being 20.0 m long, and yours as being 19.0 m long. According to your observations, a. how long is your ship? b. how long is his ship? c. what is the speed of his ship? ans: 20.0 m, 19.0 m, .312c B. 1. (2pts) A certain electron's total energy is 1.17 MeV. What is its kinetic energy? ans: .66 MeV 2. (8) A proton is given a kinetic energy of 3 750 MeV. What is its speed, v? ans: .980c C. 1. (2 pts) Explain in words why it is impossible for an object (of nonzero mass) to reach a speed of c, regardless of the size and duration of the force on it.

8. (8) Consider the decay 55

24Cr 55

25Mn + e, where e is an electron. The 55

Cr nucleus has a mass of 9.12099 x 10

-26 kg, and the

55Mn nucleus has a mass of 9.12041 x 10

-26 kg. (a) Calculate the mass

difference between the two nuclei in mega electron-volts. (b) What is the maximum kinetic energy of the emitted electron? ans: 3.26 MeV, 2.75 MeV D. 1. (2 pts) An astronaut moves away from the earth at a speed close to the speed of light. What changes, if any, would be measured in the astronaut's size and pulse rate (a) by an observer on Earth? (b) by the astronaut herself? 2. (Review) A train is going 18.0 m/s when a rivet falls from a boxcar, from a point where it takes 1.25 seconds to reach the ground. Neglecting air drag, what is the speed of the rivet (the magnitude of its velocity) when it hits the ground? ans: 21.8 m/s E. 1. (2 pts) What two speed measurements do two observers in relative motion always agree on? 2. (8) The average lifetime of a pi meson in its own frame of reference is 2.6 x 10

-8s. If the meson

moves at .95c relative to an observer on Earth, what will that observer measure for (a) its average lifetime, (b) the average distance it travels before decaying? ans: 83.3 ns, 23.7 m

F. Some air in a cylinder is compressed to one-third of its original volume. Its original pressure is 100 kPa. What is the final pressure if the compression is (a) adiabatic? (b) isothermal?

ans: 466 kPa, 300 kPa