Physics 201 Homework 1Jan 9, 2013

1. (a) What is the magnitude of the average acceleration of a skier who, starting (a) 1.6 m/s2

(b) 20 metersfrom rest, reaches a speed of 8.0 m/s when going down a slope from 5.0 seconds?(b) How far does the skier travel in this time?

2. A car is traveling at a constant speed of 33 m/s on a highway. At the 0.87 m/s2

instant this car passes an entrance ramp, a second car enters the highway fromthe ramp. The second car starts from rest and has a constant acceleration. Whatacceleration must it maintain, so that the two cars meet for the first time at thenext exit, which is 2.5 km away?

3. At the beginning of a basketball game, a referee tosses the ball straight up 0.47 seconds

with a speed of 4.6 m/s. A player cannot touch the ball until after it reachesits maximum height and begins to fall down. What is the minimum time that aplayer must wait before touching the ball?

4. A dynamite blast at a quarry launches a chunk of rock straight upward, and (a) 35 m/s(b) 14 m/s2.0 seconds later it is rising at a speed of 15 m/s. Assuming air resistance has

no effect on the rock, calculate its speed (a) at launch and (b) 5.0 seconds afterlaunch.

5. While standing on a bridge 15.0 meters above the ground, you drop a stone -11.3 m/s

from rest. When the stone has fallen 3.20 meters, you throw a second stonestraight down. What initial velocity must you give the second stone if they areboth to reach the ground at the same instant?

6. A soccer player kicks the ball toward a goal that is 16.8 meters in front of him. 14.7 m/s

The ball leaves his foot at a speed of 16.0 m/s and an angle of 28.0◦ above theground. Find the speed of the ball when the goalie catches it in front of the net.

7. A major-league pitcher can throw a baseball in excess of 41.0 m/s. If a ball is 0.84 meters

thrown horizontally at this speed, how much will it drop by the time it reaches acatcher who is 17.0 meters away from the point of release?

8. A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 33.2 meters

60.0◦ above the horizontal. The rocket is fired toward an 11.0-meter wall, whichis located 27.0 meters away. The rocket attains its launch speed in a negligiblyshort period of time, after which its engines shut down and the rocket coasts. Byhow much does the rocket clear the top of the wall?

9. A golfer standing on a fairway, hits a shot to a green that is elevated 5.50 5.17 seconds

meters above the point where she is standing. If the ball leaves her club with avelocity of 46.0 m/s at an angle of 35.0◦ above the ground, find the time that theball is in the air before it hits the green.

10. A projectile is launched from ground level at an angle of 12.0◦ above the 27.2◦

horizontal. It returns to ground level. To what value should the launch angle beadjusted, without changing the launch speed, so that the range doubles?

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Physics 201 Homework 2Jan 16, 2013

1. A 20.0-kilogram sled is being pulled across a horizontal surface at a constant 0.444

velocity. The pulling force has a magnitude of 80.0 newtons and is directed at anangle of 30.0◦ above the horizontal. Determine the coefficient of kinetic friction.

2. A force vector has a magnitude of 575 newtons and points at an angle of 36.0◦ (a) 465 N(b) -338 Nbelow the positive x axis. What are (a) the x scalar component and (b) the y

scalar component of the vector?

3. The displacement vector ~A has scalar components of Ax = 80.0 meters and ~A and ~C are the same

Ay = 60.0 meters. The displacement vector ~B has a scalar component of Bx =

60.0 meters and a magnitude of B = 75.0 meters. The displacement vector ~C hasa magnitude of C = 100.0 meters and is directed at an angle of 36.9◦ above the+x axis. Two of these vectors are equal. Determine which two, and support yourchoice with a calculation.

4. A golfer, putting on a green, requires three strokes to “hole the ball.” During 7.1 meters at 9.9◦ north of east

the first putt, the ball rolls 5.0 meters due east. For the second putt, the balltravels 2.1 meters at an angle of 20.0◦ north of east. The third putt is 0.50 metersdue north. What displacement (magnitude and direction relative to due east)would have been needed to “hole the ball” on the very first putt?

5. An ocean liner leaves New York City and travels 18.0◦ north of east for 155 (a) 147 km(b) 47.9 kmkm. How far east and how far north has it gone? In other words, what are the

magnitudes of the components of the ship’s displacement vector in the directions(a) due east and (b) due north?

6. Three forces are applied to an object, as indicated in Figure 1. Force ~F1 has a 18.7 newtons, θ = 76.6$dg$

magnitude of 21.0 newtons and is directed 30.0◦ to the left of the +y axis. Force~F2 has a magnitude of 15.0 newtons and points along the +x axis. What mustbe the magnitude and direction (specified by the angle θ in the drawing) of the

third ~F3 such that the vector sum of the three forces is zero?

Figure 1: Problem 1.66

7. The helicopter in Figure 2 is moving horizontally to the right at a constant (a) 57.6 kN(b) 20.7 kNvelocity. The weight of the helicopter is W = 53800 newtons. The lift force

~L generated by the rotating blade makes an angle of 21.0◦ with respect to thevertical. (a) What is the magnitude of the lift force? (b) Determine the magnitude

of the air resistance ~R that opposes the motion.

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Figure 2: Problem 4.52

8. A supertaker (mass = 1.70×108 kilograms) is moving with a constant velocity. (a) 7.40 × 105 newtons(b) 1.67 × 109 newtonsIts engines generate a forward thrust of 7.40 × 105 newtons. Determine (a) the

magnitude of the resistive force exerted on the tanker by the water and (b) themagnitude of the upward buoyant force exerted on the tanker by the water.

9. A worker stands still on a roof sloped at an angle of 36◦ above the horizontal. 68 kilograms

He is prevented from slipping by a static frictional force of 390 newtons. Find themass of the worker.

10. During a storm, a tree limb breaks off and comes to rest across a barbed 436 newtons at 5.6$dg$

wire fence at a point that is not in the middle between two fence posts. The limbexerts a downward force of 151 newtons on the wire. The left section of the wiremakes an angle of 14.0◦ relative to the horizontal and sustains a tension of 447newtons. Find the magnitude and direction of the tension that the right sectionof the wire sustains.

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Physics 201 Homework 3Jan 23, 2013

1. Only two forces act on an object (mass = 3.00 kg), as in the drawing. Find the 30.9 m/s2 at 27.2◦

magnitude and direction (relative to the x axis) of the acceleration of the object.

Figure 3: Problem 4.13

2. A 1380-kg car is moving due east with an initial speed of 27.0 m/s. After 8.00 1730 N due west

s the car has slowed down to 17.0 m/s. Find the magnitude and direction of thenet force that produces the deceleration.

3. When a 58-gram tennis ball is served, it accelerates from rest to a speed of 130 newtons

45 m/s. The impact with the racket gives the ball a constant acceleration over adistance of 44 cm. What is the magnitude of the net force acting on the ball?

4. During a circus performance, a 72-kilogram human cannonball is shot out 2900 newtons

of an 18-meter-long cannon. If the human cannonball spends 0.95 seconds inthe cannon, determine the average net force exerted on him in the barrel of thecannon.

5. A 1450-kilogram submarine rises straight up toward the surface. Seawater 0.621 m/s2

exerts both an upward buoyant force of 16140 newtons on the submarine and adownward resistive force of 1030 newtons. What is the submarine’s acceleration?

6. A fisherman is fishing from a bridge and is using a “45-newton test line.” (a) 45 newtons(b) 37 newtonsIn other words, the line will sustain a maximum force of 45 newtons without

breaking. What is the weight of the heaviest fish that can be pulled up verticallywhen the line is reeled in (a) at a constant speed and (b) with an accelerationwhose magnitude is 2.0 m/s2?

7. A 205-kilogram log is pulled up a ramp by means of a rope that is parallel 2730 newtons

to the surface of the ramp. The ramp is inclined at 30.0◦ with respect to thehorizontal. The coefficient of kinetic friction between the log and the ramp is0.900, and the log has an acceleration of 0.800 m/s2. Find the tension in therope.

8. The space probe Deep Space I was launched on October 24, 1998. Its mass 79 days

was 474 kilograms. The goal of the mission was to test a new kind of engine calledan ion propulsion drive. This engine generated only a weak thrust, but it coulddo so over long periods of time with the consumption of only small amounts offuel. The mission was spectacularly successful. At a thrust of 0.056 newtons howmany days were required for the probe to attain a velocity of 805 m/s, assumingthat the probe started from rest and that the mass remained nearly constant.

9. Two objects (45.0 and 21.0 kilograms) are connected by a massless string that (a) 3.56 m/s2

(b) 281 newtonspasses over a massless, frictionless pulley. The pulley hangs from the ceiling. Find(a) the acceleration of the objects and (b) the tension in the string.

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10. A 12-kilogram box is released from the top of an incline that is 5.0 meters (a) 1.3 m/s2

(b) 2.8 secondslong and makes an angle of 40◦ to the horizontal. A fricton force with coefficientof µk = 0.67 impedes the motion of the box. (a) What will be the acceleration ofthe box and (b) how long will it take to reach the bottom of the incline?

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Physics 201 Homework 4Jan 30, 2013

1. There is a clever kitchen gadget for drying lettuce leaves after you wash them. 19 m/s2

It consists of a cylindrical container mounted so that it can be rotated about itsaxis by turning a hand crank. The outer wall of the cylinder is perforated withsmall holes. You put the wet leaves in the container and turn the crank to spinoff the water. The radius of the container is 0.12 meters. When the cylinder isrotating at 2.0 revolutions per second, what is the magnitude of the centripetalacceleration at the outer wall?

2. A jet flying at 123 m/s banks to make a horizontal circular turn. The radius of 2.11 × 106 meters

the turn is 3810 meters, and the mass of the jet is 2.00×105 kilograms. Calculatethe magnitude of the necessary lifting force.

3. A car travels at a constant speed around a circular track whose radius is 0.79 m/s2

2600 meters. The car goes once around the track in 360 seconds. What is themagnitude of the centripetal acceleration of the car?

4. In a skating stunt known as crack-the-whip, a number of skaters hold hands 606 newtons

and form a straight line. They try to skate so that the line rotates about theskater at one end, who acts as the pivot. The skater farthest out has a mass of80.0 kilograms and is 6.10 meters from the pivot. He is skating at a speed of 6.80m/s. Determine the magnitude of the centripetal force that acts on him.

5. The National Aeronautics and Space Administration (NASA) studies the 33 m/s

physiological effects of large accelerations on astronauts. Some of these studiesuse a machine known as a centrifuge. This machine consists of a long arm, to oneend of which is attached a chamber in which the astronaut sits. The other end ofthe arm is connected to an axis about which the arm and chamber can be rotated.The astronaut moves on a circular path, much like a model airplane flying in acircle on a guideline. The chamber is located 15 meters from the center of thecircle. At what speed must the chamber move so that an astronaut is subjectedto 7.5 times the acceleration due to gravity?

6. The hammer throw is a track-and-field event in which a 7.3-kilogram ball (the 3500 newtons

“hammer”) is whirled around in a circle several times and released. It then movesupward on the familiar curving path of projectile motion and eventually returnsto earth some distance away. The world record for this distance is 86.75 meters,achieved in 1986 by Yuriy Sedykh. Ignore air resistance and the fact that the ballis released above the ground rather than at ground level. Furthermore, assumethat the ball is whirled on a circle that has a radius of 1.8 meters and that itsvelocity at the instant of release is directed 41◦ above the horizontal. Find themagnitude of the centripetal force acting on the ball just prior to the moment ofrelease.

7. A car moving at 5.0 m/s tries to round a corner in a circular arc of 8.0 meters 0.32

radius. The roadway is flat. How large must the coefficient of fricton be betweenthe wheels and roadway if the car is not to skid?

8. Mars has a mass of 6.46 × 1023 kilograms and a radius of 3.39 × 106 meters. (a) 3.75 m/s2

(b) 244 newtons(a) What is the acceleration due to gravity on Mars? (b) How much would a65-kilogram person weigh on this planet?

9. The moon orbits the earth at a distance of 3.85×108 meters. Assume that this 27.5 days

distance is between the centers of the earth and the moon and that the mass ofthe earth is 5.98× 1024 kilograms. Find the period for the moon’s motion aroundthe earth. Express the answer in days and compare it to the length of a month.

10. A satellite orbits the Earth at a height of 200 kilometers. Find (a) the speed (a) 7.8 km/s(b) 88 minutesof the satellite and (b) the time taken (in minutes) to complete one revolution.

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Physics 201 Homework 5Feb 6, 2013

1. A 7420-kilogram satellite has an elliptical orbit, as in Figure 4. The point on (a) 2.35 × 1011 joules(b) -2.35 × 1011 joulesthe orbit that is farthest from the earth is called the apogee and is at the far right

side of the drawing. The point on the orbit that is closest to the earth is calledthe perigee and is at the left side of the drawing. Suppose that the speed of thesatellite is 2820 m/s at the apogee and 8450 m/s at the perigee. Find the workdone by the gravitational force when the satellite moves from (a) the apogee tothe perigee and (b) the perigee to the apogee.

Figure 4: Problem 6.18

2. In 2.0 minutes, a ski lift raises four skiers at constant speed to a height of 3000 watts

140 meters. The average mass of each skier is 65 kilograms. What is the averagepower provided by the tension in the cable pulling the lift?

3. A 1300-kilogram car is to accelerate from rest to a speed of 30.0 m/s in a 132 horsepower

time of 12.0 seconds as it climbs a 15◦ hill. Assuming uniform acceleration, whatminimum horsepower is needed to accelerate the car in this way?

4. The (non-conservative) force propelling a 1500-kilogram car up a mountain -1.21 × 106 joules

road does 4.70×106 joules of work on the car. The car starts from rest at sea leveland has a speed of 27.0 m/s at an altitude of 200 meters above sea level. Obtainthe work done on the car by the combined forces of friction and air resistance,both of which are non-conservative forces.

5. A person pushes a 16.0-kilogram shopping cart at a constant velocity for a (a) 54.9 newtons(b) 1060 joules(c) -1060 joules(d) none

distance of 22.0 meters. She pushes in a direction 29.0◦ below the horizontal.A 48.0-newton frictional force opposes the motion of the cart. (a) What is themagnitude of the force that the shopper exerts? Determine the work done by (b)the pushing force, (c) the frictional force, and (d) the gravitational force.

6. A 0.075-kilogram arrow is fired horizontally. The bowstring exerts an average 39 m/s

force of 65 newtons on the arrow over a distance of 0.90 meters. With what speeddoes the arrow leave the bow?

7. “Rocket man” has a propulsion unit strapped to his back. He starts from rest 23 kJ

on the ground, fires the unit, and is propelled straight upward. At a height of16 meters, his speed is 5.0 m/s. His mass, including the propulsion unit, has theapproximately constant value of 136 kilograms. Find the work done by the forcegenerated by the propulsion unit.

8. A small lead ball, attached to a 1.5 meter rope, is being whirled in a circle 42 meters

that lies in the vertical plane. The ball is whirled at a constant rate of threerevolutions per second and is released on the upward part of the circular motionwhen it is 0.75 meters above the ground. The fall travels straight upward. In theabsence of air resistance, to what maximum height above the ground does theball rise?

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9. A pendulum consists of a small object hanging from the ceiling at the end 43◦

of a string of negligible mass. The string has a length of 0.75 meters. With thestring hanging vertically, the object is given an initial velocity of 2.0 m/s parallelto the ground and swings upward on a circular arc. Eventually, the object comesto a momentary halt at a point where the string makes an angle θ with its initialvertical orientation and then swings back downward. Find the angle θ.

10. A semitrailer is coasting downhill along a mountain highway when its brakes 27.0 m/s

fail. The driver pulls onto a runaway-truck ramp that is inclined at an angle of14.0◦ above the horizontal. The semitrailer coasts to a stop after traveling 154meters along the ramp. What was the truck’s initial speed? Neglect air resistanceand friction

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Physics 201 Homework 6Feb 13, 2013

1. John’s mass is 86 kilograms, and Barbara’s is 55 kilograms. He is standing -1.5 meters

on the x axis at x1 = 9.0 meters, while she is standing on the x axis at x2 = 2.0meters. They switch positions. How far and in which direction does their centerof mass move as a result of the switch?

2. A 50.0-kg skater is traveling due east at a speed of 3.00 m/s. A 70.0-kg skater (a) 73.0◦ south of east(b) vf = 4.27 m/sis moving due south at a speed of 7.00 m/s. They collide and hold on to each

other after the collision, managing to move off at an angle θ south of east, witha speed of vf . Find (a) the angle θ and (b) the speed vf , assuming that frictioncan be ignored.

3. A cannon of mass 5800 kilograms is rigidly bolted to the earth so it can recoil 547 m/s. (The cannon recoils at -8 m/s.)

only by a negligible amount. The cannon fires an 85.0-kilogram shell horizontallywith an initial velocity of 551 m/s. Suppose the cannon is then unbolted fromthe earth, and no external force hinders its recoil. What would be the velocity ofa shell fired by this loose cannon? (Hint: In both cases assume that the burninggunpowder imparts the same kinetic energy to the system.)

4. A projectile (mass = 0.20 kilograms) is fired at and embeds itself in a target 7.4%

(mass = 2.50 kilograms). The target (with the projectile in it) flies off after beingstruck. What percentage of the projectile’s incident kinetic energy does the target(with the projectile in it) carry off after being struck?

5. Two identical balls are traveling toward each other with velocities of -4.0 and They exchange velocities

+7.0 m/s, and they experience an elastic head-on collision. Obtain the velocities(magnitude and direction) of each ball after the collision.

6. A 2.50-gram bullet, traveling at a speed of 425 m/s, strikes the wooden block (a) 4.89 m/s(b) 1.22 metersof a ballistic pendulum, such as that in Figure 5. The block has a mass of 215

grams. (a) Find the speed of the bullet/block combination immediately after thecollision (b) How high does the combination rise above its initial position?

Figure 5: Problem 7.55

7. A volleyball is spiked so that its incoming velocity of +4.0 m/s is changed -8.8 N-s

to an outgoing velocity of -21 m/s. The mass of the volleyball is 0.35 kg. Whatimpulse does the player apply to the ball?

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8. A space probe is traveling in outer space with a momentum that has a 5.1 × 107 kg-m/s

magnitude of 7.5 × 107 kg-m/s. A retrorocket is fired to slow down the probe.It applies a force to the probe that has a magnitude of 2.0 × 106 newtons anda direction opposite to the probe’s motion. It fires for a period of 12 seconds.Determine the momentum of the probe after the retrorocket ceases to fire.

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Physics 201 Homework 7Feb 20, 2013

1. A uniform board is leaning against a smooth vertical wall. The board is at 37.6◦

an angle θ above the horizontal ground. The coefficient of static friction betweenthe ground and the lower end of the board is 0.650. Find the smallest value forthe angle θ, such that the lower end of the board does not slide along the ground.

2. Figure 6 shows a uniform horizontal beam attached to a vertical wall by a P = 270 newtons. H = 210 newtons. V =170 newtonsfrictionless hinge and supported from below at an angle θ = 39◦ by a brace that is

attached to a pin. The beam has a weight of 340 newtons. Three additional forceskeep the beam in equilibrium. The brace applies a force ~P to the right end of thebeam that is directed upward at the angle θ with respect to the horizontal. Thehinge applies a force to the left end of the beam that has a horizontal component~H and a vertical component ~V . Find the magnitudes of these three forces.

Figure 6: Problem 9.21

3. Figure 7 shows a jet engine suspended beneath the wing of an airplane. The (a) 13.5 kN-m(b) 132 kN-mweight of the engine is 10200 newtons and acts as shown in the drawing. In flight

the engine produces a thrust of 62300 newtons that is parallel to the ground. Therotational axis in the drawing is perpendicular to the plane of the paper. Withrespect to this axis, find the magnitude of the torque due to (a) the weight and(b) the thrust.

Figure 7: Problem 9.69

4. Figure 8 shows a person (weight = 584 newtons) doing push-ups. Find the 96 newtons from each foot and 196 newtonsfrom each handnormal force exerted by the floor on each hand and each foot, assuming that the

person holds this position.

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Figure 8: Problem 9.72

5. The steering wheel of a car has a radius of 0.19 m, while the steering wheel of 1.3

a truck has a radius of 0.25 m. The same force is applied in the same direction toeach. What is the ratio of the torque produced by this force in the truck to thetorque produced in the car?

6. A table has a 100 kg mass on it. The 50 kg table is 2.0 m long and the mass (a) On the left: 1200 N(b) On the right: 290 Nis 0.10 m from the left edge. What are the support forces in the four legs?

2.0 m

m = 100 kg

m = 50 kg

0.1 m

Figure 9: Mass on table

7. A person exerts a horizontal force of 190 newtons in the test apparatus shown 1200 newtons

in Figure 10. Find the magnitude of the horizontal force ~M that his flexor muscleexerts on his forearm.

Figure 10: Problem 9.15

8. Figure 11 shows a bicycle wheel resting against a small step whose height is 29 newtons

0.120 meters. The weight and radius of the wheel are 25.0 newtons and 0.340meters, respectively. A horizontal force ~F is applied to the axle of the wheel. Asthe magnitude of ~F increases, there comes a time when the wheel just begins torise up and loses contact with the ground. What is the magnitude of the forcewhen this happens?

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Figure 11: Problem 9.24

9. A 1220 newton uniform beam is attached to a vertical wall at one end and is (a) 2260 newtons(b) 1450 newtons(c) 1450 newtons

supported by a cable at the other end. A 1960 newton crate hangs from the farend of the beam. Using the data shown in Figure 12, find (a) the magnitude ofthe tension in the wire and (b) the magnitude of the horizontal and (c) verticalcomponents of the force that the wall exerts on the left end of the beam.

Figure 12: Problem 9.25

10. An inverted “V” is made of uniform boards and weighs 356 newtons. Each 51.4 newtons

side has the same length and makes a 30.0◦ angle with the vertical, as Figure 13shows. Find the magnitude of the static frictional force that acts on the lowerend of each leg of the “V”.

Figure 13: Problem 9.79

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Physics 201 Homework 8Feb 27, 2013

1. A flywheel has a constant angular deceleration of 2.0 rad/s2. (a) Find the (a) 12000 rad(b) 110 sangle through which the flywheel turns as it comes to rest from an angular speed

of 220 rad/s. (b) Find the time required for the flywheel to come to rest.

2. A person lowers a bucket into a well by turning the hand crank, as the drawing 0.300 m/s

illustrates. The crank handle moves with a constant tangential speed of 1.20 m/son its circular path. Find the linear speed with which the bucket moves down thewell.

Figure 14: Problem 8.35

3. The wheels of a bicycle have an angular velocity of 20.0 rad/s. Then, the (a) 10.0 seconds(b) -2.00 rad/s2brakes are applied. In coming to rest, each wheel makes an angular displacement

of 15.92 revolutions. (a) How much time does it take for the bike to come to rest?(b) What is the angular acceleration (in rad/s2) of each wheel?

4. A fan blade is rotating with a constant angular acceleration of 12.0 rad/s2. At 0.817 meters

what point on the blade, measured from the axis of rotation, does the magnitudeof the tangential acceleration equal that of the acceleration due to gravity?

5. A train is rounding a circular curve whose radius is 200 meters. At one instant, (a) 0.583 rad/s2

(b) 149◦the train has an angular acceleration of 0.00150 rad/s2 and an angular speed of0.0500 rad/s. (a) Find the magnitude of the total acceleration (centripetal plustangential) of the train (b) Determine the angle of the total acceleration relativeto the radial direction.

6. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s2

The blades have a total moment of inertia of 0.22 kg-m2. What is the angularacceleration of the blades?

7. A bicycle wheel has a radius of 0.330 m and a rim whose mass is 1.20 kg. The (a) 0.131 kg-m2

(b) 3.63 × 10−4 kg-m2

(c) 0.149 kg-m2wheel has 50 spokes, each with a mass of 0.010 kg. (a) Calculate the moment ofinertia of the rim about the axle. (b) Determine the moment of inertia of any onespoke, assuming it to be a long, thin rod that can rotate about one end. (c) Findthe total moment of inertia of the wheel, including the rim and all 50 spokes.

8. A horizontal disk with mass 2.0 kg has a radius of 0.10 m. Around the 1.0 s

circumference is a string that runs over a pulley supporting a 0.25 kg mass. Fromrest, how long does it take the mass to fall 1.0 m?

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a

Side View

Top View α

Figure 15: Flywheel and pulley

9. A stationary bicycle is raised off the ground, and its front wheel (mass = 1.3 0.78 newtons

kilograms) is rotating at an angular velocity of 13.1 rad/s (see Figure 16). Thefront brake is then applied for 3.0 seconds, and the wheel slows down to 3.7 rad/s.Assume that all the mass of the wheel is concentrated in the rim, the radius ofwhich is 0.33 meters. The coefficient of kinetic friction between the brake padand the rim is µk = 0.85. What is the magnitude of the normal force that eachbrake pad applies to the rim?

Figure 16: Problem 9.45

10. The crane shown in Figure 17 is lifting a 180 kilogram crate upward with an 1700 newton-meters

acceleration of 1.2 m/s2. The cable from the crate passes over a solid cylindricalpulley at the top of the boom. The pulley has a mass of 130 kilograms. The cableis then wound onto a hollow cylindrical drum that is mounted on the deck of thecrane. The mass of the drum is 150 kilograms, and its radius is 0.76 meters. Theengine applies a counterclockwise torque to the drum in order to wind up thecable. What is the magnitude of this torque? Ignore the mass of the cable.

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Figure 17: Problem 9.47

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Physics 201 Homework 9Mar 6, 2013

1. Suppose we are considering putting a rocket into low earth orbit. (The Apollo 88%

program is the only example of human spaceflight beyond low earth orbit.) Thetotal ∆v required is 9.7 km/s. If the exhaust velocity of the rocket is 4.5 km/s,calculate the percent of the initial total mass that must be propellant.

2. An earth satellite is observed to have a height of perigee of 185 kilometers and 5,850 seconds = 1.63 hours

a height of apogee of 1,100 kilometers. Find the period of the orbit.

3. For a certain Earth satellite it is known that its semi-major axis is 9,140 (a) r0 = 7,310 kilometers(b) r1 = 11,000 kilometers(c) 2.18 × 107 J/kg

kilometers. The orbit eccentricity is 0.2. (a) Find its perigee and (b) apogeedistances from the center of the earth. (c) Find the specific energy of its trajectory.

4. A satellite is injected into an elliptical orbit with a semi-major axis equal ∆v = 1.64 km/s

to 25,500 kilometers. When it is precisely at the end of the semi-minor axis itreceives an impulsive velocity change just sufficient to place it into an escapetrajectory. What was the magnitude of the velocity change?

5. A communication satellite is in a circular orbit of radius 12,800 kilometers. 1.02 km/s

Find the minimum ∆v required to double the altitude of the satellite.

6. (a) Calculate the burnout velocity required to transfer a probe between the (a) 11 km/s(b) 0.88 km/svicinity of the Earth and the Moon’s orbit using a Hohmann transfer. (b) What

additional $Delta v$ would be required to place the probe in the same orbit asthat of the Moon? Neglect the Moon’s gravity in both parts.

7. A Venus probe departs from a 12,800 kilometers radius circular parking orbit 3.7 km/s

around the Earth with a burnout speed of 8.7 km/s. Find the excess escape speed.

8. To accomplish a certain measurement of phenomena associated with sunspot 11.6 km/s

activity, it is necessary to establish a heliocentric orbit with perihelion of 0.5 AU.The departure from the Earth’s orbit will be at aphelion. What must the burnoutvelocity be at an altitude of 1270 kilometers to accomplish this mission?

9. In 1910, on its sixth trip around the Sun after that of 1456, Halley’s comet (a) 5.3 × 1012 meters(b) 0.967was observed to pass near the Sun at a distance of 9.0 × 1010 meters. Calculate

(a) how far the comet travels from the Sun at the outer extreme of its orbit, and(b) the eccentricity of its orbit.

10. The maximum and minimum altitudes of the International Space Station 7.71 km/s

(ISS) are 424 and 402 kilometers respectively. Determine its average speed. (Hint:Use v = 2πa/T where a is the semi-major axis of the orbit and T is its period.)

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