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					                                   Chapter 2 Homework

10. If the average speed of an orbiting space shuttle is 19,800 mi/h, determine the time
    required for it to circle earth. The shuttle orbits about 200 mi above earth and assume
    that earth’s radius is about 3,963 mi.

23. The engine of a model rocket accelerates the rocket vertically upward for 2.0s as follows:
    At t=0, the rocket’s speed is zero; at t=1.0s, its speed is 5.0 m/s; and at t=2.0s, its speed
    is 16 m/s. Plot a velocity vs time graph for this motion, and use the graph to determine
    (a) the rocket’s average acceleration during the 2.0s interval and (b) the instantaneous
    acceleration of the rocket at t=1.5s.

30. A truck on a straight road starts from rest and accelerates at 2.0 m/s² until it reaches a
    speed of 20 m/s. Then the truck travels for 20s at a constant speed until the brakes are
    applied, stopping the truck in a uniform manner in an additional 5.0s. (a) How long is
    the truck in motion? (b) What is the average velocity of the truck during the motion

36. A car accelerates uniformly from rest to a speed of 40 mi/h in 12.0s. Find (a) the
    distance the car travels during this time and (b) the constant acceleration of the car.

37. A car starts from rest and travels for 5s with a uniform acceleration of +1.5 m/s². The
    driver then applies the brakes, causing a uniform acceleration of -2.0 m/s². If the brakes
    are applied for 3.0s, (a) how fast is the car going at the end of the braking period, and (b)
    how far has the car gone?

43. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise?
    (b) How long does it take to reach the highest point? (c) How long does the ball take to
    hit the ground after it reaches the highest point? (d) What is its velocity when it returns
    to the level from which it started?

49. A model rocket is launched straight upward with an initial speed of 50 m/s. It
    accelerates with a constant upward acceleration of 2 m/s until its engines stop at an
    altitude of 150m. (a) What is the max height reached by the rocket? (b) How long after
    lift off does the rocket reach its max height? (c) How long is the rocket in the air?
50. A parachutist with a camera descends in free fall at a speed of 10 m/s. The parachutist
    releases the camera at an altitude of 50m. (a) How long does it take the camera to reach
    the ground? (b) What is the velocity of the camera just before it hits the ground?

57. A ball is thrown upward from the ground with an initial speed of 25 m/s; at the same
    instant, another ball is dropped from a building 15m high. After how long will the balls
    be at the same height?

58. Two students are on a balcony 19.6m above the street. One student throws a ball
    vertically down at 14.7 m/s; at the same instant, the other student throws a ball vertically
    upward at the same speed. The second ball just misses the balcony on the way down. (a)
    What is the difference in the two balls’ time in the air? (b) What is the velocity of each
    ball as it strikes the ground? (c) How far apart are the balls .8s after they are thrown?
                                            CHAPTER 3

Chapter 3 Homework
   18. The helicopter view in figure P3.18 shows two people pulling on a stubborn mule. Find
       (a) the single force that is equivalent to the two forces shown and (b) the force that a
       third person would have to exert on the mule to make the net force equal to zero. The
       forces are measured in units of newtons (N).

   24. A student stands at the edge of a cliff and throws a stone horizontally over the edge with
       a speed of 18 m/s. The cliff is 50 m above a flat, horizontal beach, as shown below.
       How long after being released does the stone strike the beach below the cliff? With what
       speed and angle of impact does the stone land?

   29. A brick is thrown upward from the top of a building at an angle of 25 degrees to the
       horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall
       is the building?

   31. A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24
      degrees below the horizontal. The negligent driver leaves the car in neutral, and the
      emergency brakes are defective. The car rolls from rest down the incline with a constant
      acceleration of 4.00 m/s² for a distance of 50.0 m to the edge of the cliff, which is 30 m
      above the ocean. Find (a) the cars position relative to the base of the cliff when the car
      lands in the ocean, and (b) the length of time the cat is in the air.

   33. A projectile is launched with an initial speed of 60 m/s at an angle of 30 degrees above
      the horizontal. The projectile lands on a hillside 4s later. Neglect air friction. (a) what is
      the projectile’s velocity at the highest point of its trajectory? (b) what is the straight line
      distance from where the projectile was launched to where it hits its target?

   49. A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed
       of 100 m/s. The rocket moves for 3s along its initial line of motion with an acceleration
       of 30 m/s². At this time, its engines fail and the rocket proceeds to move as a projectile.
       Fine (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c)
       its horizontal range.

   55. A home run is hit in such a way that the baseball just clears a wall 21m high, located 120
       m from home plate. The ball is hit at an angle of 35 degrees to the horizontal and air
       resistance in negligible. Fine (a) the initial speed of the ball, (b) the time is takes the ball
       to reach the wall, and (c) the velocity components and the speed of the ball when it
       reaches the wall. (Assume that the ball is hit at a height of 1.0m above the ground.)
56. A ball is thrown straight upward and returns to the thrower’s hand after 3s in the air. A
    second ball is thrown at an angle of 30 degrees with the horizontal. At what speed much
    the second ball be thrown so that it reaches the same height as the one thrown vertically?

57. A quarterback throws a football toward a receiver with an initial speed of 20m/s at an
    angle of 30 degrees above the horizontal. At that instant, the receiver is 20m from the
    quarterback. In what direction and with what constant speed should the receiver run in
    order to catch the football at the level at which it was thrown?

58. A 2.00m-tall basketball player is standing on the floor 10m from the basket. If he shoots
     the ball at a 40 degree angle with the horizontal, at what initial speed must he throw the
    basketball so that it goes through the hoop without striking the backboard? The height of
                                   Chapter 4 Homework

16. Find the tension in the two wires that support the 100 N light fixture in the figure.

20. Two people are pulling a boat through the water as in the figure. Each exerts a force of
    600 N directed at a 30 degree angle relative to the forward motion of the boat. If the
    boat moves with constant velocity, find the resistive force exerted by the water on the

26. Two packing crates of masses 10 kg and 5 kg are connected by a light string that passes
    over a frictionless pulley as shown in the figure. The 5 kg crate lies on a smooth incline
    of angle 40 degrees. Find the acceleration of the 5 kg crate and the tension in the string.

30. An object with a mass m1=5 kg rests on a frictionless horizontal table and is connected
    to a cable that passes over a pulley and is then fastened to a hanging object with mass
    m2=10 kg, as shown in the figure. Find the acceleration of each object the the tension in
    the cable.

34. Two objects with masses of 3 kg and 5 kg are connected by a light string that passes over
    a frictionless pulley, as in the figure. Determine (a) the tension in the string, (b) the
    acceleration of each object, and (c) the distance each object will move in the first second
    of motion if both objects start from rest.

41. The coefficient of static friction between the 3 kg crate and the 35 degree incline of the
    figure is .3. What minimum force must be applied to the crate perpendicular to the
    incline to prevent the crate from sliding down the incline?

49. Find the acceleration reached by each of the two objects shown in the figure if the
    coefficient of kinetic friction between the 7 kg object and the plane is .25.

50. A 2 kg black is held in equilibrium on an incline of angle 60 degrees by a horizontal
    force applied in the direction shown in the figure. If the coefficient of static friction
    between the block and the incline is .3, determine (a) the minimum value of the force
    pushing the block, and (b) the normal force exerted by the incline on the block.
55. What is the resultant force exerted by the 2 cables supporting the traffic light in the
    figure? What is the weight of the light?

58. (a) What is the minimum force of friction required to hold the system if the figure in
    equilibrium? (b) What coefficient of static friction between the 100N block and the table
    ensures equilibrium? (c) If the coefficient of kinetic friction between the 100N block and
    the table is .25, what hanging weight should replace the 50 N weight to allow the system
    to move at a constant speed one it is set in motion?
                                       Chapter 5 Homework

13. A 70-kg base runner begins his slide into second base when he is moving at a speed of 4 m/s.
    The coefficient of friction between his clothes and the earth is .70. He slides so that his
    speed is zero just as he reaches the base. (a) how much mechanical energy is lost due to
    friction acting on the runner? (b) How far does he slide?

15. A 2-kg bullet leaves the barrel of a gun at a speed of 300 m/s. (a) Find its kinetic energy. (b)
    Find the average force exerted by the expanding gases on the bullet as it moves the length
    of the 50 cm long barrel.

17. A 2000 kg car moves down a level highway under the actions of two forces: a 1000 N
    forward force exerted on the drive wheels by the road and a 950 N resistive force. Use the
    work energy theorem to find the speed of the car after it has moved a distance of 20m,
    assuming that it starts from rest.

25. The chin up is one exercise that can be used to strengthen the biceps muscle. This muscle
    can exert a force approximately 800N as it contracts a distance of 7.5cm in a 75kg male.
    How much work can the biceps muscles (one in each arm) perform in a single contraction?
    Compare this amount of work with the energy required to life a 75kg person 40cm in
    performing a chin up. Do you think the biceps muscle is the only muscle involved in
    performing a chin up?

28. A .400 kg bead slides on a curved wire, starting from rest at point A. If the wire is
    frictionless, find the speed of the bead at B and C.

32. Three objects with masses M1=5kg, M2=10kg, and M3=15kg, respectively, are attached by
    strings over frictionless pulleys. The horizontal surface is frictionless and the system is
    released from rest. Using energy concepts, find the speed of M3 after it moves down a
    distance of 4.0m.

33. The launching mechanism of a toy gun consists of a spring of unknown spring constant. If
    the spring is compressed a distance of .120m and the gun fired vertically, the gun can
    launch a 20g projectile from rest to a max height of 20m above the starting point of the
    projectile. Neglecting all resistance of forces, determine (a) the spring constant, and (b) the
    speed of the projectile as it moves through the equilibrium position of the spring (where
42. A 25 kg child on a 2m long swing is released from rest when the ropes of the swing make an
    angle of 30 degrees with the vertical. (a) neglecting friction, find the child’s speed at the
    lowest position. (b) If the actual speed of the child at the lowest point is 2m/s, what is the
    mechanical energy lost due to friction?

63. Two objects are connected by a light string passing over a light, frictionless pulley. The 5
    kg object is released from rest at a point 4m above the floor. (a) Determine the speed of
    each object at the moment the 5kg object hits the floor. (b) How much higher does the 3kg
    object travel after the 5kg object hits the floor?

64. Two blocks, A and B (with mass 50kg and 100kg respectively) are connected by a string.
    The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between
    Block A and the incline is .25. Determine the change in the kinetic energy of block A as it
    moves from C to D, a distance of 20m up the incline if the system starts from rest.

 31. Tarzan swings on a 30m vine initially inclined at an angle of 37 degrees with the vertical.
   What is his speed at the bottom of the swing (a) if he starts from rest? (b) If he pushes off
                                         Chapter 6 Homework

15. The front 1.20m of a 1400kg car is designed as a “crumple zone” that collapses to absorb the
shock of a collision. If a car traveling 25m/s stops uniformly in 1.2m (a) how long does the
collision last, (b) what is the magnitude of the average force on the car, (c) what ids the
acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.

22. A 65kg person throws a .045 0-kg snowball forward with a ground speed of 30m/s. a second
person, with a mass of 60 kg catches the snowball. Both people are on skates. The first person
is initially moving forward at a speed of 2.5 m/s, and the second person is initially at rest. What
are the velocities of the two people after the snowball is exchanged? Disregard friction between
skates and the ice.

28. A 7g bullet is fired into a 1.5kg ballistic pendulum. The bullet emerges from the block with a
speed of 200 m/s, and the block rises to a maximum height of 12cm. Find the initial speed of the

30. An 8g bullet is fired into a 250g block that is initially at rest at the edge of a table with a
height of 1m. The bullet remains in the block, and after the impact the block lands 2m from the
bottom of the table. Determine the initial speed of the bullet.

35. A 5g object moving to the right at 20cm/s makes an elastic head on collision with a 10g
object that is initially at rest. Find (a) the velocity of each object after the collision and (b) the
fraction of the initial kinetic energy transferred to the 10g object.

52. A .4kg green bead slides on a curved frictionless wire, starting from rest at Point A. At Point
B, the bead collides elastically with a .6kg blue ball at rest. Find the maximum height the blue
ball rises as it moves up the wire.

56. Two blocks of masses m1 = 2 kg and m2= 4kg are each released from rest at a height of 5m
on a frictionless track, and undergo an elastic head on collision (a) determine the velocity of each
block just before the collision and (b) determine the velocity of each block immediately after the
collision and (c) determine the maximum heights to which m1 and m2 rise after the collision.

57. A .5kg block is released from rest at the top of a frictionless track 2.5m above the top of the
table. It them collides elastically with a 1kg object that is initially at rest on the table. (a)
Determine the velocities of the two objects just after the collision. (b) How high up the track
does the .5 kg object travel back after the collision? (c) How far away from the bottom of the
table does the 1kg object land, given that the table is 2m high? (d) How far away from the
bottom of the table does the .5kg object eventually land?
59. A small block of mass m1= .5kg is released from rest from the top of a curved wedge of mass
m2=3kg, which sits on a frictionless horizontal surface. When the block leaves the wedge, its
velocity is measured to be 4m/s to the right. (a) what is the velocity of the wedge after the block
reaches the horizontal surface? (b) What is the height h of the wedge?

60. Two carts of equal mass m= .25kg are placed on a frictionless track that has a light spring of
force constant k= 50N/m attached to one end of it. The red cart is given an initial velocity of
3m/s to the right and the blue cart is initially at rest. If the carts collide elastically find (a0 the
velocity of the carts just after the first collision and (b) the maximum compression of the spring.
Chapter 7 Homework
7. A machine part rotates at an angular speed of 60rad/s; its speed is then increased to 2.2 rad/s
at am angular acceleration of .7rad/s². Find the angle through which the part rotates before
reaching this final speed.

17. (a) What is the tangential acceleration of a bug on the rim of a 10in diameter disk if the disk
moves from rest to an angular speed of 78 rev/min in 3s? (b) When the disk is at its final speed,
what is the tangential velocity of the bug? (c) One second after the bug starts from rest, what are
its tangential acceleration, centripetal acceleration, and total acceleration?

18. A race car starts from rest on a circular track of radium 400m. The car’s speed increases at a
constant rate of .5m/s². At the point where the magnitudes of the centripetal and tangential
accelerations are equal, determine (a) the speed of the race car, (b) the distance traveled, and (c)
the elapsed time.

23. A 50 kg child stands at the rim of a merry go round of radius 2m, rotating with an angular
speed of 3rad/s. (a) What is the child’s centripetal acceleration? (b) What is the minimum force
between the feet and the floor of the carousel that is required to keep the child in a circular path?
(c) What minimum coefficient of static friction is required? Is the answer you found reasonable?
In other words is she likely to stay on the merry go round?

26. Tarzan (m=85kg) tries to cross a river by swinging from a 10m long vine. His speed at the
bottom of the swing (as he just clears the water) is 8m/s. Tarzan doesn’t know that the vine has a
breaking strength of 1000N. Does he make it safely across the river? Justify your answer.

27. A 40kg child takes a ride on a ferris wheel that rotates 4 times each minute and has a
diameter of 18m. (A) what is the centripetal acceleration of the child? (B) What force
(magnitude and direction) does the seat exert on the child at the lowest point of the ride? (C)
What force does the seat exert on the child at the highest point of the ride? (D) What force does
the seat exert on the child when the child is halfway between the top and the bottom?
28. A roller coaster vehicle has a mass of 500kg when fully loaded with passengers. (A) if the
vehicle has a speed of 20m/s at point A, what is the force of the track on the vehicle at this point?
(B) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on
the track?

48. A .4kg pendulum bob passes through the lowest part of its path at a speed of 3m/s. (A) what
 is the tension in the pendulum cable at this point if the pendulum is 80 cm long? (B) When the
pendulum reaches its highest point, what angle does the cable make with the vertical? (C) What
                                       Chapter 8 Homework

2. A steel band exerts a horizontal force of 80N on a tooth at point B. What is the torque on the
root of the tooth about point A?

33. A cylindrical fishing reel has a moment of inertia I=6.8x10^-4 kgm² and a radius of 4cm. A
friction clutch in the reel exerts a restraining torque of 1.3Nm if a fish pulls on the line. The
fisherman gets a bite, and the reel begins to spin at an angular acceleration of 66rad/s². (A) What
is the force exerted by the fish on the line? (B) How much line unwinds in .5s?

36. A 5kg cylindrical reel with a radius of .6m and a frictionless axle start from rest and speeds
up uniformly as a 3kg bucket falls into a well, making a light rope unwind from the reel. The
bucket starts from rest and falls for 4s. (A) What is the linear acceleration of the falling bucket?
(B) How far does it drop? (C) What is the angular acceleration of the reel?

37. An airliner lands with a speed of 50m/s. Each wheel of the plane has a radius of 1.25 m and
a moment of inertia of 110 kgm². At touchdown, the wheels begin to spin under the action of
friction. Each wheel supports a weight of 1.4x10^4N, and the wheels attain their angular speed
in .48s while rolling without slipping. What is the coefficient of kinetic friction between the
wheels and the runway? Assume that the speed of the plane is constant.

44. A 240 N sphere .2m in radius rolls without slipping 6m down a ramp that is incline at 37
degrees with the horizontal. What is the angular speed of the sphere at the bottom of the slope if
it starts from rest?

49. A solid, horizontal cylinder of mass 10 kg and radius 1m rotates with an angular speed of
7rad/s about a fixed vertical axis through its center. A .25kg piece of putty is dropped vertically
onto the cylinder at a point .9m from the center of rotation and sticks to the cylinder. Determine
the final angular speed of the system.

  60. A 12 kg object is attached to a cord that is wrapped around a wheel of radius 10cm. The
 acceleration of the object down the frictionless incline is measured to be 2m/s². Assuming the
  axle of the wheel to be frictionless, determine (A) the tension in the rope (B) the moment of
 inertia of the wheel, and (C) the angular speed of the wheel 2s after it begins rotating, starting
                                       Chapter 9 Homework

24. Piston 1 in the figure has a diameter of .25 in; piston 2 has a diameter of 1.5in. In the
absence of friction, determine the force necessary to support the 500-lb weight.

35. A sample of an unknown material appears to weight 300N in air and 200N when immersed
in alcohol of specific gravity .7. What are (a) the volume, and (b) the density of the material?

36. An object weighing 300N in air is immersed in water after being tied to a string connected to
a balance. The scale now reads 265N. Immersed in oil, the object appears to weigh 275N. Find
(a) the density of the object and (b) the density of the oil.

39. A 1.00kg beaker containing 2.00kg of oil (density = 916 kg/m³) rests on a scale. A 2.00kg
block of iron is suspended from a spring scale and is completely submerged in the oil. Find the
equilibrium readings of both scales.

43. A hypodermic syringe contains a medicine with a density of water. The barrel of the syringe
has a cross sectional area of 2.5 x 10^-5 m². In the absence of a force on the plunger, the
pressure everywhere is 1.00 atm. A force of magnitude 2.00N is exerted on the plunger, making
medicine squirt from the needle. Determine the medicine’s flow speed through the needle.
Assume that the pressure in the needle remains equal to 1.00atm and that the syringe is

45. A jet of water squirts out horizontally from a hole near the bottom of the take. If the hole
has a diameter of 3.5 mm, what is the height of the water level in the tank?

  47. The inside diameters of the larger portions of the horizontal pipe in the figure are 2.5 cm.
   Water flows to the right at a rate of 1.8 x 10^-4 m³/s. Determine the inside diameter of the
                                     Chapter 10 Homework

10. A cylindrical brass sleeve is to be shrink-fitted over a brass shaft whose diameter is 3.212
cm at 0 degrees Celsius. The diameter of the sleeve is 3.196 cm at 0 degrees Celsius. (a) To
what temperature must the sleeve be heated before it will slip over the shaft? (b) Alternatively,
to what temperature must the shaft be cooled before it will slip into the sleeve?

11. The New River George bridge in West Virginia is a 518m long steel arch. How much will
its length change between temperature extremes of -20 degrees Celsius and 35 degrees Celsius?

13. A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion = 1.20 x
10^-4 Π˚C ^-1). At room temperature (20 degrees C), the frames have circular lens holes 2.20
cm in radius. To what temperature must the frames be heated if lenses 2.21cm in radius are to be
inserted into them?

15. A brass ring of diameter 10.00 cm at 20 degrees C is heated and slipped over an aluminum
rod of diameter 10.01 cm at 20 degrees C. Assuming the average coefficients of linear
expansion are constant, (a) to what temperature must the combination be cooled to separate the
two metals? Is that temperature attainable? (b) What id the aluminum rod were 10.02 cm in

20. The Trans-Alaskan pipeline is 1300km long, reaching from Prudhoe Bay to the port of
Valdez, and is subject to temperatures ranging from -73 degrees C to +35 degrees C. How much
does the steel pipeline expand due to the different in temperature? How can this expansion be
compensated for?

21. An automobile fuel tank is filled to the brim with 45 L (12 gal) of gasoline at 10 degrees C.
Immediately after, the vehicle is parked in the sunlight, where the temperature is 35 degrees C.
    How much gasoline overflows from the tank as a result of the expansion? (Neglect the
                                      Chapter 11 Homework

11. A 200g aluminum cup contains 800g of water in thermal equilibrium with the cup at 80
degrees C. The combination of cup and water is cooled uniformly so that the temperature
decreases by 1.5 degrees C per minute. At that rate is energy being removed? Express your
answer in watts.

16. It is desired to cool iron parts from 500 degrees F to 100 degrees F by dropping them into
water that is initially 75 degrees F. Assuming that all the heat from the iron is transferred to the
water and that none of the water evaporated, how many kilograms of water are needed per
kilogram of iron?

17. A 100g aluminum calorimeter contains 250g of water. The two substances are in thermal
equilibrium at 10 degrees C. Tow metallic blocks are placed in the water. One is a 50g piece of
copper at 80 degrees C. The other sample has a mass of 70g and is originally at a temperature of
100 degrees C. The entire system stabilizes at a final temperature of 20 degrees C. Determine
the specific heat of the unknown second sample.

19. A student drops to metallic objects into a 120 g steel container holding 150 g of water at 25
degrees C. One object is a 200g cube of copper that is initially at 85 degrees C, and the other is a
chunk of aluminum that is initially at 5 degrees C. To the surprise of the student, the water
reaches a final temperature of 25 degrees C, precisely where it started. What is the mass of the
aluminum chunk?

26. When you jog, most of the food energy you burn above your Basal Metabolic Rate (BMR)
ends up as internal energy that would raise your body temperature if it were not eliminated. The
evaporation of perspiration is the primary mechanism for eliminating this energy. Determine the
amount of water you lose to evaporation when running for 30 minutes at a rate that uses
400kcal/h above your BMR. (That amount is often considered to be the “maximum-fat-burning”
energy output.) The metabolism of 1g of fat generates approximately 1g of water. (The
hydrogen atoms in the fat molecule are transferred to oxygen to form water.) What fraction of
your need for water will be provided by fat metabolism? (The latest heat of vaporization of
water at room temperature is 2.5 x 10^6 J/kg).

27. A 40g black of ice is cooled to -78 degrees C and is then added to 560g of water in an 80g
copper calorimeter at a temperature of 25 degrees C. Determine the final temperature of the
system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how
much ice is left.) Remember that the ice must first warm to 0 degrees C, melt, and then continue
warming as water. The specific heat of ice is .5 cal/g·˚C = 2090 J/kg·˚C.
51. A 40g ice cube floats in 200g of water in a 100g copper cup; all are at a temperature of 0
degrees C. A piece of lead at 98 degrees C is dropped into the cup, and the final equilibrium
temperature is 12 degrees C. What is the mass of the lead?

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