Review Problems

REVIEW PROBLEMS aircraft is effectively in free fall.

80. An apple falls down 35 m from the fifth floor of an apartment 88. In a roller coaster, a car starts from rest on the top of a 30-m- building to the street. The mass of the apple is 0.20 kg. How high mountain. It rolls down into a valley, and then up a 20- much work does gravity do on the apple during this fall? m-high mountain. What is the speed of the car at the bottom of the valley, at ground level? What is the speed of the car at the top of the second mountain? 81. A woman pulls a sled by a rope. The rope makes an upward angle of 45° with the ground, and the woman exerts a pull of 89. In a compound bow (see Fig. 7.37), the pull of the limbs of the bow is 150 N on the rope. How much work does the woman do if she communicated to the arrow by an arrangement of strings and pulleys that pulls this sled 20 m? ensures that the force of the string against the arrow remains roughly constant while you pull the arrow back in preparation for letting it fly (in 82. A man pushes a crate along a flat concrete floor. The mass of the an ordinary bow, the force of the string increases as you pull back, which makes it difficult to continue pulling). A typical compound bow provides crate is 120 kg, and the coefficient of friction between the crate a steady force of 300 N. Suppose you pull an arrow of 0.020 kg back 0.50 m against this force. and the floor is µk = 0.50. How much work does the man do if, (a) What is the work you do? pushing horizontally, he moves the crate 15 m at constant speed? (b) When you release the arrow, what is the kinetic energy with which it

leaves the bow? 83. A 1500-kg automobile is traveling at 20 m/s on a level road. (c) What is the speed of the arrow? How much work must be done on the automobile to accelerate (d) How far will this arrow fly when launched with an elevation angle of it from 20 m/s to 25 m/s? From 25 m/s to 30 m/s? 45°? Ignore friction and assume that the heights of the launch and impact points are the same. 84. A woman slowly lifts a 20-kg package of books from the floor (e) With what to a height ofl.8 m, and then slowly returns it to the floor. How speed will it hit the target? much work does she do on the package while lifting? How much work does she do on the package while lowering? What is the total work she does on the package? For the information given, can you tell how much work she expends internally in her muscles, that is, how many calories she expends?

85. An automobile of 1200 kg is traveling at 25 m/s when the driver suddenly applies the brakes so as to lock the wheels and cause the automobile to skid· to a stop. The coefficient of FIGURE 7.37 A compound bow. sliding friction between the tires and the road is 0.90. (a) What is the deceleration of the automobile, and what is the stopping distance? 90. A large stone-throwing engine designed by Archimedes could throw a 77-kg stone over a range of 180 m. Assume that the stone is thrown at an (b) What is the friction force of the road on the wheels, and initial angle of 45° with the horizontal. what is the amount of work that this friction force does during the stopping process? (a) Calculate the initial kinetic energy of this stone. (b) Calculate the kinetic energy of the stone at the highest point of its 86. A golf ball of mass 50 g released from a height of 1.5 m above a trajectory. concrete floor bounces back to a height of 1.0 m. (a) What is the kinetic energy of the ball just before contact 91. The luge track at Lillehammer, the site of the 1994 Olympics, starts at a

with the floor begins? Ignore air friction. height of 350 m and finishes at 240 m. Suppose that a luger of95 kg, (b) What is the kinetic energy of the ball just after contact including the sled starts from rest and reaches the finish at 130 km/h. with the floor ends? . How much energy has been lost to friction against the ice and the air? (c) What is the loss of energy during contact with the floor? 92. A pendulum consists of a mass m tied to one end of a string of length l. 87. A small aircraft of mass 1200 kg is cruising at 250 km/h at an The other end of the string is attached to a fixed point on the ceiling. altitude of 2000 m. Suppose that the pendulum is initially held at an angle of 90° with the (a) What is the gravitational potential energy (relative to the vertical. If the pendulum is released from this point, what will be the ground), and what is the kinetic energy of the aircraft? speed of the pendulum at the instant it passes through its lowest point? (b) If the pilot puts the aircraft into a dive, what will be the gravitational potential energy, what will be the kinetic What will be the tension in the string at this instant? energy, and what will be the speed when the aircraft reaches an altitude of 1500 m? Assume that the engine of the aircraft compensates the friction force of air, so the 93. A roller coaster near St. Louis is 34 m high at its highest point. (a) What is the maximum speed that the car can attain by rolling down from the highest point if initially at rest? Ignore friction. (b) Some people claim that cars reach a maximum speed of 100 km/h. If this is true, what must be the initial speed of the car at the highest point?

94. At a swimming pool, a water slide starts at a height of 6.0 m and ends at a height of 1.0 m above the water level with a short horizontal segment (see Fig. 7.38). A girl slides down the water slide. FIGURE 7.38 A water slide. (a) What is her speed at the bottom of the slide? (b) How far from the slide does she lands in the water?

95.94.