Page 33 - Fisika Terapan for Engineers and Scientists

Review Problems 233

*89. In a compound bow (see Fig. 7.37), the pull of the limbs of a luger of 95 kg, including the sled starts from rest and reaches
the bow is communicated to the arrow by an arrangement of the finish at 130 km/h. How much energy has been lost to
strings and pulleys that ensures that the force of the string friction against the ice and the air?
against the arrow remains roughly constant while you pull the *92. A pendulum consists of a mass m tied to one end of a string of
arrow back in preparation for letting it fly (in an ordinary bow, length l. The other end of the string is attached to a fixed
the force of the string increases as you pull back, which makes point on the ceiling. Suppose that the pendulum is initially
it difficult to continue pulling). A typical compound bow pro- held at an angle of 90 with the vertical. If the pendulum is
vides a steady force of 300 N. Suppose you pull an arrow of released from this point, what will be the speed of the pendu-
0.020 kg back 0.50 m against this force. lum at the instant it passes through its lowest point? What
(a) What is the work you do? will be the tension in the string at this instant?
(b) When you release the arrow, what is the kinetic energy *93. A roller coaster near St. Louis is 34 m high at its highest point.
with which it leaves the bow? (a) What is the maximum speed that the car can attain by
(c) What is the speed of the arrow? rolling down from the highest point if initially at rest?
(d) How far will this arrow fly when launched with an eleva- Ignore friction.
tion angle of 45 ? Ignore friction and assume that the (b) Some people claim that cars reach a maximum speed of
heights of the launch and impact points are the same. 100 km/h. If this is true, what must be the initial speed of
(e) With what speed will it hit the target? 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.
(a) What is her speed at the bottom of the slide?
(b) How far from the slide does she land in the water?

FIGURE 7.37 A compound bow. 6.0 m

*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 initial angle of 45 with the horizontal. 1.0 m
(a) Calculate the initial kinetic energy of this stone.
(b) Calculate the kinetic energy of the stone at the highest
point of its trajectory.
*91. The luge track at Lillehammer, the site of the 1994 Olympics,
FIGURE 7.38 A water slide.
starts at a height of 350 m and finishes at 240 m. Suppose that

Answers to Checkups

Checkup 7.1
2. For both the pushing and the pulling, the force is in the same
1. The normal force, which is perpendicular to the motion, does direction as the displacement (you push when the saw moves
no work. The weight of the roller-coaster car does negative forward and pull when the saw moves backward); thus, the
work as the car travels upward, and positive work as the car work is positive in both cases.
moves downward, since it has a component against or along 3. The dog’s pull is in the same direction as the displacement,
the motion, respectively. At the peak, the work done by the and thus does positive work on the woman. The woman’s pull
weight is zero, since the weight is then perpendicular to the is in the opposite direction to the displacement, and thus does
displacement. negative work on the dog.