Page 29 - Fisika Terapan for Engineers and Scientists

Problems 229

*31. Suppose that the force acting on a particle is a function of 36. The electron in a hydrogen atom has a speed of 2.2 10 m/s.
6
2
position; the force has components F 4x 1, F 2x, What is the kinetic energy of this electron?
y
x
F 0, where the force is measured in newtons and distance 37. The fastest skier is Graham Wilkie, who attained 212.52 km/h
z
in meters. What is the work done by the force if the particle
on a steep slope at Les Arcs, France. The fastest runner is
moves on a straight line from x 0, y 0, z 0 to x 2.0 m,
Robert Hayes, who briefly attained 44.88 km/h on a level
y 2.0 m, z 0?
track. Assume that the skier and the runner each have a mass
*32. A horse pulls a sled along a snow-covered curved ramp. Seen of 75 kg. What is the kinetic energy of each? By what factor is
from the side, the surface of the ramp follows an arc of a the kinetic energy of the skier larger than that of the runner?
circle of radius R (Fig. 7.31). The pull of the horse is always
38. The Skylab satellite disintegrated when it reentered the
parallel to this surface. The mass of the sled is m, and the
atmosphere. Among the pieces that crashed down on the surface
coefficient of sliding friction between the sled and the sur-
of the Earth, one of the heaviest was a lead-lined film vault of
face is . How much work must the horse do on the sled to 1770 kg that had an estimated impact speed of 120 m/s on the
k
pull it to a height (1 22 /2)R, corresponding to an angle
surface. What was its kinetic energy? How many kilograms of
of 45 along the circle (Fig. 7.31)? How does this compare
TNT would we have to explode to release the same amount of
with the amount of work required to pull the sled from the 6
energy? (One kilogram of TNT releases 4.6 10 J.)
same starting point to the same height along a straight ramp
39. An automobile of mass 1600 kg is traveling along a straight
inclined at 22.5 ?
road at 80 km/h.
(a) What is the kinetic energy of this automobile in the refer-
ence frame of the ground?
(b) What is the kinetic energy in the reference frame of a
motorcycle traveling in the same direction at 60 km/h?
(c) What is the kinetic energy in the reference frame of a
45° truck traveling in the opposite direction at 60 km/h?
40. According to statistical data, the probability that an occupant
R of an automobile suffers lethal injury when involved in a crash
is proportional to the square of the speed of the automobile. At
a speed of 80 km/h, the probability is approximately 3%. What
2 are the probabilities at 95 km/h, 110 km/h, and 125 km/h?
(1 – — ) R
2
41. For the projectile described in Problem 47 of Chapter 2, cal-
culate the initial kinetic energy (t 0) and calculate the final
kinetic energy (t 3.0 s). How much energy does the projec-
FIGURE 7.31 A horse pulling a sled tile lose to friction in 3.0 s?
along a curved ramp. 42. Compare the kinetic energy of a 15-g bullet fired at 630 m/s
with that of a 15-kg bowling ball released at 6.3 m/s.
43. Compare the kinetic energy of a golf ball (m 45 g) falling
**33. The force between two inert gas atoms is often described by a
at a terminal velocity of 45 m/s with that of a person (75 kg)
function of the form
walking at 1.0 m/s.
F Ax 13 Bx 7 44. A child’s toy horizontally launches a 20-g ball using a spring
x
that was originally compressed 8.0 cm. The spring constant is
where A and B are positive constants and x is the distance 30 N/m. What is the work done by the spring moving the ball
between the atoms. Answer in terms of A and B. from its compressed point to its relaxed position, where the
(a) What is the equilibrium separation? ball is released? What is the kinetic energy of the ball at
launch? What is the speed of the ball?
(b) What is the work done if the atoms are moved from their
equilibrium separation to a very large distance apart? 45. A mass of 150 g is held by a horizontal spring of spring
constant 20 N/m. It is displaced from its equilibrium position
and released from rest. As it passes through equilibrium, its
7.3 Kinetic Energy speed is 5.0 m/s. For the motion from the release position to
the equilibrium position, what is the work done by the spring?
34. In a serve, a champion tennis player sends the ball flying at What was the initial displacement?
160 km/h. The mass of the ball is 60 g. What is the kinetic 46. A 60-kg hockey player gets moving by pushing on the rink
energy of the ball? wall with a force of 500 N. The force is in effect while the
35. Calculate the kinetic energy that the Earth has owing to its skater extends his arms 0.50 m. What is the player’s kinetic
motion around the Sun. energy after the push? The player’s speed?