Page 160 - Fisika Terapan for Engineers and Scientists

360 CHAPTER 11 Collisions

*49. Regard the two automobiles described in Example 7 as a of mass 15 g fired into a block of 4.0 kg sitting on a 1.8-m
system of two particles. fence causes the block to land 1.4 m from the bottom of the
fence. Calculate the speed of the bullet.
(a) What is the translational kinetic energy of the center of
mass before the collision? After the collision?
(b) What is the total kinetic energy before the collision? After 11.4 Collisions in Two and
the collision? Three Dimensions
*50. A cat crouches on the floor, at a distance of 1.2 m from a desk
chair of height 0.45 m. The cat jumps onto the chair, landing 56. A cheetah intercepts a gazelle on the run, and grabs it (a totally
with zero vertical velocity (this is standard procedure for cat inelastic collision). Just before this collision, the gazelle was
jumps). The desk chair has frictionless coasters and rolls away running due north at 20 m s, and the cheetah was running on
when the cat lands. The mass of the cat is 4.5 kg, and the mass an intercepting course of 45 east of north at 22 m s.The mass
of the chair is 12 kg. What is the speed of recoil of the chair of the cheetah is 60 kg, and the mass of the gazelle is 50 kg.
and cat? What are the magnitude and the direction of the velocity of
the entangled animals at the instant after the collision?
*51. A crude but simple method for measuring the speed of a
bullet is to shoot the bullet horizontally into a block of wood 57. Two hydrogen atoms (m 1.0 u) with equal speeds, initially
resting on a table. The block of wood will then slide until its traveling in perpendicular directions, collide and join together
22
kinetic energy is expended against the friction of the surface to form a hydrogen molecule. If 6.1 10 J of the initial
of the table. Suppose that a 3.0-kg block of wood slides a kinetic energy is transferred to internal energy in the collision,
distance of 6.0 cm after it is struck by a bullet of 12 g. If the what was the initial speed of the atoms?
coefficient of sliding friction for the wood on the table is *58. Two automobiles of equal masses collide at an intersection.
0.60, what impact speed can you deduce for the bullet? One was traveling eastward and the other northward. After
*52. Another way (not recommended) to measure the speed of the collision, they remain joined together and skid, with
bullets with a ballistic pendulum is to shoot a steady stream of locked wheels, before coming to rest. The length of the skid
bullets into the pendulum, which will push it aside and hold marks is 18 m, and the coefficient of friction between the
it in a rough equilibrium position at some angle. The speed locked wheels and the pavement is 0.80. Each driver claims
can be calculated from this equilibrium angle. Suppose that his speed was less than 14 m s (50 km h) before the collision.
you shoot .22-caliber bullets of mass 15 g into a 4.0-kg ballis- Prove that at least one driver is lying.
tic pendulum at the rate of 2 per second. You find that the *59. Two hockey players (see Fig. 11.17) of mass 80 kg collide
equilibrium angle is 24 . What is the speed of the bullets? while skating at 7.0 m s. The angle between their initial direc-
*53. You shoot a .22-caliber bullet through a piece of wood sitting tions of motion is 130 .
on a table. The piece of wood acquires a speed of 8.0 m s, and (a) Suppose that the players remain entangled and that the
the bullet emerges with a reduced speed. The mass of the collision is totally inelastic. What is their velocity immedi-
bullet is 15 g, and its initial speed is 600 m s; the mass of the ately after collision?
piece of wood is 300 g. (b) Suppose that the collision lasts 0.080 s. What is the mag-
(a) What is the change of velocity of the bullet? nitude of the average acceleration of each player during
(b) What is the change of kinetic energy of the bullet? the collision?
(c) What is the change of kinetic energy of the wood?
(d) Account for the missing kinetic energy.
*54. An automobile traveling at 50 km h strikes the rear of a
parked automobile. After the collision, the two automobiles
remain joined together. The parked automobile skids with all
its wheels locked, but the other automobile rolls with negligi-
ble friction. The mass of each automobile is 1300 kg, and the
coefficient of sliding friction between the locked wheels and
the pavement is 0.90. How far do the joined automobiles
move before they stop? How long do they take to stop?
*55. You can make a fairly accurate measurement of the speed of a
bullet by shooting it horizontally into a block of wood sitting
on a fence. The collision of the bullet and the block is inelas-
tic, and the block will fall off the fence and land on the ground
at some distance from the bottom of the fence. The speed of
the bullet is proportional to this distance. Suppose that a bullet FIGURE 11.17 Collision of two hockey players.