Page 159 - Fisika Terapan for Engineers and Scientists

Problems 359

besieged city and the enemy camp, he jumped on a cannonball *45. Two automobiles of 540 and 1400 kg collide head-on while
as it was being fired from the city, rode the cannonball toward moving at 80 km h in opposite directions. After the collision
the enemy camp, and then, in midair, jumped onto an enemy the automobiles remain locked together.
cannonball and rode back to the city. The collision of Münch- (a) Find the velocity of the wreck immediately after the collision.
hausen and the enemy cannonball must have been inelastic,
(b) Find the kinetic energy of the two-automobile system
since he held on to it. Suppose that his speed just before hit-
before and after the collision.
ting the enemy cannonball was 150 m s southward and the
speed of the enemy cannonball was 300 m s northward. The (c) The front end of each automobile crumples by 0.60 m
mass of Münchhausen was 90 kg, and the mass of the enemy during the collision. Find the acceleration (relative to the
cannonball was 20 kg. What must have been the speed just ground) of the passenger compartment of each automobile;
after the collision? Do you think he made it back to the city? make the assumption that these accelerations are constant
during the collision.
39. As described in Problem 6, the change of velocity v of an
automobile during a collision is a measure of the severity of *46. A speeding automobile strikes the rear of a parked automobile.
the collision. Suppose that an automobile moving with an ini- After the impact the two automobiles remain locked together,
tial speed of 15 m s collides with (a) an automobile of equal and they skid along the pavement with all their wheels locked.
mass initially at rest, (b) an automobile of equal mass initially An investigation of this accident establishes that the length of
moving in the opposite direction at 15 m s, or (c) a stationary the skid marks made by the automobiles after the impact was
rigid barrier. Assume that the collision is totally inelastic. 18 m; the mass of the moving automobile was 2200 kg and that
What is v in each case? of the parked automobile was 1400 kg, and the coefficient of
sliding friction between the wheels and the pavement was 0.95.
40. A 25-kg boy on a 10-kg sled is coasting at 3.0 m s on level ice
toward his 30-kg sister. The girl jumps vertically and lands on (a) What was the speed of the two automobiles immediately
her brother’s back. What is the final speed of the siblings and after impact?
sled? Neglect friction. (b) What was the speed of the moving automobiles before
41. A 75-kg woman and a 65-kg man face each other on a friction- impact?
less ice pond. The woman holds a 5.0-kg “medicine ball.” The *47. A proton of energy 8.0 10 13 J collides head-on with a
woman throws the ball to the man with a horizontal velocity proton at rest. How much energy is available for inelastic reac-
of 2.5 m s relative to the ice. What is her recoil velocity? What tions between these protons?
is the man’s velocity after catching the ball? The man then *48. According to test procedures laid down by the National
throws the ball horizontally to the woman at 3.0 m s relative Highway Traffic Safety Administration, a stationary barrier
to himself at the instant before release. What is his final veloc- (of very large mass) and a towed automobile are used for tests
ity? What is the woman’s final velocity after catching it? of front impacts (Fig. 11.16a), but a moving barrier of 1800 kg
42. A 16-u oxygen atom traveling at 600 m s collides head-on and a stationary, unbraked automobile are used for tests of rear
with another oxygen atom at rest. The two join and form an impacts (Fig. 11.16b). Explain how this test with the moving
oxygen molecule. With what speed does the molecule move? barrier and the stationary automobile could be replaced by an
What fraction of the original translational kinetic energy is equivalent test with a stationary barrier and an automobile
transferred to internal energy of the molecule? towed backward at some appropriate speed. If the automobile
*43. A circus clown in a cannon is shot vertically upward with an has a mass of 1400 kg and the moving barrier has a speed of 8
initial speed of 12 m s. After ascending 3.5 m, she collides km h, what is the appropriate equivalent speed of the moving
with and grabs a performer sitting still on a trapeze. They automobile towed backward to the stationary barrier? Assume
ascend together and then fall. What is their speed when they the collision is inelastic.
reach the original launch height? The clown and trapeze artist
(a)
have the same mass.
*44. As described in Problem 6, the change in velocity v of an
automobile during a collision is a measure of the severity of
the collision. For a collision between two automobiles of equal
masses, v has the same magnitude for each automobile. But
for a collision between automobiles of different masses, v is (b)
larger for the automobile of smaller mass. Suppose that an
automobile of 800 kg moving with an initial speed of 15 m s
collides with (a) an automobile of 1400 kg initially at rest, (b)
an automobile of 1400 kg initially moving in the opposite
direction at 15 m s, or (c) a stationary rigid barrier. Assume
that the collision is totally inelastic. What is v in each case FIGURE 11.16 (a) Test procedure for front impact.
for each participating automobile? (b) Test procedure for rear impact.