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356 CHAPTER 11 Collisions

3. The photographs in Fig. 11.1 show the impact of an automo- 9. Assume that the Super Ball of Example 3 has a mass of 60 g
bile on a rigid wall. and is initially traveling with speed 15 m s. For simplicity,
(a) Measure the positions of the automobile on these photo- assume that the acceleration is constant while the ball is in
graphs and calculate the average velocity for each of the contact with the wall. After touching the wall, the center of
3
20 10 -s intervals between one photograph and the mass of the Super Ball moves 0.50 cm toward the wall, and
next; calculate the average acceleration for each time interval then moves the same distance away to complete the bounce.
from the change between one average velocity and the next. What is the impulse delivered by the wall? What is the time-
average force?
(b) The mass of this automobile is 1700 kg. Calculate the
average force for each time interval. 10. A 0.50-kg hammerhead moving at 2.0 m s strikes a board and
stops in 0.020 s. What is the impulse delivered to the board?
(c) Make a plot of this force as a function of time and find the
What is the time-average force?
impulse by estimating the area under this curve.
11. A soccer player applies an average force of 180 N during a
4. The “land divers” of Pentecost Island (Vanuatu) jump from
kick. The kick accelerates a 0.45-kg soccer ball from rest to a
platforms 21 m high. Long liana vines tied to their ankles jerk
speed of 18 m s. What is the impulse imparted to the ball?
them to a halt just short of the ground. If the pull of the liana
What is the collision time?
takes 0.020 s to halt the diver, what is the average acceleration
of the diver during this time interval? If the mass of the diver is 12. When an egg (m 50 g) strikes a hard surface, the collision
64 kg, what is the corresponding average force on his ankles? lasts about 0.020 s. The egg will break when the average force
during impact exceeds 3.0 N. From what minimum height
5. A shotgun fires a slug of lead of mass 28 g with a muzzle velocity
will a dropped egg break?
of 450 m s.The slug acquires this velocity while it accelerates
along the barrel of the shotgun, which is 70 cm long. *13. The net force on a body varies with time according to F
x
2
3.0t 0.5t , where F is in newtons and t is in seconds. What
(a) What is the impulse the shotgun gives the slug? x
is the impulse imparted to the body during the time interval
(b) Estimate the average impulsive force; assume constant 0 t 3.0 s?
acceleration of the slug along the barrel.
*14. Suppose that in a baseball game, the batter succeeds in hitting
6. A rule of thumb for automobile collisions against a rigid bar- the baseball thrown toward him by the pitcher. Suppose that
rier is that the collision lasts about 0.11 s, for any initial speed just before the bat hits, the ball is moving toward the batter
and for any model of automobile (for instance, the collision horizontally with a speed of 35 m s; and that after the bat has
illustrated in Fig. 11.1 lasted 0.120 s, in rough agreement with hit, the ball is moving away from the batter and upward at an
this rule of thumb). Accordingly, the deceleration experienced angle of 50 and finally lands on the ground 110 m away. The
by an automobile during a collision is directly proportional to mass of the ball is 0.15 kg. From this information, calculate
the change of velocity v (with a constant factor of propor- the magnitude and direction of the impulse the ball receives in
tionality), and therefore v can be regarded as a measure of the collision with the bat. Neglect air friction and neglect the
the severity of the collision. initial height of the ball above the ground.
(a) If the collision lasts 0.11 s, what is the average decelera- *15. Bobsleds racing down a bobsled run often suffer glancing col-
tion experienced by an automobile in an impact on a rigid lisions with the vertical walls enclosing the run. Suppose that a
barrier at 55 km h? 65 km h? 75 km h? bobsled of 600 kg traveling at 120 km h approaches a wall at
(b) For each of these speeds, what is the crush distance of the an angle of 3.0 and bounces off at the same angle. Subsequent
front end of the automobile? Assume constant decelera- inspection of the wall shows that the side of the bobsled made
tion for this calculation. a scratch mark of length 2.5 m along the wall. From these
(c) For each of these speeds, what is the average force the seat data, calculate the time interval the bobsled was in contact
belt must exert to hold a driver of 75 kg in his seat during with the wall, and calculate the average magnitude of the force
the impact? that acted on the side of the bobsled during the collision.
7. Suppose that a seat-belted mother riding in an automobile 11.2 Elastic Collisions in One Dimension †
holds a 10-kg baby in her arms. The automobile crashes and
decelerates from 50 km h to 0 in 0.10 s. What average force 16. A particle moving at 10 m s along the x axis collides elastically
would the mother have to exert on the baby to hold it? Do you with another particle moving at 5.0 m s in the same direction
think she can do this? along the x axis. The particles have equal masses. What are
8. In a test, an air force volunteer belted in a chair placed on a their speeds after this collision?
rocket sled was decelerated from 143 km h to 0 in a distance 17. In a lecture demonstration, two masses collide elastically on a
of 5.5 m. Assume that the mass of the volunteer was 75 kg, a frictionless air track. The moving mass (projectile) is 60 g,
and assume that the deceleration was uniform. What was the
deceleration? What impulse did the seat belt deliver to the † For help, see Online Concept Tutorial 13 and 14 at
volunteer? What time-average force did the seat belt exert? www.wwnorton.com/physics