Chapter 7
Momentum and Collisions
Collisions
When two objects collide there are usually two things that happen with the kinetic energy. In elastic collisions the kinetic energy is conserved. On the other hand if the kinetic energy is not the same before and after then the collision is called inelastic.
Inelastic Collisions In an inelastic collision, the momentum of a system is conserved,
but its kinetic energy is not,
|
Completely Inelastic Collisions When objects stick together after colliding, the collision is completely inelastic. (In completely inelastic collisions, the maximum amont of kinetic energy is lost.) |
Elastic Collisions In an elastic collision, momentum and kinetic energy are conserved. That is,
and
|
Example 7-13
A 1200 kg car moving at 2.5 m/s is struck in the rear by a 2600 kg truck moving at 6.2 m/s. If the vehicles stick together after the collision, what is their speed immediately after colliding?
Example 7-14
A railroad car of mass m and speed v collides and sticks to an identical railroad car that is initially at rest. After the collision, is the kinetic energy of the system (a) 1/2, (b) 1/3, or (c) 1/4 of its initial kinetic energy?
Example 7-15
On a touchdown attempt, a 95.0 kg running back runs toward the end zone at 3.75 m/s. A 111 kg linebacker moving at 4.10 m/s meets the runner in a head-on collision. If the two players stick together, (a) what is their velocity immediately after the collision? (b) What are the initial and final kinetic energies of the system?
Example 7-16
A pitched 140 g baseball, in horizontal
flight with a speed 
of
39.0 m/s, is struck by a bat. After leaving the bat, the ball travels in the
opposite direction with speed 
,
also 39.0 m/s.
(a) What impulse acts on the ball while it is in contact with the bat during
the collision?
(b) The impact time 
for
the baseball-bat collision is 1.20 ms. What average force acts on the baseball?
(c) Now suppose the collision is not head-on, and the ball leaves the bat with
a speed of
45.0 m/s at an upward angle of 
.
What now is the impulse on the ball?
Example 7-17
In a ballistic pendulum, an object of mass
m is fired with an initial speed 
at
the bob of a pendulum. The bob has a mass M, and is suspended by a rod of negligible
mass. After the collision, the object and the bob stick together and swing
through an arc, eventually gaining a height h. Find the height h in terms of
m, M, ,
and g.
Example 7-18
The ballistic pendulum was used to measure the speeds of bullets before electronic timing devises were developed. The version shown in the figure consists of a large block of wood of mass M = 5.4 kg, hanging from two long cords. A bullet of mass m = 9.5 g is fired into the block, coming quickly to rest. The block +bullet then swing upward, their center of mass rising a vertical distance h = 6.3 cm before the pendulum comes momentarily to rest at the end of its arc. What is the speed of the bullet just prior to the collision?
Example 7-19
Two metal spheres, suspended by vertical
cords, initially just touch, as in the figure. Sphere 1, with mass 
,
is pulled to the left to height 
,
and then released from rest. After swinging down, it undergoes an elastic collision
with sphere 2, whose mass 
.
What is the velocity 
of
sphere 1 just after the collision?
Example 7-20
A car with a mass of 950 kg and a speed of 16 m/s approaches an intersection, as shown. A 1300 kg minivan traveling at 21 m/s is heading for the same intersection. The car and minivan collide and stick together. Find the speed and direction of the wrecked vehicles just after the collision, assuming external forces can be ignored.
Example 7-21
Two skaters collide and embrace, in a completely
inelastic collision. Thus, they stick together after impact, as in the figure,
where the origin is placed at the point of collision. Alfred, whose mass 
,
is originally moving east with speed 
.
Barbara, whose mass is 55 kg, is originally moving north with speed 
.
What is the velocity 
of
the couple after they collide?
Elastic Collisions
Example 7-22
At an amusement park, a 96.0 kg bumper car moving with a speed of 1.24 m/s bounces elastically off a 135 kg bumper car at rest. Find the final velocities of the cars.
Example 7-23
A hover fly is happily maintaining a fixed
position about 10 ft above the ground when an elephant charges our of the bush
and collides with it. The fly bounces elastically off the forehead of the elephant.
If the initial speed of the elephant is ,
is the speed of the fly after the collision equal to (a) , (b) 1.5,
or (c) 2?
On to the Practice Multiple Choice Problems
