### Conservation of Momentum

```Conservation of Momentum
Conservation of Momentum
• Allows us to determine what happens in
collisions or explosions
• The total momentum of all objects before a
collision must equal the total momentum
after the collision
*objects with the same
mass will exchange
velocities
Explosions
• Are a collision of sorts before the explosion
the momentum is often zero – the object is at
rest. Ex: firecrackers
• After the explosion, parts of the object go off
in different directions
*pay attention to the directions
1. A 31 kg swimmer runs with a horizontal velocity of 4 m/s off a boat dock into
a stationary 8 kg rubber raft. Find the velocity that the swimmer and raft would
have after the impact, if there were no friction or resistance due to the water.
2. A 275 kg bumper car containing one rider is traveling at 3.2 m/s when it
bumps a stationary car containing 2 riders (345 kg). The 275 kg car bounces
back with a speed of 1.7 m/s. What is the speed and direction of the 345 kg
car?
3. A 60 kg astronaut becomes separated in space from her spaceship. She is
15.0 m away from it and at rest relative to it. In an effort to get back, she
throws a 700-g wrench in a direction way from the ship with a speed of 8.0
m/s. How long does it take her to get back to the ship?
Ballistic Pendulum
Collision with a bullet and a pendulum
*find the final velocity of the bullet/pendulum with
conservation of momentum
*find the max. height reached with conservation of
energy
Ballistic Pendulum
4. A 0.05 kg bullet with a velocity of 150 m/s is shot into a 3 kg ballistic
pendulum initially at rest. Determine how high the pendulum rises after the
bullet is shot into it.
Elastic and Inelastic Collisions
Regardless of the type of collision the momentum
is always conserved
Inelastic Collisions
- a collision in which kinetic energy is lost
*KEbefore ≠ KEafter
- the KE lost is converted most often to
friction (thermal energy) or to the energy
to produce a sound or light
- often involve objects that stick together
Elastic and Inelastic Collisions
Elastic Collision
- when no kinetic energy is lost, the collision
is said to be perfectly elastic
- only in elastic collisions are both
momentum and kinetic energy are
conserved
*KEbefore = KEafter
- objects usually bounce off each other
* you must check KE values to determine
whether you have an inelastic or elastic
collision
5. A toy car (4 kg) is initially moving with a velocity of 2.0 m/s when it collides
with a 6 kg toy truck initially moving at -4.0 m/s. After the collision the toy
truck has a velocity of 0.8 m/s. What is the velocity of the car? Is the collision
6. A 15 kg medicine ball is thrown at a velocity of 5.5 m/s to a 60 kg person who is
at rest on the ice. The person catches the ball and they begin sliding across the
ice. Determine the velocity of the person/ball combination after the collision. Is
7. Several students are riding in bumper cars at an amusement park. The combined mass
of car A and its occupants is 250 kg. The combined mass of car B and its occupants is 200
kg. Car A is 15 m away from car B and moving to the right at 2.0 m/s, as shown, when the
driver decides to bump into car B, which is at rest.
• (a) Car A accelerates at 1.5 m/s2 to a speed of 5.0 m/s and then continues at constant
velocity until it strikes car B. Calculate the total time for car A to travel the 15 m.
(b) After the collision, car B moves to the right at a speed of 4.8 m/s.
i. Calculate the speed of car A after the collision
ii. Indicate the direction of motion of car A after the collision.
_________to the left
________to the right
_______None; car A is at rest
(c) Is this an elastic collision? ______yes
_______no