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Conservation of Momentum
In all situations, momentum is _conserved !
Example: Think of the game of pool. When a stationary ball is hit by a moving ball, the momentum of the moving
ball is transferred to the stationary ball, which continues on in the same direction and velocity as the first ball. As it
turns out, the momentum the first ball loses is exactly equal to the momentum the second ball gains
The two cases of things colliding involve:
1. Things that bounce off of each other (elastic collision)
m1v1i + m2v2i = m1v1f + m2v2f
(the momentum of the 1st object PLUS the momentum of the 2nd object before they hit MUST BE EQUAL
to the momentum of the 1st object PLUS the momentum of the 2nd object after they hit)
2. Things that stick together after they hit, or are stuck together before they separate (inelastic collisions)
m1v1i + m2v2i = (m1 + m2)vf
OR
(m1 + m2)vi = m1v1f + m2v2f
(notice that when the things are stuck together, it is like they are ONE TOTAL mass with ONE TOTAL velocity)
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Momentum is conserved in __collisions__ which means that total momentum remains constant
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Momentum is also conserved for objects _pushing_ _away_ from each other.
Practice Problem #1 A 3500 kg truck slams into the back of a 1500 kg parked car with a velocity of 14.3 m/s. The truck
comes to a halt. What is the car’s velocity after the collision?
Given:
m1 = 3500 kg
m2 = 1500 kg
NOTICE: it is implying that the cars velocity is NOT
v1i = 14.3 m/s
v1f = 0 m/s
the same as the truck’s velocity after they hit, so they
v2i = 0 m/s
v2f = ?
must have BOUNCED off of each other!
Choose the equation:
m1v1i + m2v2i = m1v1f + m2v2f
Substitute the values:
(3500 kg)(14.3 m/s) + (1500 kg)(0 m/s) = (3500 kg)(0 m/s) + (1500 kg) (v2f)
50,050 =
(1500 kg) (v2f)
v2f = 33.4 m/s
PLEASE ALSO NOTE: You have to pick a direction to call positive. Any velocities in the
opposite direction must be negative.
Name
Period
Worksheet 8-2 Conservation of Momentum
1. The same truck from practice problem #1 (2250 kg) traveling at the same initial velocity again slams into a parked
car with the same mass. This time, instead of the truck coming to rest, it rolls forward with a velocity of 1.5 m/s.
What is the car’s velocity?
2. The driver of the truck from question #1, again, traveling the same speed hits a car of the same mass. This time, the
car had been moving with a velocity of 10 m/s. If their bumpers become locked in the collision, what is their
collective velocity after the collision?
3. A child in a boat throws a 5.40 kg package out horizontally with a speed of 10.0 m/s. Calculate the velocity of the
boat, which was originally at rest, immediately after the boy tossed the package. The mass of the child is 26.0 kg
and that of the boat is 55.0 kg.
4. Two rail freight cars are being hitched together. The first car has a mass of 15,750 kg and is moving at a speed of
4.00 m/s toward the second car. The second car is stationary and has a mass of 19,250 kg. Calculate the final
velocity of the two hitched cars.
5. Jimmy disobeys his mother’s stern orders and plays with a BB gun in the house. The gun accidentally goes off and
sends a BB hurling across the room. If the 1.000 x 10-3 kg projectile traveling at a speed of 89.3 m/s lodges in a 0.203
kg block of cheese on a frictionless table, how fast would the BB/Cheese combo slide across the table?
6. A 9500 kg boxcar traveling at 16.0 m/s strikes a second car at rest. The two stick together and move off with a speed
of 6.0 m/s. What is the mass of the second car?
7. 95 kg Running back, Tiki Barber breaks away from the line. It appears that he will easily score. His 85 kg brother
Ronde, at 85 runs him down from behind and tackles him. Tiki, was running 4.1 m/s when tackled by Ronde, who
was running 5.5 m/s. If momentum was conserved, what was their speed, as they collectively fell to the ground?
8.
Two 0.123 kg pool balls came off the bunkers headed directly at each other. The one ball had a speed of 4.7 m/s,
the fifteen ball was rolling with a speed of 0.014 m/s. After the balls collide, the one ball continues to roll in the
same direction that it was originally rolling in, but with a speed of 1.2 m/s. What would be the new speed of the
fifteen ball?