# Momentum calculations

```Conservation of momentum calculations - Inelastic collisions (moving together after)
Instructions
Calculate the total momentum before
the collision
Worked example
Question 1
Question 2
A Car of mass 1000 kg travelling at a
velocity of 20 m/s collides with a
stationary car of mass 1000kg. The
vehicles move together after the impact.
Calculate their velocity.
A car of mass 1500 kg travelling at 15 m/s
collides with a stationary van of mass
2000 kg. The vehicles move together
after the collision. Calculate their velocity.
A car of mass 1200 kg travelling at a
velocity of 30 m/s collides with a car of
mass 800 kg travelling at 12 m/s. The
cars move together after the collision.
Calculate their velocity.
Momentum 1:
Momentum = mass x velocity
Momentum = 1000 x 20
Momentum = 20 000 kg m/s
Momentum 2:
Momentum = mass x velocity
Momentum = 1000 x 0
Momentum = 0 kg m/s
Total momentum:
Total Momentum = 20 000 + 0
Total Momentum = 20 000 kg m/s
State the total momentum after the
collision
Total momentum after the collision is
equal to the the total momentum before
the collision, therefore:
Total momentum = 20 000 kg m/s
Calculate the total mass after the
collision
Total mass = 1000 + 1000
Calculate the velocity after the
collision
Velocity = momentum ÷ mass
Total mass = 2000 kg
Velocity = 20 000 ÷ 2000
Velocity = 10 m/s
Conservation of momentum calculations - Elastic collisions (moving separately after)
Instructions
Calculate the total momentum before
the collision
Worked example
Question 1
Question 2
Car A of mass 1000 kg travelling at a
velocity of 20 m/s collides with a
stationary car B of mass 1000kg. Car A
travels with a velocity of 5 m/s after the
collision, what is the velocity of car B?
Car A of mass 1500 kg travelling at a
velocity of 20 m/s collides with a
stationary car B of mass 1300kg. Car A
travels with a velocity of 8 m/s after the
collision, what is the velocity of car B?
Car A of mass 1000 kg travelling at a
velocity of 20 m/s collides with a car B of
mass 1000kg, travelling at 6 m/s. Car A
travels with a velocity of 6 m/s after the
collision, what is the velocity of car B?
Momentum 1:
Momentum = mass x velocity
Momentum = 1000 x 20
Momentum = 20 000 kg m/s
Momentum 2:
Momentum = mass x velocity
Momentum = 1000 x 0
Momentum = 0 kg m/s
Total momentum:
Total Momentum = 20 000 + 0
Total Momentum = 20 000 kg m/s
State the total momentum after the
collision
Total momentum after the collision is
equal to the the total momentum before
the collision, therefore:
Total momentum = 20 000 kg m/s
Calculate the momentum of the
known vehicle after the collision
Momentum = mass x velocity
Momentum = 1000 x 5
Momentum = 5000 kg m/s
Calculate the momentum of the
vehicle with the unknown velocity
Momentum = total - known momentum
Momentum = 20 000 - 5000
Momentum = 15 000 kg m/s
Calculate the unknown velocity
Velocity = momentum ÷ mass
Velocity = 15 000 ÷ 1000
Velocity = 15 m/s
Conservation of momentum calculations - Unknown masses
Instructions
Worked example
Car A of mass 800 kg, collides with car B,
which is stationary, at a velocity of 11
m/s. The two cars couple and move
together at a velocity of 7 m/s after the
collision. Calculate the mass of car B.
Calculate the total momentum before
the collision
Momentum 1:
Momentum = mass x velocity
Momentum = 800 x 11
Momentum = 8800 kg m/s
Momentum 2:
Momentum = mass x velocity
Question 1
Car A of mass 2000 kg, collides with car
B, which is stationary, at a velocity of 33
m/s. The two cars couple and move
together at a velocity of 15 m/s after the
collision. Calculate the mass of car B.
Question 2
Car A of mass 2000 kg, collides with car
B, which has a velocity of 0 m/s, at a
velocity of 1- m/s. The two cars couple
and move together at a velocity of 8 m/s
after the collision. Calculate the mass of
car B.
Momentum = ? x 0
Momentum = 0 kg m/s
Total momentum:
Total Momentum = 8800 + 0
Total Momentum = 8800 kg m/s
State the total momentum after the
collision
Total momentum after the collision is
equal to the the total momentum before
the collision, therefore:
Total momentum = 8800 kg m/s
Calculate the total mass after the
collision
Mass = Momentum ÷ velocity
Mass = 8800 ÷ 7
Mass = 1257.14 kg
Calculate the momentum of the
vehicle with the unknown velocity
Mass = total - known mass
Momentum = 1257.14 - 800
Momentum = 457.14 kg
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