MomentumIB MYP Physics: Revision notes
Section 1
What is momentum?
Every moving object has momentum. It depends on both its mass and its velocity:
p = m v
where p is momentum in kg m/s, m is mass in kg and v is velocity in m/s.
Example: a 0.16 kg cricket ball moving at 30 m/s has p = 0.16 × 30 = 4.8 kg m/s.
A heavy lorry and a fast bullet can both have large momentum: one because of its mass, the other because of its velocity.
Rearrange p = m v to find velocity (v = p / m) or mass (m = p / v).
Section 2
Momentum is a vector
Momentum has direction as well as size, so it is a vector quantity. Its direction is the same as the velocity.
In a straight line choose one direction as positive. Motion the other way is negative.
A 2.0 kg trolley moving right at 3.0 m/s has p = +6.0 kg m/s. Moving left at 3.0 m/s, it has p = −6.0 kg m/s.
Section 3
Conservation of momentum in collisions
In a collision between objects with no external forces (such as friction), the total momentum before = the total momentum after. This is the conservation of momentum.
Worked example: a 1.0 kg trolley moving at 4.0 m/s hits a stationary 3.0 kg trolley and they stick together.
- Momentum before = 1.0 × 4.0 = 4.0 kg m/s
- Momentum after = (1.0 + 3.0) × v = 4.0 v
- 4.0 v = 4.0, so v = 1.0 m/s in the original direction.
If the objects bounce apart, add the momentum of each one after the collision (with signs).
Momentum is conserved in every collision, but kinetic energy is not always conserved. Do not mix them up.
Section 4
Conservation of momentum in explosions
In an explosion (or objects pushing apart) the objects start at rest, so the total momentum before is zero. The total after must also be zero, so the objects move in opposite directions.
Worked example: a 60 kg skater and a 40 kg skater at rest push each other apart. The 40 kg skater moves at 3.0 m/s east.
0 = 60 × v + 40 × 3.0, so v = −120 / 60 = −2.0 m/s, which is 2.0 m/s west.
The smaller mass moves faster.
Section 5
Force and change in momentum
A force changes an object's momentum. The force is the rate of change of momentum:
F = change in p / t
where F is in newtons, change in p in kg m/s and t in seconds.
Worked example: a 60 kg cyclist slows from 5.0 m/s to rest in 0.50 s. The change in momentum is 60 × 5.0 = 300 kg m/s, so F = 300 / 0.50 = 600 N.
This is Newton's second law written another way: F = m a = m (change in v) / t.
Section 6
Safety features
For the same change in momentum, a longer collision time means a smaller force (F = change in p / t).
- Crumple zones collapse in a crash, so the car takes longer to stop.
- Air bags inflate and cushion the passenger, so the head and chest stop more slowly.
- Seat belts stretch slightly and spread the force.
All of these reduce the force on the passengers and so reduce injury.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Momentum
- A cricket coach in Chennai studies a ball of mass 0.16 kg that is bowled along a straight line at 30 m/s towards a batter. The batter hits the ball straight back along the same line at the same speed.Taking the direction in which the ball was bowled as positive, state the momentum of the ball after it is hit. Explain why it is different from the momentum before, although the speed is the same.2 marks
- Two trolleys are on a level, low-friction laboratory track. Trolley X has a mass of 2.0 kg and moves at 3.0 m/s towards trolley Y, which has a mass of 1.0 kg and is at rest. When they collide they stick together and move off along the track as one object.Calculate the velocity of the two trolleys just after the collision.2 marks
- A group of students investigates how the force on a hand catching a ball depends on the time the ball takes to stop. A ball of mass 0.40 kg is thrown at 5.0 m/s into a hand holding a force sensor. When the hand is held rigid, the ball stops in 0.05 s. When the hand moves backwards with the ball, the ball stops in 0.20 s.State the independent variable and the dependent variable. Write a testable hypothesis for this investigation and give a scientific reason for it.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).