 1. Momentum
2. Conservation of momentum
3. Force and momentum

All moving objects have momentum. Momentum can be defined as the tendency of an object to keep moving in the same direction and it is a vector quantity. It can be calculated by multiplying mass and velocity, and its unit is kgm/s. Total momentum is conserved in collisions and explosions unless an external force is exerted on the system. This is called the law of conservation of momentum. The law states that for an isolated system, provided that there are no external forces acting and no energy is provided, momentum will remain constant. For many collision and explosion questions this law results in equating total momentum before and total momentum after. By Newton's second law, a force is given by F = m × a. Substituting the acceleration equation into this gives F × t = mv − mu. Given that v is the final velocity and u is the initial velocity, mv − mu = change in momentum. This is a way to derive an equation relating the rate of change of momentum and force.

Change in momentum is also known as impulse and force is also known as the rate of change of momentum. Newton's second law can be rewritten as: a force acting on a body is proportional to the rate of change of momentum it produces in its direction. # 1

When a car crashes, an airbag inflates in front of the driver. Explain, using ideas about rate of change of momentum, how an airbag reduces the possibility of injury during a car crash.

Since F × t = change in momentum, the airbag increases the time taken to reduce momentum to 0, as it ensures that it takes more time for the driver to stop. A greater time period reduces the force that acts on the driver, therefore reducing the risk of injury.

F × t = change in momentum; airbag increases time, therefore reducing force. # 2

A car is travelling in a straight line at a constant velocity of 11 m/s. Given that the momentum of the car is 15125 kgm/s, find the mass of the car.

p = m × v
15125 kgm/s = mass × 11 m/s
mass = 15125 ÷ 11 = 1375 kg

1375 kg # 3

Two go-karts of equal mass are travelling towards each other and collide. The first go-kart is travelling towards the right at 4 m/s and the second is travelling towards the left at 2.75 m/s. Given that the first go-kart changes direction after the collision and has a speed of 2 m/s, find the velocity of the second go-kart after the collision.

By the law of conservation of momentum, total momentum before = total momentum after.
mass × 4 m/s − mass × 2.75 m/s = mass × velocity − mass × 2 m/s
Since the masses of the two go-karts are equal, we can cancel mass out of the equation.
velocity = 4 − 2.75 + 2 = 3.25 m/s to the right

3.25 m/s to the right # 4

A tennis ball of mass 0.056 kg is moving towards a racquet at a velocity of 13 m/s. The impact with the racquet last for 6 ms and the tennis ball now travels in the opposite direction at a velocity of 15.4 m/s. Calculate the magnitude of the force exerted by the racquet on the ball.

The right can be taken to be the positive direction.
change in momentum = (0.056 kg × (−15.4 m/s)) − (0.056 kg × 13 m/s) = −1.5904 kgm/s
force = −1.5904 kgm/s ÷ 0.006 s = −265 N (3 s. f.)

265 N # 5

A snooker ball of mass 0.17 kg is travelling towards another stationary snooker ball of mass 0.15 kg at 10 m/s. After the collision, the first snooker ball slows down to 3.5 m/s. Calculate the velocity of the second snooker ball after the collision.

By the law of conservation of momentum, total momentum before = total momentum after.
0.17 kg × 10 m/s = 0.17 kg × 3.5 m/s + 0.15 kg × velocity
velocity = (0.17 kg × 10 m/s − 0.17 kg × 3.5 m/s) ÷ 0.15 kg = 7.37 m/s (3 s. f.)

7.37 m/s End of page