Momentum

The momentum of an object depends on its mass and its velocity.

In fact:

Momentum = mass x velocity

NOTE THAT :

Using the equation of motion: a = v-u
t

We can substitute for ‘a’ in Newton’s second law of motion:

Therefore : Resultant Force = mv – mu
t

or in words:

Resultant Force = Change in Momentum
Time Taken

This equation also means that:
The Resultant Force = The Rate of change of Momentum

We can conclude that:

THE LONGER THE TIME OF COLLISION, THE SMALLER THE FORCE.

On crashes passengers continue to move forward because of Inertia.

– Seat belts
– Crumple zone
– Airbags

The Principal of conservation of momentum

The Principle of Conservation of Momentum suggests that:

When two or more bodies act on each other, their total momentum remains constant, providing there is no external force acting.

In other words:

Total momentum before collision = Total momentum after collision provided there are no external forces.

14. Collisions

Example: During an accident, a car (A) collided with a car (B). After collision the two cars moved together.

Using the information in the diagram calculate:

a. Calculate the momentum of car A before collision.
b. Calculate the common velocity of the cars after collision.

a. momentum = mass x velocity
= 1000kg 20m/s
= 20000kgm/s

b. Total momentum before collision = Total momentum after collision
m1v1 + m2v2 = m3v3
(1000kg x 20m/s) + (800kg x 0m/s) = (1800kg) v3
20000kgm/s + 0kgm/s = (1800kg) v3
20000kgm/s = v3
1800kg
11.1m/s = v3

Example: A 2600 kg SUV moving forward at 15 m/s collides head on with a 1300 kg car which is initially at rest Determine the speed and direction of the two cars immediately after impact if they lock together.

Total momentum before collision = Total momentum after collision
m1v1 + m2v2 = m3v3
(2600kg x 15m/s) + (1300kg x 0m/s) = (3900kg) v3
39000kgm/s + 0kgm/s = (3900kg) v3
39000kgm/s = v3
3900kg
10m/s = v3

15. Explosions

An explosion is the opposite of a collision – objects move apart instead of coming together.

Two trolleys are stationary but when the spring-loaded piston is released between them, they shoot off in opposite directions.

Hence what is the velocity of trolley B.

Total momentum before = Total momentum after
m1v1 = m2 v2 + m3v3
(6kg x 0m/s) = (4kg x 0.5m/s) + (2kg x v3)
0kgm/s – 2kgm/s = 2kg x v3
-2kgm/s = v3
2kg
-1m/s = v3

Example: A bullet of mass 0.01kg is fired at 400m/s from a rifle of mass 4kg. What is the recoil velocity of the rifle?

Total momentum before = Total momentum after
m1v1 = m2 v2 + m3v3
(4.01kg x 0m/s) = (4kg x v2) + (0.01kg x 400)
0kgm/s – 4kgm/s = 4kg x v3
-4kgm/s = v3
4kg
-1m/s = v3