###### Audrey Anne Vella

###### April 8, 2020

###### 10:50 am

### This Lesson Was Contributed By:

Audrey Anne Vella Bondin

### This Lesson is For:

### Lesson Duration:

80 mins.

#### What Should You Expect From This Lesson?

Momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity, then the objectâ€™s momentum is equal to m x v.

#### How To Carry Out This Lesson At Home:

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 â€˜aâ€™ in Newtonâ€™s second law of motion:

Therefore : Resultant Force = mv â€“ 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.

â€“ Seat belts

â€“ Crumple zone

â€“ 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 â€“ 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 â€“ 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 â€“ 4kgm/s = 4kg x v3

-4kgm/s = v3

4kg

-1m/s = v3