2.5 Momentum

OBJECTIVES • Define momentum of an object • Define momentum as the product of mass and velocity • State the principle of conservation of momentum • Describe applications of conservation of momentum • Solve problems involving momentum

Why???????

Why did the revolver recoil after it was fired?

MOMENTUM • Momentum is defined as the product of mass and velocity. • Momentum is a vector quantity. It has both magnitude and direction. The SI unit of momentum is kgms-1

m s-1

kg

• The direction of a momentum of an object is the same as the direction of the velocity of the object. • If an object moving to the right denotes a positive velocity, the left direction will denote a negative velocity.

Conservation of Momentum • The principle of conservation of momentum states that in a collision, the total momentum of the object before the collision is equal to the total momentum after the collision, provided that there is no external force acting on the colliding objects

P (before collision) = P (after collision) m1v1 = m2v2

Elastic Collision • An elastic collision is a collision where the two colliding objects separate after colliding. • Momentum is conserved in elastic collision.

P (before collision) = P (after collision) m1u1 + m2u2 = m1v1 + m2v2

Inelastic Collision • An inelastic collision is a collision where the two colliding objects stick together after colliding. • Momentum is conserved in an inelastic collision

P (before collision) = P (after collision) m1u1 + m2u2 = m1v1 + m2v2 m1u1 + m2u2 = (m1 + m2)v

Collisions Demonstration

Explosion • Momentum is conserved in an explosion. An example of an explosion is when a gun is fired. • The momentum before the explosion is zero.

P (before explosion) = P (after explosion) m1u1 + m2u2 = m1(-v1) + m2v2 0 = m1(-v1) + m2v2 m1v1 = m2v2

Exercise 1. A bullet of mass 20 g is fired towards a stationary target with a mass of 2 kg. The bullet is embedded in the target and both move together at a common velocity of 2 m s-1. Find the velocity of the bullet before hitting the target.

2. A car of mass 1 200 kg was involved in a head on collision with a lorry of mass 4 800 kg travelling at 79.2 km h-1 . After the collision, the car and the lorry were locked together and continued moving at a velocity of 21.6 km h-1. Find the velocity of the car before collision.

3. A bullet of mass 10 g was fired from a 4 kg rifle with a velocity of 200 m s-1. Find the recoil velocity of the rifle.