2.4 Analysing Momentum

Define the momentum of an object Define momentum (p) as the product

of mass ( m) and velocity (v), e. p=mv State the principle of conversation of

momentum Describe applications of conservation

of momentum.

Learning Outcome :

Momentum is a commonly used term in sports

A team that has the

The momentum of an object is the product of the mass and the velocity of the object

Situation 1 Car A and car B

have the same mass but they move with different velocities.

Which car possess more momentum?

Situation 2 The lorry and the

car move with the same velocity but they have different masses.

Which vehicle possess more momentum ?

The principle of conservation of momentum states that in a system make out of objects that react (collide or explode), the total momentum is constant if no external force is acted upon the system.

Sum of Momentum Before Reaction = Sum of Momentum After Reaction

Formula of Principle of Conservation of Momentum

Example : Both objects are same direction before collision

A Car A of mass 600 kg moving at 40 ms-1 collides with a car B of mass 800 kg moving at 20 ms-1 in the same direction. If car B moves forwards at 30 ms-1 by the impact, what is the velocity, v, of the car A immediately after the crash?

m1 = 600kg m2 = 800kgu1 = 40 ms-1 u2 = 20 ms-1

v1 = ? v2 = 30 ms -1

Answer :

According to the principle of conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

(600)(40) + (800)(20) = (600)v1 + (800)(30) 40000 = 600v1 + 24000

600v1 = 16000v1 = 26.67 ms-1

Example 2 : Both objects are in opposite direction before collision

A 0.50kg ball traveling at 6.0 ms-1 collides head-on with a 1.0 kg ball moving in the opposite direction at a speed of 12.0 ms-1. The 0.50kg ball moves backward at 14.0 ms-1 after the collision. Find the velocity of the second ball after collision.

m1 = 0.5 kgm2 = 1.0 kgu1 = 6.0 ms-1 u2 = -12.0 ms-1v1 = -14.0 ms-1 v2 = ?

(IMPORTANT: velocity is negative when the object move in opposite siredtion)

Answer :

According to the principle of conservation of momentum, m1u1 + m2u2 = m1v1 + m2v2(0.5)(6) + (1.0)(-12) = (0.5)(-14) + (1.0)v 2

-9 = - 7 + 1v2

v2 = -2 ms-1

Additional notes:-In an elastic collision, the 2 objects

separated right after the collision, and-the momentum is conserved after the

collision.

Elastic collision is the collision where the kinetic energy is conserved after the collision.

Total Kinetic Energy before Collision= Total Kinetic Energy after Collision

Inelastic collision is the collision where the kinetic energy is not conserved after the collision.

Additional notes:-In a perfectly elastic collision, the 2 objects

attach together after the collision, and-the momentum is also conserved after the

collision.

Example 3 : Perfectly Inelastic Collision

A lorry of mass 8000kg is moving with a velocity of 30 ms-1. The lorry is then accidentally collides with a car of mass 1500kg moving in the same direction with a velocity of 20 ms-1. After the collision, both the vehicles attach together and move with a speed of velocity v. Find the value of v.

According to the principle of conservation of momentum, m1u1 + m2u2 =( m1+ m2) v (8,000)(30) + (1,500)(20) = (8,000)v+ (1,500)v

270,000 = 9500v v = 28.42 ms-1

Answer:(IMPORTANT: When 2 object attach together, they move with same speed.)

Application of Conservation of Momentum

: Jet Engine

•Air is taken in from the front and is compressed by the compressor.

•Fuel is injected and burnt with the compressed air in the combustion

chamber.

•The hot gas is forced through the engine to

turn the turbine blade, which turn the compressor.

• High-speed hot gases are ejected from the back with

high momentum. This produces an equal and

opposite momentum to push the jet plane forward.