Chapter 2.4 Momentum

Momentum1. Momentum is defined as the product of mass and velocity.2. Momentum is a vector quantity. It has both magnitude and direction.3. The SI unit of momentum is kgms-1

4. Principle of Conservation of MomentumThe 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

5. Elastic Collision

Elastic collision is the collision where thekinetic energy is conservedafter the collision.

Total Kinetic Energy before Collision= Total Kinetic Energy after Collision

Additional notes:

In an elastic collision, the2 objects separatedright after the collision, andthemomentum is conservedafter the collision.Total energy is conservedafter the collision.

6. Inelastic Collision

Inelastic collision is the collision where thekinetic energy is not conservedafter the collision.

Additional notes:

In a perfectly elastic collision, the2 objects attach together after the collision, andthemomentum is also conservedafter the collision.Total energy is conservedafter the collision.

Formula

Example 1 - Both Object are in the Same Direction before CollisionA Car A of mass 600 kg moving at 40 ms-1collides with a car B of mass 800 kg moving at 20 ms-1in the same direction. If car B moves forwards at 30 ms-1by the impact, what is the velocity, v, of the car A immediately after the crash?Answer:m1= 600kgm2= 800kgu1= 40 ms-1u2= 20 ms-1v1= ?v2= 30 ms-1

Example2 - Both Object are in opposite direction Before CollisionA 0.50kg ball traveling at 6.0 ms-1collides 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-1after the collision. Find the velocity of the second ball after collision.

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

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

m1= 8000kgm2= 1500kgu1= 30 ms-1u2= 20 ms-1v1= vv2= v_______________________________________________________________ExplosionBefore explosion both object stick together and at rest.After collision, both object move at opposite direction.

Total Momentum before collision Is zeroTotal Momentum after collision :

m1v1+ m2v2

From the law of conservation of momentum:Total Momentum Before collision = Total Momentum after collision

0 = m1v1+ m2v2

m1v1= - m2v2

(-ve sign means opposite direction)

Example:A man fires a rifle which has mass of 2.5 kg. If the mass of the bullet is 10 g and it reaches a velocity of 250 m/s after shooting, what is the recoil velocity of the pistol?Answer:This is a typical question of explosion.

m1= 2.5 kgm2= 0.01 kgu1= 0 ms-1u2= 0 ms-1v1= ?v2= 250 ms-1______________________________________________________________________________________________________________________

Application use the MomentumRocket1. Mixture of hydrogen and oxygen fuels burn in the combustion chamber.2. Hot gases are expelled through the exhausts at very high speed .3. The high-speed hot gas produce a high momentum backwards.4. By conservation of momentum, an equal and opposite momentum is produced and acted on the rocket, pushing the rocket upwards.

Jet Engine1. Air is taken in from the front and is compressed by the compressor.2. Fuel is injected and burnt with the compressed air in the combustion chamber.3. The hot gas is forced through the engine to turn the turbine blade, which turns the compressor.4. High-speed hot gases are ejected from the back with high momentum.5. This produces an equal and opposite momentum to push the jet plane forward.

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