**Learn.**

**Momentum is the mass of the object multiplied by its velocity.**

**p=m**v

Think of this as you would rather be hit by a slow moving tennis ball then a fast moving cricket ball. The slow moving tennis ball will have a smaller momentum.

**Law of conservation of momentum.**

Momentum of an isolated system remains constant in time. This means it can’t be created or destroyed.

**Law of conservation of energy**

Energy is never created nor destroyed just changed from one form to another.

A collision occurs when two or more objects crash into one another.

**There are three types of collisions.**

**Perfectly**elastic

An idealised case where there is no kinetic energy lost. In reality kinetic energy will be lost to sound and heat energy. Momentum is conserved in this case hence the sum of momentum before is equal to the sum of momentum after the collision. Since Kinetic energy is also conserved the kinetic energy before is equal to the sum of kinetic energy after.

Momentum before = momentum after

P_{1i }+ P_{2i }+…+ P_{ni }= P_{1f }+ P_{2f }+…+ P_{nf}

Kinetic energy before = Kinetic energy after

1/2 * m v^{2} = 1/2 * m v^{2}

- Inelastic collision

This collision results in some of the kinetic energy from the objects being converted into another form of energy.

Momentum before = momentum after

P_{1i }+ P_{2i }+…+ P_{ni }= P_{1f }+ P_{2f }+…+ P_{nf}

**Perfectly**Inelastic collision

An object striking another object and they stick together.

Momentum before = momentum after

P_{1i }+ P_{2i }+…+ P_{ni }= P_{f}

m_{1}v_{1 }+m_{2}v_{2 }+…+ m_{n}v_{n }= (m_{1 }+m_{2 }+…+ m_{n})v

**In one direction**

The momentum of the object can be thought of as acting in one direction

**In two dimension**

We have to consider the momentum in the x and y plane and break the object’s motion in the x direction and y direction.

Think Billiard balls colliding

Fun Fact:In maritime law allusion refers to a boat crashing into a stationary object but collision means a boat crashed into a moving boat. In physics, we don’t use the word allision. |

**Memorise.**

**Perfectly**elastic

An idealised case where there is no kinetic energy lost.

Momentum before = momentum after

P_{1i }+ P_{2i }+…+ P_{ni }= P_{1f }+ P_{2f }+…+ P_{nf}

Kinetic energy before = Kinetic energy after

12mv2 = 12mv2

- Inelastic collision

This collision results in some of the kinetic energy converted into another form of energy.

Momentum before = momentum after

P_{1i }+ P_{2i }+…+ P_{ni }= P_{1f }+ P_{2f }+…+ P_{nf}

**Perfectly**Inelastic collision

An object striking another object and they stick together.

Momentum before = momentum after

P_{1i }+ P_{2i }+…+ P_{ni }= P_{f}

m_{1}v_{1 }+m_{2}v_{2 }+…+ m_{n}v_{n }= (m_{1 }+m_{2 }+…+ m_{n})v

**Master.**

Momentum

**Problem 1:**

Determine the momentum of …

**a.** A positron (m= 9.1 x10-31 kg) moving at 2.18 x 10^(6) m/s (as if it were in a Bohr orbit in the H atom).

**B.** a bullet (m = 170 g) leaving the muzzle of a gun at 850 m/s.

**C. **a 110 kg professional fullback running across the line at 9.2 m/s.

Collision

**Problem 2:**

A 2200kg car travelling at 30 m/s collides with another 2200kg car that is at rest. The two bumpers lock and the cars move forward together. What is their final velocity? What type of collision is this?

**Problem 3:**

A 1kg ball moving at 1.3 m/s strikes a 2kg ball at rest. After the collision the 1kg ball is moving with a velocity of 0.7 m/s. What is the velocity of the 2 kg ball? What type of collision did you assume it was?

**Problem 4:**

A 1.2kg ball moving at 4 m/s strikes a second ball at rest. After the collision the 1.2kg ball is moving with a velocity of 2 m/s and the second ball is moving with a velocity of 4m/s. What is the mass of the second ball? What type of collision is this?

**Challenge Question**

What type of collision is this and why? Is Kinetic energy conserved. (3 marks)

**Answers**

**Problem 2:**

Challenge Problem