Momentum

Principle of conservation of momentum

The momentum of a system is always conserved unless an external force is acting on it

$\rho=mv$

Change in momentum ($\Delta p$ )

Δp = (final p) - (initial p)

Don't forget the sign conventions: Left = negative, Right = positive

Impulse

It is the force exerted in a short period of time that causes a change of momentum.

$I=F\Delta t=m\Delta v=\Delta p$

Collisions

During a collision, an object experiences an impulse which causes a change in momentum.

The object either speeds up, slows down, or changes direction.

Ways of reducing damage during a collision

Seatbelts: Stretch slightly to increase the amount of time the person is in contact with them which reduces the force acting on the chest.

Crumple zones: Deforms plastically on impact which causes the car to take longer to stop and reduces the force on the passengers Crumple zones: Deforms plastically on impact which causes the car to take longer to stop and reduces the force on the passengers.

* Same concept as airbags

Note:

Area of a force - time graph is impulse.

When observing the Momentum of different objects , the force is the same but the acceleration isn't

Explosion of a stationary object

Use principle of momentum

The momentum before is zero

After the explosion, no further acceleration as speed is constant e.g. firing a canon.

Explosion of a moving object

Principle of momentum applies too

Types of Collision

Inelastic: total KE is not conserved

Elastic: total KE is conserved

Note: The total energy of the system is always constant

2D Collisions

*Use the angles to the horizontal