# P2.2 Work, Energy and Momentum

## Work and Energy

We do 'work' whenever we transfer energy from one type to another by use of or against a force. The work done is a measure of the energy transferred and is measured in Joules (J).

Work Done (J) = Force (N) x Distance Moved (m)

**The distance moved in the direction of the force**

**Power**Power is the measure of the rate of energy transfer (work done). the more energy which is transferred each second, the more powerful the device/object.

Power (W) = Energy transferred (J) / Time (s)

## Gravitational Potential Energy (Ep)

The Ep an object has depends on it mass, the g.f.s. of the area and the height of the object above the ground.

Ep = m x g x h

Ep = Joules (J)

m = mass (m)

g = gravitational field strength (N/kg)

h = height (m)

This is a specific case of work done.

Work done = force x distance

Ep = weight x height

Weight = mass x g.f.s

Ep = mass x g.f.s. x height

Ep = m x g x h

## Kinetic Energy (Ek)

Kinetic is the energy an object has because it is moving. A stationary object has 0J of kinetic energy.

Kinetic Energy of an object depends on the object **mass** and the objects **velocity** and is calculated using the following formula:

Ek = 1/2 x m x v^2

Ek = kinetic energy (J)

m = mass (kg)

v = velocity (m/s)

## Conservation of Energy

The **law of conservation of Energy** states that: *Energy cannot be created or destroyed only transferred*.

A falling object transfers **gravitational potential energy **into **kinetic energy **and **heat energy **(caused by air resistance).

For many situations we assume air resistance is negligible, therefore no heat energy is produced and **all** the gravitational potential energy is transferred into kinetic energy.

## Momentum

Momentum is something all moving objects have. The more momentum an object has, the harder it is to stop. Momentum is the product of **mass and velocity.** It has the letter **p** as a symbol.

P = m x v

P = momentum (kgm/s)

m = mass (kg)

v = velocity (m/s)

## Law of Conservation of Energy

The law of conservation of energy states that:

*In a closed system, the total momentum before an event is equal to the total momentum after an event.*

In a closed system --> no external forces acting.

An 'event' can be either a collision or an explosion

## Collisions

A fast moving object collides with a stationary object facing the same direction. After the collision the objects may move together or separately.

The truck collides into the back of the car; the velocity of the car is increased from 0m/s to 15m/s in the collision. The initial velocity of the truck is 10m/s, what is the velocity of the truck after the collision?

P = m x v Before = 3000 x 10 = 30000 After = 1000 x 15 = 15000

= 1000 x 0 = 0 = 30000 - 15000

= 30000 + 0 = 15000 / 3000

= 30000 kgm/s v = 5 m/s

## Momentum in Explosions

The law of momentum states that

**In a closed system, the total momentum before a event is equal to the total momentum after an event.**

We have seen how this applies to **collisions** but an event can also be a explosion.

The momentum would be 0 kgm/s before **and** after the explosion because momentum is in one direction but when an object has been exploded the particles of an object move in all directions.

This is possible as the opposite directions cancel each other out because each particle would have the same velocity.

Common examples: Cannon/Gun fire, Ice skaters pushing apart.

## Impact Time and Impact Force

Newton's 3rd law states that:

Impact Force (N) = Change in momentum (kgm/s) / impact time (s)

This shows that the force on an object in a collision (the impact force) is proportional to the **rate of change of momentum**. This means that the more quickly the momentum changes, the bigger the force on the object.

By increasing the impact time (collision time) we can decrease the rate of change of momentum and therefore decrease the impact force.

In car design, it is very important features like air bags, seat belts and crumple zones are all designed to increase the impact time.

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