# Energy and Work

**Work** is done when force moves through a distance.

No movement, no work!

These people are doing work, because they are lifting weights

This guy did work to get the weights up,

but right now he is **not doing any work** as the weights aren't moving

This guy is also **not doing any work**

This tractor **is doing work** as it pulls the hay bales along.

## Same Direction!

The force and movement are measured **in the same direction**.

Work = **Force** × **Distance **× cos θ

Where **θ is the angle between** the force and the direction of motion.

### Example: John pushes a box 3 m straight forward using 200 N of force. But his push is a little upwards by 20°.

Start with:

Work = **Force** × **Distance **× cos θ

Put in the values we know:

Work = **200 N** × **3 m **× cos 20°

Work = **200 N** × **3 m **× 0.9397...

Work = 564 N m (to nearest N m)

1 N m is **1 Joule** (J) the preferred unit for work and energy (more on this later):

**Work = 564 J **

(Without cos θ, the * wrong* value would be 600 J)

Here are some other angles:

cos(0°)=1 | cos(60°)=0.5 | cos(90°)=0 | ||

W = Fd | W = Fd × 0.5 | W = 0 |

So remember:

- Without movement there is no work
- Force and movement in the same direction
- Work =
**Force**×**Distance**× cos θ

## Energy

**Energy** is the capacity to **do work**.

It is like energy is **stored up work**.

- When work is done
**by**something it**loses**energy - When work is done
**on**something it**gains**energy

Energy can be in many forms!

A coiled spring has elastic energy.

A battery contains electrical energy. We can drain that energy out to do work.

Fuel contains chemical energy. An engine can turn that fuel (with oxygen) into work, making your car go!

A hammer has mechanical energy:

- when raised up it has
**potential**energy (the energy of position) - when falling down it has
**kinetic**energy (the energy of motion)

Energy goes from one storage to another, or goes to heat:

Heat is a type of energy, too. In fact the total amount of energy stays the same:

Energy can't be created or destroyed.

This is called **Conservation of Energy**: energy just gets transformed and the total stays constant.

Energy is **lost to a system** when it leaves it. A battery loses energy when it powers a light. Our bodies lose heat all the time.

And when we say "energy is lost as heat" we really mean the energy is **dissipated** (spread out) into the environment, it is **not gone from the Universe**.

## Sankey Diagrams

A "Sankey Diagram" shows where the energy goes. The width of the arrow shows how much goes where.

Here is a Sankey Diagram for a car's gasoline engine:

Note: "MJ" is Megajoule (Million Joules). Add them up to make sure the totals match!

## The Joule

The basic unit of energy and work is the **Joule** (J):

1 Joule is the work done by 1 Newton moving 1 meter

1 J = 1 N × 1 m

The Joule has the units **N m**, or **kg m ^{2}/s^{2}** (because a Newton is kg m/s

^{2})

Only force and movement in **the same direction** count, so a more accurate description is:

1 J is the work done to an object when a force of 1 N acts on that object in the direction of its motion through a distance of 1 meter.

### Example: How much energy is needed to lift an 0.1 kg apple up 1 meter?

To **hold** a 0.1 kg apple against gravity needs 1 Newton of force:

**F** = m*g*

**F** = 0.1 kg × **9.8 m/s ^{2}**

**F** ≈ **1 N**

But holding an apple is not work, the apple needs to **move**!

So, raising it using **1 N** for **1 m** (both in same direction!) gives:

Work = **1 N ** × **1 m **× cos 0°

= 1 J

## How Much?

### One joule is about:

- the energy needed to lift an 0.1 kg apple up 1 meter
- The energy released when the apple falls back down again
- The heat needed to raise a single
**drop**of water by 5° C - 1 watt of electricity for 1 second

And:

- An LED light uses about
**3 J**every second - A human at rest releases about
**60 J**of heat every second

### A kilojoule (kJ) is 1000 J:

- A fan heater releases about
**2 kJ**of heat every second - to heat the water for a cup of coffee needs
**80 kJ**

### A Megajoule (MJ) is 1 million J:

- A 2500 kg car going at highway speed has
**1 MJ**of energy - A big TV uses about
**1 MJ**of electricity every hour - One kW h (kilowatt hour) of electricity is
**3.6 MJ** - A fan heater releases about
**8 MJ**of heat every hour

### A Gigajoule (GJ) is 1 billion J:

- The solar energy falling on a roof is about
**1 GJ**to**5 GJ**every day - A person uses about
**20 GJ**in their home every year

## Efficiency

Efficiency is how much of the energy is **useful** as a **percent of the total energy**.

Efficiency = \frac{Useful Energy}{Total Energy} as a percentage

### Example: For every 100 MJ (Megajoule) of energy a gasoline engine uses, only 25 MJ goes to driving it forward.

Efficiency = \frac{25 MJ}{100 MJ}= 25%

## Summary

- Work is force times distance (in the same direction!)
- W =
**F****d**cos θ - Energy is the ability to do work
- Energy goes from one storage to another, or goes to heat
- Energy can't be created or destroyed (Conservation of Energy)
- The basic unit of energy is 1 Joule (J)
- 1 J = 1 N m