# Power

Power is energy flowing! It is measured as **energy per unit of time**

- Energy is in
**Joules**(J) - Power is in
**Joules per second**(J/s) which has the special unit of**Watts**(W)

1 Watt = 1 Joule of energy per second

1 W = 1 J/s

## Power Formulas

**No**, not that type of Power Formula!

Power is the **rate of energy per time**:

P = \frac{Energy}{Time}

### Example: 3000 J of energy is used in 20 seconds, what is the power?

P = \frac{3000 J}{20 s} = 150 W

We can also change the formula this way:

P = \frac{Energy}{Time} | ||

Energy is also Force × Distance, so: | P = \frac{Force × Distance}{Time} | |

Distance/Time is Velocity, so: | P = Force × Velocity |

### Example: These guys pull with a combined force of 4000 N, and manage a velocity of 0.4 m/s, what power are they using?

P = 4000 N x 0.4 m/s

= 1600 N m/s

= 1600 W

Hang on! Is **N m/s** (Newton meter per second) really the same as **W** (Watt)?

In fact all these are the same:

Power is: | ||

Start with: | N m/s | |

A Newton is kg m/s:^{2} | kg m/s^{2} m/s | |

Simplify: | kg m^{2}/s^{3} | |

A Joule is kg m:^{2}/s^{2} | J/s | |

A Watt is J/s: | W |

## Horsepower

**1 horsepower** (hp) is 745.7 W (or 746 W for electrical motors)

### Example: Sam's car has a 200 hp engine. What is that in watts?

200 × 745.7 = 149,140 W = **149 kW** (to nearest kW)

## What is a kiloWatt Hour?

**1 kWh** is the **Energy** used when the Power is 1 kW for 1 hour.

### This is a little **1 kW** radiator. How much energy does it use in an hour?

- 1 kW is 1000 Watts which is
**1000 J/s** - There are 3600 seconds in an hour

So in an hour it uses:

1000 J/s × 3600 s = 3,600,000 J = **3.6 MJ**

**1 kWh**(kiloWatt hour) is

**3.6 MJ**of

**Energy**