# Power

Power is the measure of how much work is done (the distance an object is moved multiplied by the force required to do so) in a given time. The formula for power is:

The **Power** lifter** work**ed the weights to the top but it took **over **3 minutes.

Alternatively

The **Power** lifter **work**ed out in the gym** over time** to build his physique.

**NOTE:**

Power is measured in watts, or Joules per second.

**Example 1**

If a chair lift carries two skiers, Lindsey and Julia, `200m` vertically up a mountain, with Lindsey weighing `700N` and Julia `500N`, what is the work done on them by the lift and if the journey takes `5` minutes what is the power required?

**Answer:**

Work done = energy transferred = gain in gravitational potential energy

`W\o\r\k\ d\o\n\e = massxxgravityxxchan\g\e\ i\n\ height`

`Weight = massxxgravity` therefore:

`W\o\r\k\ d\o\n\e = weightxxchan\g\e\ i\n\ height=(700+500)xx200=1200xx200=240,000\ Jo\u\l\e\s`

`Power=(w\o\r\k\ d\o\n\e)/(time)`

Don’t forget to convert the time the lift takes into the standard units required for the formula. This means we must convert `5` minutes to seconds.

`5xx60=300\ s\e\c\o\n\d\s`

`Power=(240,000)/300=800\ W\a\t\t\s`

**Example 2**

If Lindsey uses `800` watts to ski back to the bottom of the lift and Julia `600` watts, how long does it take each skier to make it back to the base of the lift?

**Answer:**

`Power=(w\o\r\k\ d\o\n\e)/(time)`

Multiply both sides by time to make work done the subject,

`Powerxxtime=(w\o\r\k\ d\o\n\exxcancel(time))/(cancel(time))`

Divide both sides by power to make time the subject,

`(cancel(power)xxtime)/cancel(power)=(w\o\r\k\ d\o\n\e)/(power)`

`L\i\n\d\s\ey\ time=(w\o\r\k\ d\o\n\e)/(L\i\n\d\s\ey\ power)=(700xx200)/800=(140,000)/800=175\ se\c\o\n\ds`

`175\ se\c\o\n\ds = 2\ m\i\n\u\t\es\ 55\ s\e\c\o\n\ds`

`J\u\l\i\a\ time=(w\o\r\k\ d\o\n\e)/(J\u\l\i\a\ power)=(500xx200)/600=(100,000)/600=166.67\ se\c\o\n\ds`

`166.67\ s\e\c\o\n\ds = 2\ m\i\n\u\t\es\ 46.67\ s\e\c\o\n\ds`