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 worked the weights to the top but it took over 3 minutes.
Alternatively
The Power lifter worked 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`
