physics question- power

Question

A student with mass 66 kg runs up a flight of stairs that's 4.7 meters high. It takes him 4 seconds to move from the bottom to the top of the stairs, and we'll assume his KE is essentially zero at beginning and end. Find the power he exerted. 

 

please help :) thank you!

Answer 1

Hi!  As you've probably just learned, Power is the measure of how quickly work is being done (that is, one Watt of power is one Joule per second).

 

First, we find out how much work was done.  Work = force x distance, so we need to multiply the distance he went up by the force that he needed to raise that distance (in this case, his weight, which is mg).  Multiplying 66 kg by 9.8 gives us 648.8, so 648.8 J of work were done.

 

Now that we know how much work was done, we need to use the equation Power = Work/Time.  In this case, when we plug the work and time into this equation we get Power = 648.8J/4s.  By doing this simple division problem, we find that the rate of work output was 162.2 J/s, or 162.2 Watts.

 

 

Here's one interesting thing to note about this problem:  Because work is defined as adding energy to an object, we can also say that Power = Energy Added/Time.  Therefore...

It's a lot like the Distance = Speed x Time problems you've probably already done in the past!  Only in this case, we can say that the "Distance" we changed the amount of energy (648.8J) = the Rate at which the energy was changing (that's the Power), times the Time!