work performed?

Question

a student weighing 120 lbs climbs a 12 ft flight of stairs in 9 seconds. how much work have they performed and how do you mathmatically write this out?

Answer 1

The 9 seconds doesn't matter when it comes to work performed. The easiest way to calculate it would be the change in potential energy due to a change in height. Change in PE = Change in height * mass * gravitation acceleration = 12 ft * 120 lbs = 1440 ft-lbs.

Answer 2

mgh=the potential energy=work
where m = mass, g= gravitational acceleration, h=height

work/time=power

So let's plug in our data:
mass=120 pounds
g=32 feet/second^2
h=12 feet
t=9 seconds

First the Work:

120*32*12=46080 ft-pound force

A "foot-pound force" is a unit of work that is equal to about
.324 calories. So 46080 ft-lb force*.324=
14939.63calories

Keep in mind that when we think of calories in terms of energy from food, we are actualy thinking of kilocalories. That means our 14939.63 calories are actually just
14939.63/1000=14.94 food calories

So when a 120 pound student runs up 12 feet of stairway in 9 seconds, he or she burns about 14.94, or approximately 15 calories. It's not really that much energy.

And expressed as Power:

46080/9=5120ft-pound force/second

Which can convert to Watts by:
5120ft-pound/second *1.355 817Watts/ft-pound/sec
=6941.78Watts

Or about 69 100 Watt light bulbs of Power. This seems like a lot of power, but keep in mind no one is able to maintain a constant speed up a flight of stairs. So this is a lot of power, but only for a short burst.