# Energy & work -- simple question

1. Oct 5, 2014

### kirsten_2009

1. The problem statement, all variables and given/known data

Compare the amount of metabolic energy used by a typical person running up a flight of stairs to the energy required to light a 100 W light bulb for 1 hour.

2. Relevant equations

3. The attempt at a solution

Assumptions: A “typical person” in this situation is being arbitrarily defined as a 578.26 N (130 lb) person and the vertical height of a “flight of stairs” as 4m and the time to climb these stairs as 5 seconds (as per the textbook on pg. 130).

The energy needed by this person to go up this flight of stairs:

Work = weight * height = 578.26 N * 4m = 2313 J /5 sec. = 462.6 J/s (W) = 27,756 J/hr

The energy needed to light a 100W light bulb for 1 hour:

If one watt = 1 J/s then 100W =100 J/s x 3600s/1 hour = 360,000 J/hr

So, a person utilizes relatively a small amount of energy while going up a flight of stairs compared to running a light bulb for 1 hour?

2. Oct 6, 2014

### RUber

It seems like you multiplied by 60 instead of 3600 to convert J/s to J/hr for going up the stairs.

3. Oct 6, 2014

### Simon Bridge

work = weight x height = 2313J ... you can stop there: you are comparing the energy needed, not the power.
note: you wrote W=...=2313J/5s This is incorrect.
The work is 2313K, the power is 2313J/5s.
That is likely what you meant to write but you should actually write it.

running the bulb for the same time would use 500J of energy - but you are not runnig it for the same time.
in fact running the bulb for much more that 23s will consume more energy.

the work done climbing stairs is the gravity part only - not the "total metabolic energy consumed" in the process ... which includes energy that goes to heat and increased respiration and accelerating at the bottom and decelerating at the top and so on.

4. Oct 6, 2014

### kirsten_2009

Hello,

Thanks for replying. I am a little confused with this one. I understand what you are saying about power not being the same as energy since I guess power is sort of how fast work can be done? But, isn't energy "the capacity to do work"? so wouldn't the person's energy to climb a flight of stairs be 2313 J in those 5 seconds that it took him/her to go up the stairs? In calories= 2313 J x 1cal / 4.184J = 552.82 cal (I understand that this is not the "metabolic" energy but I don't believe there is enough information provided to actually calculate the person's total metabolic energy)......?

And then....may I ask how you reached the number 500J for the light bulb? Isn't it that a light bulb with a power rating of 100W would consume 360 kJ for 1 hour? = 360,000 J...? Thanks for all your help and time, it's really appreciated!

5. Oct 6, 2014

### RUber

500J was for 5 secs.

6. Oct 6, 2014

### Staff: Mentor

Lets not compare apples and oranges. The work to climb the stairs was 2313 J, irrespective of the amount of time it took. The energy to run the light bulb for 1 hour was 360000 J.

Chet

7. Oct 6, 2014

### kirsten_2009

So...I would be correct in saying that the light bulb does require a considerable larger amount of energy to run for an hour than the energy it takes an "average" person to go up a flight of stairs? are my numbers correct? Thanks for your help! :)

8. Oct 6, 2014

### kirsten_2009

Oh I see....totally understand. Thanks!

9. Oct 6, 2014

### Staff: Mentor

Yes. Have you ever been to a museum where they have a electro-mechanical setup where you turn a crank to power a light bulb? Try doing that for an hour.

10. Oct 6, 2014

### kirsten_2009

Thanks for your help! No, I've never...but it sounds like a workout.