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Power Question Help

  1. May 16, 2006 #1
    You can run up a set of stairs (2.55m) in 2.94s and your body mass is 59.5kg. After hearing about this, the local power company wants to contract you as the next power source. If you were able to sustain your power output for one full hour (and magically have it transferred without any losses to electrical power) and the power company can charge $0.0922 for a kWh, what could they get for an hour of your time? What could they get for your 40-hour workweek? What could they get for your 48-week work year?

    -First I calculated the work, then with that (and time) the power.

    Work = (mass)(gravity)(distance)
    Work = (59.9kg)(9.81m/s^2)(2.55m)
    Work = 1488.42 J

    Power = 1488.42 J / 2.94s
    Power = 506.27W

    -Next I changed Watts to Kilowatts.

    506.27W x 1kW / 1000W = 0.50627kW

    -Then I calculated the money you would make in 1 hour.

    0.50627kW / $0.0922 = $5.49

    -Then I calculated the money you would make in 40 hours.

    (0.50627kW)(40) / $0.0922 = $219.64
    or ($5.49)(40) = $219.6

    -Then I calculated the money you would make in 48 weeks.

    (0.50627kW)(40)(48) / $0.0922
    (0.50627kW)(1920) / $0.0922 = $10542.72


    Did I do everything correct? I am most concerned about calculating the money. I used division, maybe I should multiply? Help me with my sigfigs perhaps (I am horrible with the rules)? Please share your advice so I can have this question 100% right :). Thanks!

    Last edited: May 16, 2006
  2. jcsd
  3. May 16, 2006 #2
    You have 0.50627 kW (or kJ/s). A kilowatt-hour is a unit of energy representing the power of one watt over one hour, so to get Joules again we multiply by time, which is in the this case 60 s.

    kJ/s * s = kWh

    Then you can find your total money because you have your energy in kWh.
  4. May 17, 2006 #3
    Why 60s? Maybe 3600s (hour)?

    So I have 0.50627 kW = kJ / 3600s, so 0.50627 kW (3600s) = kJ = 1822.6?
  5. May 17, 2006 #4
    So after that I just multiply my 1822.57 kWh by $0.0922 (# of hours), correct?

    1822.57 (0.0922) = $168.04 for one hour of work.
    1822.57 (0.0922)(40) = 6721,64 for 40 hours of work
    1822.57 (0.0922)(1920) = 322638.63 for 48-40hour work weeks.

  6. May 17, 2006 #5


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    Watch out. If you write it in full, the 0.0922 number should be written as

    [itex] 0.0922 {$ \over kw \cdot hr} [/itex]

    so to get an amount of money, this number must be *multiplied* by the number of kw produced and by the amount of time it is produced. You will get something much smaller than 5$!
  7. May 17, 2006 #6
    After taking the advice from some other people I had to change kW to kWh. After finding that number I multiplied them by however many hours were worked to give my how much money the company made. I got much higher numbers than 5$.
  8. May 17, 2006 #7


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    (btw, my dolar sign did not show up in my previous post, I meant 0.0922 $/(kw hr), hopefully that was clear).

    If you get higher than 5$ then there is something wrong for sure.

    There are two ways to approach the problem. For sure, you could owrk with kw* hr which is a unit of *energy*, equal to 3.6 x10^6 Joules.

    If you go that way then you must find how much *energy* you can porduce in one hour (you know how much energy you produce in 2.94 second so it's easy to find how much energy in one hour). Now you must calculate how many kw-hr this represents. Then multiply this result by 0.0922 $. It will be *less* than one dollar!

  9. May 17, 2006 #8


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    If you produce 0.506 kW for an hour, you've produced 0.506 kWh of energy.

    If the electric company will pay you a little more than 9 cents per kWh, you'd get a little more than half of that 9 cents.

    - Warren
  10. May 18, 2006 #9
    Sorry for sort of the redone work but I wanted to make it clearer for myself and people reading.

    Work = (mass)(gravity)(distance)
    Work = (59.9kg)(9.81m/s^2)(2.55m)
    Work = 1488.42 J

    Power = 1488.42 J / 2.94s
    Power = 506.27W

    506.27W are put out over 2.94 seconds. So I need to see how many Joules are put out over an hour.

    506.27W = J / 3600s
    506.27W(3600s) = 1822572 J
    506.27Wh = 1822572 J

    Then I'll redo it over in kWh (extra work because it's an assignment :p).

    506.27W x 1kW / 1000W = 0.50627 kW

    0.50627 kW(hour = 3600s) = 1822572 J
    0.50627 kWh = 1822572 J

    Then I find the ammount of $ made?

    0.50627 kWh ($0.0922) = $0.0467 ?

    So the company would make $0.047 for every hour the person worked? Sorry if it has taken me a few 'redos' to understand the concept of kWh etc. but my teacher usually puts basic questions of what we learn next into assignments. Correct me if I did anything wrong! Yay for comprehension (I think :P )

  11. May 19, 2006 #10
    Spot on.

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