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Math Help - power, mass, speed, time and height

  1. #1
    Senior Member furor celtica's Avatar
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    power, mass, speed, time and height

    A child of mass 30 kg runs up a flight of stairs in 6 seconds. The top of the flight is 3 metres above the bottom, and at the top he is running at 2ms^-1. What average power does he need to produce?

    This is one of the first exercises I have had to tackle concerning power, so I'm pretty sure its meant to be simple. However, in terms of power both force x velocity and work/time i have no idea where to start.

    Without the child's starting speed, horizontal distance covered or total distance run I'm at a loss for what to use and what to look for...any suggestions would help.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: power, mass, speed, time and height

    Quote Originally Posted by furor celtica View Post
    A child of mass 30 kg runs up a flight of stairs in 6 seconds. The top of the flight is 3 metres above the bottom, and at the top he is running at 2ms^-1. What average power does he need to produce?

    This is one of the first exercises I have had to tackle concerning power, so I'm pretty sure its meant to be simple. However, in terms of power both force x velocity and work/time i have no idea where to start.

    Without the child's starting speed, horizontal distance covered or total distance run I'm at a loss for what to use and what to look for...any suggestions would help.
    Note that the initial speed is assumed to be zero.

    Power = Change in energy per unit time = (PE + KE)/time = 30(9.8*3 + 1/2 *2^2)/6 = 5(29.4 + 2) = 157 W
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  3. #3
    Senior Member furor celtica's Avatar
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    Re: power, mass, speed, time and height

    then why am i given the height of the flight of steps?
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Re: power, mass, speed, time and height

    Quote Originally Posted by furor celtica View Post
    then why am i given the height of the flight of steps?
    I used the height to find the PE.
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  5. #5
    Senior Member furor celtica's Avatar
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    Re: power, mass, speed, time and height

    PE and KE being potential and kinetic energy? I'm pretty sure I'm not supposed to be using those in this exercise.
    Why don't you just use 0.5m(v^2) - 0.5m(u^2)?
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  6. #6
    MHF Contributor alexmahone's Avatar
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    Re: power, mass, speed, time and height

    Quote Originally Posted by furor celtica View Post
    PE and KE being potential and kinetic energy?
    Yes.

    Why don't you just use 0.5m(v^2) - 0.5m(u^2)?
    Because the child has potential energy in addition to kinetic energy.
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  7. #7
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    Re: power, mass, speed, time and height

    Hi alexmahone.
    Shouldn't the KE power be 60 Watts not 10 Watts
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  8. #8
    MHF Contributor alexmahone's Avatar
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    Re: power, mass, speed, time and height

    Quote Originally Posted by bjhopper View Post
    Hi alexmahone.
    Shouldn't the KE power be 60 Watts not 10 Watts
    I have got KE = 30*1/2*2^2 = 60 J
    Last edited by alexmahone; September 1st 2011 at 07:45 AM.
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  9. #9
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    Re: power, mass, speed, time and height

    So why was your total power 157 Watts not 207 Watts
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  10. #10
    MHF Contributor alexmahone's Avatar
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    Re: power, mass, speed, time and height

    Quote Originally Posted by bjhopper View Post
    So why was your total power 157 Watts not 207 Watts
    Why should it be 207 W?
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  11. #11
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    Re: power, mass, speed, time and height

    It' the sum of the power of the PE/6 + KE/1 = 147 +60 Watts
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  12. #12
    MHF Contributor alexmahone's Avatar
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    Re: power, mass, speed, time and height

    Quote Originally Posted by bjhopper View Post
    It' the sum of the power of the PE/6 + KE/1 = 147 +60 Watts
    You need to divide the KE by 6 as well.
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  13. #13
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    Re: power, mass, speed, time and height

    Quote Originally Posted by furor celtica View Post
    A child of mass 30 kg runs up a flight of stairs in 6 seconds. The top of the flight is 3 metres above the bottom, and at the top he is running at 2ms^-1. What average power does he need to produce?
    P_{avg} = \frac{total \, work}{total \, time}

    P_{avg} = \frac{\Delta PE_g + \Delta KE}{total \, time}

    P_{avg} = \frac{mg(h_f-h_0) + \frac{1}{2}m(v_f^2 - v_0^2)}{total \, time}

    P_{avg} = \frac{30g(3) + 15(4)}{6} = 157 \, J/s
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