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Gravity is std. therefore can we rate a 'mass at height' by watts?

  1. May 23, 2013 #1
    For example.... wind turbines are primarily listed by their wattage (1.5MW etc.)
    Presumably their output is varied according to rotational speed, so I'm guessing that the rating is simply a guide.

    However, for a given mass, at a given height; due to standard gravity, can we state that this mass, on falling can deliver a maximum amount of watts of power.

    Eg.
    Work = force times distance.
    Power = work divided by time.

    Work = 100kg @ 100m = 98,000 joules
    Time = 100m freefall = 4.5s
    Power = 21.8KW

    But that is freefall, and nothing is being driven.
    If a chain and gearbox, was attached to the mass, that then rotated a generator....... the rate of descent would be very slow.
    Leaving aside friction.... work must be done to turn the generator?

    How then do we predict the output of the generator?

    Eg. the mass takes 4 times as long to travel 100m
    Is the power output 21.8KW/4 = 5.45KW for a period of 18s ?

    Or, to put this into a 1KW element fire: we could only get 98s of use, from 100kg @ 100m.

    Surprisingly little, if the above is true.
    But is it true?

    Is 21.8KW the maximum we can get out of 100kg @ 100m?
     
  2. jcsd
  3. May 23, 2013 #2

    Nugatory

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    Staff: Mentor

    yes. The total energy released from 100 kg lowered 100 meters in the earth's surface gravity is 9.8x104 joules. You can release it over a longer time to get fewer watts (joules per second), but that's like making a glass of water last longer by drinking it more slowly; it takes longer but you don't end up with any more water than if you had gulped it at once.

    No. You could, for example, let the weight fall freely (just pulling the rope behind it) for 99 meters, and then apply the load, bringing the weight to rest just as it touches the ground. You'd get your 9.8x104 joules in about .04 seconds, a short burst of very high power output.

    21.8 kw is the (unreachable) upper limit on the average power over the entire time that the weight is falling.
     
  4. May 23, 2013 #3

    sophiecentaur

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    Science Advisor
    Gold Member

    I really like that! :wink:

    It got me thinking that a given amount of GPE can be attained by different combinations of height and mass. Each combination of m and h implies a different maximum rate of [edit: energy] transfer - the highest (mean) power being obtained with the biggest possible mass and the smallest height - because that involves the shortest possible descent time. There's a analogous electrical model with Energy stored in a capacitor. The maximum power obtainable is limited by the Inductance of the circuit.
     
    Last edited: May 23, 2013
  5. May 23, 2013 #4
    Thanks Nugatory for that solid response :smile:

    I had not considered the 'freefall to point of impact'.
    This fact therefore eliminates the possibility of rating a 'mass at height' by watts.
    Clearly it can only be rated by joules (as a single universal number).

    I must confess to feeling glad to have asked this question in this format.

    The image conjured, of a mass falling in a straight line, allows for so many 'easy to calculate scenarios', with the result being that 'power' as a concept, becomes much more accessible.

    I was thinking about your suggestion of power production over a period of 0.04s
    power = 2,450KW

    and then relating it to:
    It's really good.
    I'm really happy :biggrin:
     
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