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Math Help - [Physics]Force with Pulleys

  1. #1
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    [Physics]Force with Pulleys

    In the figure, a cord runs around two massless, frictionless pulleys; a canister with mass m = 60 kg hangs from one pulley; and you exert a force F on the free end of the cord. What must be the magnitude of F if you are to lift the canister at a constant speed?


    Originally I thought this question was pretty easy. Since a=0, I thought F=mg. However, the answer (588N) is wrong.
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    Actually I figured out that I had to include the tension on both sides.

    For the left side: F-T=ma therefore F=T. The on the right side, mg-2T=ma. Therefore mg/2=F. I got the correct answer as 293N.

    However, there is a second part that I don't understand.
    The canister is lifted 5.4 cm. During that lift, what is the work done on the canister by the weight mg of the canister? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.)


    I know that W=F*d. I tried setting W=2F*d, but that's not right.
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    Quote Originally Posted by WhoCares357 View Post
    Originally I thought this question was pretty easy. Since a=0, I thought F=mg. However, the answer (588N) is wrong.
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    you only need to pull down with a force equal to 1/2 the weight.

    note that the mass is held up by two ropes on either side of the pulley, tension in both sides the same ... a mechanical advantage of 2 ... the trade-off is that you'll have to pull down 2 m to get the mass to rise 1 m.

    the work done on the mass by the mass' weight is -Wd.
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    Quote Originally Posted by skeeter View Post
    you only need to pull down with a force equal to 1/2 the weight.

    note that the mass is held up by two ropes on either side of the pulley, tension in both sides the same ... a mechanical advantage of 2 ... the trade-off is that you'll have to pull down 2 m to get the mass to rise 1 m.

    the work done on the mass by the mass' weight is -Wd.
    Can you explain mathematically why it is -Wd? I can't really see it from your explanation. -Wd=-Fd^2? How did you get that?
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    Quote Originally Posted by WhoCares357 View Post
    Can you explain mathematically why it is -Wd? I can't really see it from your explanation. -Wd=-Fd^2? How did you get that?
    work = the dot product of force and displacement

    weight of the mass (the force) is W in the down direction

    displacement is d in the upward direction

    work = Wd cos(180) = -Wd
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    Quote Originally Posted by skeeter View Post
    work = the dot product of force and displacement

    weight of the mass (the force) is W in the down direction

    displacement is d in the upward direction

    work = Wd cos(180) = -Wd
    Okay, thank you.
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