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Math Help - Elevator + Counterweight problem

  1. #1
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    Elevator + Counterweight problem

    A 500 kg elevator is accelerated downward at a rate of 5 m/s^2. It is connected to a counterweight through a pulley system. If the force of tension on the connecting cable is 50 N what is the mass of the counterweight.

    ___

    Any help would be appreciated.

    I know how to find acceleration and tension in elevator + counterweight problems, but I'm not sure how to start here.

    Thanks
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  2. #2
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    Whoah, whoa, whoa. Something's wrong here. For an elevator of mass 500 kg to have an acceleration of 5 m/s^2 downward, the opposing force of the rope, that is the tension in the rope, must be equal to the force of gravity acting on the counterweight, and that cannot be so with a rope force of 50 N.

    Hmm, I'm gonna solve it using only the acceleration of the elevator and it's mass as givens, because the 50 N thing may be wrong.
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  3. #3
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    My teacher is incompetent, so I wouldn't doubt it.

    Any help would be appreciated.
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  4. #4
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    Ok, I can't give the diagram because my printer isn't working so I can't scan it, so I'll just give you the formula part. Fg = mg; Fnet = ma. Also note that the positive direction is the direction in which the system is moving. That is, since the elevator is accelerating downwards, Fg will be positive on the elevator's FBD, but negative on the counterweight's FBD.

    To determine Force of rope (Fr) using the elevator FBD:

    Fnet = Fg + ( - Fr)
    ma = mg + (-Fr)
    ma - mg = -Fr
    mg - ma = Fr
    Fr = 2400 N

    Using the counterweight FBD we have the equation:

    Fnet = Fr + (-Fg)
    ma = Fr + (-mg)
    ma + mg = Fr
    m (a+g) = Fr
    m = Fr/(a+g)


    Hopefully that helps. First time helping someone.

    You see, what you needed to do was first find the value of the force of the rope using the elevator's FBD so that you could find substitute that value into the fnet equation given by the counterweight's FBD.
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