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Gravitational elevator (physics Torque question)

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    After watching a news story about a fire in a high rise apartment building, you and your friend decide to design an emergency escape device from the top of a building. To avoid engine failure, your friend suggests a gravitational powered elevator. The design has a large, heavy turntable (a horizontal disk that is free to rotate about its center) on the roof with a cable wound around its edge. The free end of the cable goes horizontally to the edge of the building roof, passes over a heavy vertical pulley, and then hangs straight down. A strong wire cage which can hold 5 people is then attached to the hanging end of the cable. When people enter the cage and release it, the cable unrolls from the turntable lowering the people safely to the ground. To see if this design is feasible you decide to calculate the acceleration of the fully loaded elevator to make sure it is much less than g. Your friend's design has the radius of the turntable disk as 1.5 m and its mass is twice that of the fully loaded elevator. The disk which serves as the vertical pulley has 1/4 the radius of the turntable and 1/16 its mass. In your trusty Physics book you find that the moment of inertia of a disk is 1/2 that of a ring.


    2. Relevant equations
    I think..

    Ir=1/2MR^2
    Tnet=I(alpha)
    Fg-Fr=ma
    ar=(Fg-Fr)/Msp


    3. The attempt at a solution

    I honestly have no idea. Can someone please get me started on it?

    Like I have

    T1(1.5m)=I(alpha)
    T1= [(1/2*m*R^2)(alpha)]/1.5m b/c torque= T1(R)=I*alpha

    oh and

    there will be T1 and T2,

    so Sum of torque = T2(Rp) - T1(Rp) = I*alpha

    and... I don't know, I don't understand :(
     
    Last edited: Dec 2, 2009
  2. jcsd
  3. Dec 2, 2009 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    You need three separate free body diagrams, for the disk, for the pulley and for the hanging cage with people. Use them to write three Newton's 2nd Law equations. Note that you have three unknowns, two tensions and an acceleration. Solve for the acceleration.
     
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