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Homework Help: Kinetic energy, force, rotation

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data

    A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 49.0 N and a radius of 0.27 m. The cylinder is attached by spokes of a negligible moment of inertia to a fixed horizontal axle coincident with the axis of the cylinder; the cylinder is free to rotate without friction about this axle. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 4.95 m, at which point the end of the rope is moving at 6.25 m/s; the rope does not slip on the cylinder.

    A)What is the change in kinetic energy of the hollow cylinder as a result of the rope having been pulled?

    B) For the situation as described in the introduction, what is the value of P?

    2. Relevant equations


    k = 1/2mv2 + 1/2Iw2

    w = omega

    ki + ui + Work = kf + uf

    3. The attempt at a solution

    i didnt know how to do part a so i just skipped to part B)

    W = FD ----> W = P(4.95m)

    W = kf

    P(4.95m) = 1/2(5kg)(6.252) + 1/2(1/2(5kg)(.27m)2(6.25/.27)2)

    P = 29.59 N

    This is wrong though and i am not sure why. Also if i could get some help on part A that would be great.

    Thank you :)
  2. jcsd
  3. Apr 7, 2010 #2


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    In the equation


    what does [itex]v[/itex] stand for? Don't just say velocity. The velocity of what?
    Also, you're using the wrong moment of inertia. The key word is hollow.
  4. Apr 7, 2010 #3
    V should be the velocity of the center of mass v_cm

    i am not sure what moment of inertia to use then? would it be

    I = mr^2

    should i just be using K = 1/2Iw^2 instead of what i have?

    thanks for the help :)
  5. Apr 7, 2010 #4


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    Right. So what is the velocity of the cylinder's center of mass?
    Yes, all of the mass of the hollow cylinder is at a distance r away from the axis of rotation, so I=mr2.
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