1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    v=rw

    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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    In the equation

    [tex]K=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2[/tex]

    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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook