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Tension and Torque homework challenge problem.

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data
    A 4KG mass is connected by a weightless cord to a 3 kg mass on a smooth surface. The pully rotates about a frictionless axle and has a moment of inertia of 0.5 kgm^2 and radius of 0.3m. Assuming that the cord does not slip on the pully, find a.) the acceleration of the two masses and b.) the tensions T1 and T2.


    Click the image below to expand it to see what this looks like.

    [​IMG]


    2. Relevant equations
    T1=39.24-ma
    T2=3a
    Torque1=0.3T1
    Torque2=0.3T2
    I=mr^2
    Torque=Parallel force x radius
    Net Torque=Ialpha


    3. The attempt at a solution

    I started by finding the mass(M) of the pully.
    0.5=0.09M
    M=5.56
    I then used the net torque equation, substituting a/r for alpha.
    nettorque=1.67a
    I then summed my torques to this.
    torque1-torque2=1.67a
    0.3T1-0.3T2=1.67a
    0.3(T1-T2)=1.67a
    T1-T2=5.56a
    Next I substituted my tensions in.
    (39.24-4a)-3a=5.56a
    39.24=12.56a
    3.12a

    I figured that now I could substitute the acceleration back in my original tension equations to find the tensions.
    T2=3(3.12)
    T2=9.37
    T1=39.24-12.48
    T1=26.76

    There is no answer in the back of the book for this one, and I want somebody to check(rather than skim) my work and tell me if I have come to the right conclusion. If not, please tell me what I have done wrong. It's important that I can do this kind of equation for this week's test.
     
    Last edited: Oct 24, 2007
  2. jcsd
  3. Oct 24, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good to me except for this first step:
    (1) You don't need the mass of the pulley, only the rotational inertia, which is given.
    (2) Your equation for rotational inertia (I = mR^2) is incorrect; if you model the pulley as a uniform disk, I = 1/2mR^2.

    Luckily, you made no further use of this calculation, so the rest of your work is fine.
     
  4. Oct 24, 2007 #3
    Your answers are correct.
     
  5. Oct 24, 2007 #4
    Thanks I'll found out later what the verdict is.
     
  6. Oct 24, 2007 #5
    I was the only one in the class who got it right. Thanks for checking my work guys X)
     
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