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Math Help - rotation question

  1. #1
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    rotation question

    a uniform disc of mass 10 kg radius 1m is placed on a rough horizontal table the coefficient of friction between the disc and the surface is 0.2 a horizontal time varying force is applied on the centre of the disc whose variation with time is as shown in the graph.after 8s the force falls down to zero instantly.find the time at which following occur

    a disc rolls without slipping
    b disc rolls with slipping
    c friction force is less than applied force
    d friction force is zero

    I KNOW HOW FRICTION WORKS IN CASE OF THIS QUESTION BUT HW TO SOLVE THE PROBLEM PLEASE HELProtation question-untitled.jpg
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  2. #2
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    Quote Originally Posted by prasum View Post
    a uniform disc of mass 10 kg radius 1m is placed on a rough horizontal table the coefficient of friction between the disc and the surface is 0.2 a horizontal time varying force is applied on the centre of the disc whose variation with time is as shown in the graph.after 8s the force falls down to zero instantly.find the time at which following occur

    a disc rolls without slipping
    b disc rolls with slipping
    c friction force is less than applied force
    d friction force is zero

    I KNOW HOW FRICTION WORKS IN CASE OF THIS QUESTION BUT HW TO SOLVE THE PROBLEM PLEASE HELPClick image for larger version. 

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    from the graph , applied force at the axle as a function of time is F_a = 10t

    the force of static friction, f_s starts out opposite to F_a and increases until it reaches its maximum, f_{s\,max}.

    f_{s\,max} = \mu \cdot F_N = \mu \cdot 10g = 10t<br />

    t = \mu g \approx 2 \, sec

    so, reason out the following ...

    how does the disk roll in the first two seconds?

    how does it roll from t = 2 to t = 8 seconds?

    what happens after t = 8 seconds when F_a is removed?
    Last edited by skeeter; March 25th 2011 at 04:18 PM.
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    can yu tell me what will happen at t=5s t=7s t=7.5s and t=12s
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  4. #4
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    Quote Originally Posted by prasum View Post
    can yu tell me what will happen at t=5s t=7s t=7.5s and t=12s
    Show us what you think is going to happen at those times.

    -Dan
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  5. #5
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    i think at t=5s and t=12s the body will roll without slipping
    at t=7.5s and t=7s the body will roll with slipping
    friction force will be less than applied force at t=5s,7s,7.5s
    friction force is zero at t=12s
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