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Math Help - Tension and Pulleys! (Statics of Particles)

  1. #1
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    Question Tension and Pulleys! (Statics of Particles)

    1. The problem statement, all variables and given/known data
    See figure.


    2. Relevant equations
    Sum of Fy = 0
    Sum of Fx = 0


    3. The attempt at a solution

    I can't see how to solve this. The only thing I can think of is the vertical forces of both sides of the pulley are going to equal the gravitational force of the mass in and that the two x components on each side of the rope will cancel.

    I don't have the magnitude on the right hand side of the pulley and on the left hand side I don't have the magnitude or the angle. How do we solve this?

    Thanks in advance. (If I posted this in the wrong forum please let me know)
    Attached Thumbnails Attached Thumbnails Tension and Pulleys! (Statics of Particles)-tensionpulley.jpg  
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  2. #2
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    Hello jegues

    Welcome to Math Help Forum!
    Quote Originally Posted by jegues View Post
    1. The problem statement, all variables and given/known data
    See figure.


    2. Relevant equations
    Sum of Fy = 0
    Sum of Fx = 0


    3. The attempt at a solution

    I can't see how to solve this. The only thing I can think of is the vertical forces of both sides of the pulley are going to equal the gravitational force of the mass in and that the two x components on each side of the rope will cancel.

    I don't have the magnitude on the right hand side of the pulley and on the left hand side I don't have the magnitude or the angle. How do we solve this?

    Thanks in advance. (If I posted this in the wrong forum please let me know)
    If the pulleys are smooth and frictionless (and we must assume they are) then the tension in the string is the same throughout its length. Since the tension at the free end is T, then the tension throughout will be T. So we have a force 2T acting at 27^o to the vertical on the RHS.

    So use the equations you have written down in (2), and solve for T and \alpha.

    Here's the first one:
    2T\sin27^o+T\cos\alpha = 0

    Answers:
    Spoiler:
    Taking g = 9.8, I get \alpha = 24.8^o and T = 890 N.

    Grandad
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  3. #3
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    So,

    <br />
2T\sin27^o+T\cos\alpha = 0<br />

    and

    <br />
2T\cos27^o+T\sin\alpha = 0<br />

    How do you go about solving this?

    Is it simply,

    <br />
T(2\sin27^o+\cos\alpha) = 0<br />

    T cannot be zero so we solve for the part in brackets?

    Thanks again!
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  4. #4
    MHF Contributor
    Grandad's Avatar
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    Hello jegues
    Quote Originally Posted by jegues View Post
    So,

    <br />
2T\sin27^o+T\cos\alpha = 0<br />

    and

    <br />
2T\cos27^o+T\sin\alpha = 0<br />

    How do you go about solving this?

    Is it simply,

    <br />
T(2\sin27^o+\cos\alpha) = 0<br />

    T cannot be zero so we solve for the part in brackets?

    Thanks again!
    Yes, but (apologies!) the equation should read
    2T\sin27^o - T\cos \alpha=0 (Of course!)
    So you get:
    \cos\alpha = 2\sin27^o

    \Rightarrow \alpha = 24.8^o
    But your second equation isn't right. You've forgotten the weight force, which is -200\times 9.8 N. Add this into your equation, substitute the value you have found for \alpha, and solve for T.

    Grandad
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