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Math Help - Find the tension...

  1. #1
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    Find the tension...

    A 0.300 kg object is suspended from the ceiling of an accelerating boxcar as in the figure below. The acceleration a = 2.90 m/s2
    a) find the angle that the string makes with the vertical
    b) find the tension in the string.
    I'm not sure how to do this problem, I tried using Newton's 2nd law
    \sum F = ma and go part b to be 8.526. Please help.
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  2. #2
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    the forces acting on the mass are tension (T) in the string and weight (mg).

    weight is straight down in direction.

    let \theta be the angle the string makes with the vertical.

    the components of T are ...

    T_x = T\sin{\theta}

    T_y = T\cos{\theta}

    since there is no acceleration in the y-direction, net force in the y-direction is 0 ...

    (1) T\cos{\theta} = mg

    tension in the x-direction is providing the necessary net force ...

    (2) T\sin{\theta} = ma

    solve for T in the first equation ...

    T = \frac{mg}{\cos{\theta}}

    substitute this expression for T in the second equation ...

    \frac{mg}{\cos{\theta}} \cdot \sin{\theta} = ma

    g \tan{\theta} = a

    \tan{\theta} = \frac{a}{g}

    \theta = \arctan\left(\frac{a}{g}\right)

    go back and find T.
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