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March 27, 2017

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A light string has its ends tied to two walls separated by a distance equal to five-eighths the length of the string. A 53 kg mass is suspended from the center of the string, applying a tension in the string.

What is the tension in the two strings of length L/2 tied to the wall? The acceleration of gravity is 9.8 m/s^2.
Answer in units of N.

  • physics - ,

    Draw the triangles.

    half the weight is supported by each side.

    Let theta be the angle from the wall horizontal to the string. Then on each side, SinTheta=Weight/(2*tension)

    But tan cosTheta= half wall distance/halfstring distance
    costheta= 5/8

    But sin^2theta+cos^2theta=1
    or weight^2/4Tension^2+25/64=1
    solve for tension.

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