Bear asked in Science & MathematicsPhysics · 2 months ago

string tension?

Calculate the magnitude of the tension in string1 if θ1 = 33.91°, θ2 = 52.83° and the mass of the sign is 5.10 kg.

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  • 2 months ago
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    Answer: 

    S1 = 30.25 N

    S2 = 41.55 N

    Explanation:

    Let tension forces in string 1 and 2 are S1 and S2 respectively. Supposed directions are away from the sign.

    Condition of static equilibrium is that:

    1) the sum of all forces in x-direction is zero.

    2) the sum of all forces in y-direction is zero

    This yields 2 equations

    S1 cos θ1 - S2 cos θ2 = 0

    S1 sin θ1 + S2 sin θ2 - mg = 0

    From 1st equation

    S1 = S2 cos θ2 / cos θ1 ...... (*)

    substitute this into 2nd equation

    S2 (cos θ2 sin θ1 / cos θ1 + sin θ2) - mg = 0

    S2 = mg / (cos θ2 tan θ1 + sin θ2)

    S2 = 5.1 * 9.8  / (cos 52.83° tan 33.91° + sin 52.83°) = 41.55 N

    Back to (*)

    S1 = 41.55 cos 52.83° / cos 33.91° = 30.25 N

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