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650 N boy and a 419 N girl sit on a 150 N porch swing that is 2.0 m long. If the swing is supported by a chain at each end, what is the tension in each chain when the boys sits .8 m from one end and the girls sits .5 m from the other end

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mickymike92

The tension in the two chains T1 and T2 is 676.65 N and 542.53 N respectively.

Principle of moments

The Principle of Moments states that when a body is in equip, the sum of clockwise moment about a point is equal to the sum of anticlockwise moment about the same point.

The formula for calculating moment is given below:

  • Moment = Force × perpendicular distance from the pivot

Calculating the tension in the chains

From the principle of moments:

Let tension in chain 1 be T1 and tension in chain 2 be T2.

T1 + T2 = 150 + 650 + 419

T1 + T2 =1219

Taking all distances from chain 1,

Sum of Moments = 0

419 × 0.5 + 150 × 0.85 + 650 × 0.9 = T2 × 1.7

T2 = 922/17

T2 = 542.35 N

Then, T1 = 1219 - 542.35

T1 = 676.65 N

Therefore, the tension in the two chains T1 and T2 is 676.65 N and 542.53 N respectively.

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