A uniform rod 8m long weighing 5kg is supported horizontally by two vertical parallel strings at p and q and at distance 2m and 6m from one end. Weight of 1kg, 1.5kg and 2kg are attached at distance of 1m 5m and 7m respectively from the same end.
find the tension in each vertical string

Fp = 36 N

Fq = 58 N

Explanation:

Let the left end be the reference end with string p closest to it.

Let CCW moments be positive

Sum moments about p to zero

1(9.8)[2 - 1] + Fq[6 - 2] - 5(9.8)[8/2 - 2] - 1.5(9.8)[5 - 2] - 2(9.8)[7 - 2] = 0

                                                                              Fq[4] = 23.5(9.8)

                                                                                  Fq = 57.575 ≈ 58 N

Sum moments about q to zero

1(9.8)[6 - 1]  - Fp[6 - 2] + 5(9.8)[6 - 8/2] + 1.5(9.8)[6 - 5] - 2(9.8)[7 - 6] = 0

                                                                                                     Fp = 35.525 N

or

Sum vertical forces to zero

Fp + 57.575 - (9.8)(1 + 1.5 + 2 + 5) = 0

Fp = 35.525  ≈ 36 N

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