Question

1. Samer (ms = 75 kg) is sitting on the seat of a swing at the playground. The seat is supported by two

cables, one on each side of the seat. (You may assume the seat has negligible mass.)

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A. Determine the tension in each cable due to Samer sitting on the swing seat.

B. Given each cable has a diameter of 1 mm and each cable is exactly 5 m long before Samer sits on the seat, determine the length of each cable when Samer is sitting on the seat. (The cables are made of aluminum for which Y = 70 GN/m2.)

Answer 1

The weight is supported by two cables. hence 2T =mg =>T = mg / 2

The tension in each cable is T = 367.5 N

The youngs modulus is then

Force = 367.5 N; Y = 70 G N/m2 = 70 x 109 N/m2; L = 5m;

diameter = 1mm then radius r = 5x10-4 m Hence A = r2 = 78.54 x 10-8 m2

The elongation e = 0.0334  m

The final length of each cable is L + e = 5.03 m