A styrofoam ball is attached to the bottom of a swimming pool with a nylon cord.

Question

A styrofoam ball is attached to the bottom of a swimming pool with a nylon cord. The cord is 1.20 m long and the pool is 3.40 m deep. If the ball has a diameter of 46.0 cm and the density of styrofoam is 0.300 g/cc, find the tension in the cord.

Explanation / Answer

Volume of ball = (4/3)pir^3 diameter = 46 cm =>radius = d/2 = 23 cm = 0.23 m =>Volume = (4/3)*(22/7)*(0.23^3) = 0.050985524 m^3 mass = m = density*volume = 0.3*1000*0.050985524 = 15.29565714 Kg weight of fluid displaced = 1000*Volume*g = 1000*9.81*0.050985524 = 500.1679904 N T+Weight of ball = Weight of fluid displaced =>T = 500.1679904-(15.29565714*9.81) = 350.1175939 N

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