Question

You bet a friend that she can not completely submerge a large beach ball in your swimming pool by standing on it. Assume the beach ball, whose fabric has a mass of 1.85 kg, and has a radius of .450 meters. What must your friend weigh at the very least to accomplish this?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of water = = 1000 kg/m³

Mass of the beach ball = m = 1.85 kg

Radius of the beach ball = R = 0.45 m

Weight of your friend to completely submerge the ball by standing on it = W

Volume of the beach ball = V

V = 4R³/3

V = 4(0.45)³/3

V = 0.3817 m³

The weight of the volume of water displaced that is the buoyancy force on the ball is equal to the weight of the ball and your friend.

Vg = mg + W

(1000)(0.3817)(9.81) = (1.85)(9.81) + W

W = 3726.36 N

Your friend must weigh at least 3726.36N to submerge the beach ball.