A raft with the area A, thickness = h and the mass 600 kg, Floats in still water with 7 cm

under the water surface. When Bubba stands on the raft it sinks down further in the water so

the raft is 8.4 cm under the water surface. What is Bubba's mass?,

In this problem, we need to solve for Bubba’s mass. To do this, we let A be the area of the raft and set the weight of the displaced fluid with the raft alone as ρwAd1g and ρwAd2g with the person on the raft, where ρw is the density of water, d1 = 7cm, and d2 = 8.4 cm. Set the weight of displaced fluid equal to the weight of the floating objects to eliminate A and ρw then solve for m.

ρwAd1g = Mg

ρw Ad2g = (M + m) g

d2∕d1 = (M + m) / g

m = [ (d2 ∕d1) - 1] M = [ (8.4 cm/7.0 cm) - 1] (600 kg) = 120 kg

This means that Bubba’s mass is 120 kg.