Question

3. A scuba tank, when fully submerged, displaces 15.7 liters of seawater. The tank has a total mass of 14 kg when empty; when full, it contains 3 kg of air. a) If you release the full tank (from rest) from a spot underneath the surface of the ocean, does it sink, remain at that spot, or rise to the surface? Explain. b) If the tank is initially 2 m below the ocean surface, determine the pressure that the ocean water exerts on it there.
c) If the tank had been empty, would your answer part (a) have been the same? Explain. to d) If a 5-kg object were floating on the ocean surface, would it displace any seawater? If so, how much? If not, why not?

Answer 1

(A) Buoyant force = weight of dispalced water = 15.7 x 1.025 x g = 16.1 g

Weight of full tank = (14 + 3)g = 17g

hence Weight of tank is more than buoyant force so it will sink.

(B) P = Patm + rho g h

= (101325) + (1025 x 9.81 x 2) = 121435 Pa

(C) If empty then weight = 14g which is less than buoyant force.

so it will rise to the surface

(D) It has mass hence it will displace the water of same weight.

Water displaced = 5 kg

Volume = 5 / 1.025 = 4.878 litre