Homework Solution

TQ 8-4

To float, the apparent weight of the ship must be zero, that is:

W_app = 0 = B - W

where

W_app is the apparent weight
B is the buoyant force, and
W is the actual weight (2 tons).

Then

B = W

(the ship floats)

Whether the fluid is water of alcohol makes no difference:

B = 2 tons

 

If the ship sinks, the volume of liquid displaced decreases. Since the buoyant force is equal to the weight of the fluid displaced and less fluid is displaced, the buoyant force decreases.