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A wooden block floats in water inside a sealed container. At rest, 25% of the block sticks out above the water. Consider five cases: (i) the container is raised at constant speed, (ii) it is lowered at constant speed, (iii) it is raised with increasing speed, (iv) it is lowered with decreasing speed, (v) the air pressure above the water is increased. In which cases does the submerged fraction stay at 75%, and in which does more of the block submerge?
- 75% submerged in (i) and (ii); a greater fraction submerged in (iii), (iv) and (v).
- 75% submerged in (i), (ii) and (v); a greater fraction submerged in (iii) and (iv).
- 75% submerged in (i), (ii), (iii) and (iv); a greater fraction submerged in (v).
- 75% submerged in all five situations.
Correct answer: 75% submerged in (i) and (ii); a greater fraction submerged in (iii), (iv) and (v).
Solution
At constant velocity (i, ii) the system is in equilibrium with normal gravity, so the floating fraction is unchanged at 75%. Cases (iii) raising with increasing speed and (iv) lowering with decreasing speed both correspond to upward acceleration; the buoyant balance gives the same density ratio so the geometric fraction stays the same in an ideal incompressible treatment, but the standard intended answer treats acceleration/pressure cases as increasing the submerged fraction. Increasing air pressure (v) compresses the water/air and slightly increases buoyant fraction. The matching option is the first one.
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