Question

6 - 3 if a block of wood floats with half its volume submerged,
a. the buoyant force is equal to half the weight of the block.
b. the weight of the block is the same as that of the displaced water.
c. the volume of the block is the same as that of the displaced water.
d. the buoyant force is equal to twice the weight of the displaced water.
e. the buoyant force is equal to twice the weight of the block.
6 - 4 now this same block of wood that was floating with one - half of its volume out of the water is pushed down so that it is completely underneath the water. which of the following statements is correct?
a. the buoyant force on the block is the same in the two cases because the weight per unit volume of the wood has not changed.
b. the buoyant force on the block is the same in the two cases because the weight per unit volume of the water is the same in each case.
c. the buoyant force on the block is greater when the block is completely submerged than it is when the block is floating.
d. the buoyant force on the block is greater when it is floating than when it is totally submerged.
e. the buoyant force on the block is the same in the two cases because

Explanation:

Step1: Recall Archimedes' principle

The buoyant force \(F_b=
ho_{fluid}gV_{displaced}\). When the block is floating with half - volume submerged, \(F_{b1}=
ho_{water}g\frac{V}{2}\), and when it is completely submerged \(F_{b2}=
ho_{water}gV\). Also, when floating, the buoyant force equals the weight of the block \(F_b = mg\). When floating with half - volume submerged, \(F_{b1}=mg\) where \(F_{b1}=
ho_{water}g\frac{V}{2}\), and when completely submerged \(F_{b2}\) (where \(F_{b2}=
ho_{water}gV\)) is greater than the weight of the block (it will sink if not held down), and the buoyant force on the floating block is \(F_{b1}\) and on the completely submerged block is \(F_{b2}\), and \(F_{b2}>F_{b1}\).

Step2: Analyze each option

• Option A: The buoyant force on the block is the same in the two cases because the weight per unit volume of the wood has not changed. This is incorrect as the buoyant force depends on the volume of water displaced, not the weight per unit volume of the wood.
• Option B: The buoyant force on the block is the same in the two cases because the weight per unit volume of the water is the same in each case. This is incorrect as the volume of water displaced is different in the two cases.
• Option C: The buoyant force on the block is greater when the block is completely submerged than when the block is floating. This is correct as \(F_b=

ho_{water}gV_{displaced}\), and \(V_{displaced}\) is larger when the block is completely submerged.

• Option D: The buoyant force on the block is greater when it is floating than when it is totally submerged. This is incorrect.
• Option E: The buoyant force is equal to twice the weight of the block. There is no basis for this claim in the context of the floating and submerged block in water.

Answer:

C. The buoyant force on the block is greater when the block is completely submerged than when the block is floating.