A 500-g cubic block of a composite material floats with 40% of its volume submerged in your swimming pool.The force you have to apply to fully submerge it in the water is
A)7.4 N.
B)9.8 N.
C)13.2 N.
D)19.4 N.
E)27.5 N.

Question

Quizplus · Accepted Answer

The force required to fully submerge the block equals the buoyant force acting on it when fully submerged minus the weight of the block. The buoyant force equals the weight of the displaced water when the block is fully submerged. Since 40% of the block's volume is initially submerged, the buoyant force equals 40% of the block's weight in water. The block's weight is $500 \, \text{g} \times 9.8 \, \text{m/s}^2 = 4.9 \, \text{N}$. To fully submerge the block, the applied force must overcome the difference between the buoyant force when fully submerged and the block's weight. The volume of water displaced when fully submerged would have a weight equal to the block's weight (4.9 N), so the additional force needed is $4.9 \, \text{N} - 40\% \times 4.9 \, \text{N} = 4.9 \, \text{N} - 1.96 \, \text{N} = 2.94 \, \text{N}$. However, this calculation mistake led to an incorrect explanation. Correctly, since the block is floating, its weight is equal to the buoyant force from the displaced water when 40% submerged. To fully submerge it, the force applied must equal the weight of the water displaced by the entire volume of the block, which is greater than the weight of the block itself. Given the density of water (1000 kg/m³) and gravity (9.8 m/s²), the force to submerge the block fully is calculated based on the volume of the block and the density of water. The correct approach involves calculating the total buoyant force when fully submerged, which is equal to the weight of the displaced volume of water. The volume of the block is found from its mass and the density of the composite material, which can be derived from the given information that 40% of its volume is submerged (indicating its average density relative to water). The error in the initial explanation was in the calculation process and misunderstanding the question's requirement for the additional force needed to fully submerge the block, not just the difference based on its initial floating condition.

A 500-G Cubic Block of a Composite Material Floats with 40