A polystyrene block has a volume of 600 ml. What volume of the block is above the liquid when the block floats in carbon tetrachloride? [polystyrene density = 1060 kg/m3; density o... A polystyrene block has a volume of 600 ml. What volume of the block is above the liquid when the block floats in carbon tetrachloride? [polystyrene density = 1060 kg/m3; density of carbon tetrachloride = 1590 kg/m3]
Understand the Problem
We need to determine the volume of a polystyrene block that will be above the liquid when the block floats in carbon tetrachloride. We are given the volume of the polystyrene block and the densities of polystyrene and carbon tetrachloride. We will determine buoyancy force acting on the block and then solve for the percentage of volume above the liquid.
Answer
E) 200 ml
Answer for screen readers
E) 200 ml
Steps to Solve
- Calculate the fraction of the block submerged
When the block floats, the buoyant force equals the weight of the block. The buoyant force is the weight of the fluid displaced by the submerged portion of the block. Let $V_{sub}$ be the submerged volume and $V_{total}$ be the total volume of the block, $\rho_{ps}$ be the density of polystyrene and $\rho_{ct}$ be the density of carbon tetrachloride. Then:
Weight of the block = Buoyant force
$\rho_{ps} * V_{total} * g = \rho_{ct} * V_{sub} * g$
$V_{sub} / V_{total} = \rho_{ps} / \rho_{ct}$
$V_{sub} / V_{total} = 1060 \text{ kg/m}^3 / 1590 \text{ kg/m}^3 \approx 0.6667$
- Calculate the submerged volume
$V_{sub} = 0.6667 * V_{total} = 0.6667 * 600 \text{ ml} = 400 \text{ ml}$
- Calculate the volume above the liquid
$V_{above} = V_{total} - V_{sub} = 600 \text{ ml} - 400 \text{ ml} = 200 \text{ ml}$
E) 200 ml
More Information
The volume of the polystyrene block above the carbon tetrachloride is 200 ml.
Tips
A common mistake is to calculate only the submerged volume and not subtract it from the total volume to find the volume above the liquid. Another common mistake is to not use consistent units.
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