Final answer:
Using the principle of buoyancy and the density of alcohol, the block's volume is calculated by setting the weight loss in water and alcohol equal after adjusting for the density of each fluid. The volume is found to be approximately 2.53827 liters.
Step-by-step explanation:
The block's apparent weight loss when submerged in a fluid is equal to the weight of the fluid displaced by the block. Using the fact that the apparent weight of the block in water is 24.9 N and in alcohol is 25.8 N, along with the density of alcohol (806 kg/m³), we can determine the block's volume. This phenomenon is known as buoyancy. In water, the volume of displaced water (V) relates to the weight of the displaced water, which equals the block's apparent weight loss. The volume can be calculated as follows:
- Let Fw be the weight loss in water.
- Let Fa be the weight loss in alcohol.
- Let ρw be the density of water (1000 kg/m³).
- Let ρa be the density of alcohol (806 kg/m³).
- Using Archimedes' principle, V = Fw / (ρw * g) = Fa / (ρa * g), where g is the acceleration due to gravity (9.81 m/s²).
- Solve for V, knowing Fw = 24.9 N and Fa = 25.8 N.
Since both equations equal V, they can be set equal to each other:
24.9 / (1000 kg/m³ * 9.81 m/s²) = 25.8 N / (806 kg/m³ * 9.81 m/s²).
Solving for V gives:
V = 24.9 N / (1000 kg/m³ * 9.81 m/s²) = 0.00253827 m³ = 2.53827 liters.
So the block's volume is approximately 2.53827 liters.