Final answer:
The block's volume is 0.0004210 m³, and its density is 6080 kg/m³. This was calculated using the difference in reading of the spring scale when the block was immersed in water and alcohol, and applying the principles of buoyancy.
Step-by-step explanation:
When the block is fully immersed in water, the spring scale reads 25.1 N, which represents the weight of the block in the air minus the buoyant force exerted by water. When immersed in alcohol, the scale reads 25.9 N. Since the density of water is 1000 kg/m3, and the density of alcohol is 806 kg/m3, the loss of weight due to buoyancy will be lesser in alcohol, indicating a smaller buoyant force due to its lower density.
To find the block's volume, we use the buoyancy force difference:
Buoyant force in water = Weight in air - Weight in water
Buoyant force in alcohol = Weight in air - Weight in alcohol.
The difference between these two buoyant forces gives the additional upward force provided by the difference in alcohol's and water's densities:
(Weight in water - Weight in alcohol) = (Density of water - Density of alcohol) × Volume of block × Gravity
25.1 N - 25.9 N = (1000 kg/m3 - 806 kg/m3) × Volume of block × 9.81 m/s2
The Volume of the block = 0.8 N / (194 kg/m3 × 9.81 m/s2) = 0.0004210 m3
To find the block's density, we use its weight in air (equal to the gravitational force on the block):
Weight in air = Mass of the block × Gravity
Weight in water or alcohol is the weight in air - buoyancy force in respective liquid.
Pick any one to find the mass:
25.1 N = Mass in water × 9.81 m/s2
Mass of the block = 25.1 N / 9.81 m/s2 = 2.56 kg
Density of the block = Mass / Volume = 2.56 kg / 0.0004210 m3 = 6080 kg/m3