To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water.She finds that the specimen weighs twice as much in air as it does in water.The solid part of the specimen has a density of 5.0 multiplied by 10(cubed)kg/m(cubed).What fraction of the specimen's apparent volume is solid
The average density of the rock is 2.00*10^3 kg/m^3, which is twice that of water. That is because the buoyancy force in water equals half the weight in air. The solid part (with mass 5.0 kg/m^3) needs to occupy only 40% of the volume in order for the rock to have a total mass of 2.00*10^3 kg/m^3.
40% is the answer
To determine the fraction of the specimen's apparent volume that is solid, we need to utilize the concept of density and the weight measurements in air and water.
1. Start by understanding the concept of density: Density is defined as mass per unit volume. For a solid object, the density can be calculated using the formula: density = mass / volume.
2. Given information:
- The solid part of the specimen has a density of 5.0 * 10^3 kg/m^3.
- The weight of the specimen in air is twice its weight in water.
3. Use the weight measurements to calculate the density of the whole specimen:
- Let's assume the volume of the specimen in air is V1, and the volume of the specimen in water is V2.
- The weight of the specimen in air is equal to the weight of the solid part plus the weight of the empty space inside the specimen: Weight in air = (density of solid part * V1) + (density of air * V1).
- The weight of the specimen in water is equal to the weight of the solid part plus the weight of the water displaced by the empty space inside the specimen: Weight in water = (density of solid part * V2) + (density of water * V2).
4. Since we know that the weight in air is twice the weight in water (Weight in air = 2 * Weight in water), we can write the following equation:
(density of solid part * V1) + (density of air * V1) = 2 * [(density of solid part * V2) + (density of water * V2)].
5. Rearrange the equation to solve for V1/V2 (the ratio of volumes) and find the fraction of the specimen's apparent volume that is solid:
(density of solid part * V1 + density of air * V1) = 2 * (density of solid part * V2 + density of water * V2)
V1 * (density of solid part + density of air) = 2 * V2 * (density of solid part + density of water)
V1 / V2 = 2 * (density of solid part + density of water) / (density of solid part + density of air).
6. Finally, substitute the given values into the equation to find the desired fraction of the specimen's apparent volume that is solid.
V1 / V2 = 2 * (5.0 * 10^3 kg/m^3 + 1.0 * 10^3 kg/m^3) / (5.0 * 10^3 kg/m^3 + 1.2 kg/m^3).
By calculating the above expression, you can find the fraction of the specimen's apparent volume that is solid.