A rock weighs 100 N in air and has a volume of 0.00312 m^3.
What is its apparent weight when submerged in water? The acceleration of gravity is 9.8 m/s^2.
Answer in units of N.
To find the apparent weight of the rock when submerged in water, we need to use Archimedes' principle, which states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
To calculate the buoyant force, we first need to find the weight of the water that is displaced by the rock, which is equal to the volume of the rock submerged in water multiplied by the density of water and the acceleration due to gravity.
The density of water is approximately 1000 kg/m^3. So, the weight of the water displaced by the rock is:
Weight = Volume_submerged * Density_water * Gravity
Volume_submerged = Volume of the rock * Density_rock / Density_water
But since the density of the rock is not provided, we cannot directly calculate the volume submerged. However, we can assume that the rock's density is greater than that of water since it sinks. Therefore, the entire rock is submerged in water. Hence, we can use the entire volume of the rock for the calculation.
Using the provided values, we have:
Weight = 0.00312 m^3 * 1000 kg/m^3 * 9.8 m/s^2
Weight = 30.576 N
Therefore, the apparent weight of the rock when submerged in water is approximately 30.576 N.
To find the apparent weight of the rock when submerged in water, we need to consider the buoyant force acting on it.
The buoyant force is equal to the weight of the water displaced by the rock. It can be calculated using the formula:
Buoyant force = density of fluid × volume of fluid displaced × acceleration due to gravity
First, let's calculate the density of water. The density of water is approximately 1000 kg/m^3.
Density of water = 1000 kg/m^3
Now, let's calculate the volume of water displaced by the rock.
Volume of water displaced = volume of rock
Given: volume of rock = 0.00312 m^3
Volume of water displaced = 0.00312 m^3
Now, we can substitute the values into the formula to calculate the buoyant force.
Buoyant force = density of water × volume of water displaced × acceleration due to gravity
= 1000 kg/m^3 × 0.00312 m^3 × 9.8 m/s^2
Buoyant force = 30.912 N
Therefore, the apparent weight of the rock when submerged in water is 30.912 N.