calculate the weight ofa stone of mass 10kg and density 10000kg/m3 when it is totally immersed in water
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To calculate the weight of the stone when it is immersed 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 stone. It can be calculated using the formula:
Buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity
Given:
Mass of the stone (m) = 10 kg
Density of the stone (ρ) = 10000 kg/m^3
Density of water (ρ_water) = 1000 kg/m^3 (approximate value)
Acceleration due to gravity (g) = 9.8 m/s^2 (approximate value)
To find the volume of the stone (V), we can use the formula: V = m / ρ
V = 10 kg / 10000 kg/m^3 = 0.001 m^3
Next, we calculate the buoyant force using the formula mentioned earlier:
Buoyant force = ρ_water * V * g
Buoyant force = 1000 kg/m^3 * 0.001 m^3 * 9.8 m/s^2 = 9.8 N
So, when the stone is totally immersed in water, the buoyant force acting on it is 9.8 Newtons.
To calculate the weight of an object when it is immersed in a fluid, we need to consider the buoyant force acting on the object. The buoyant force is the upward force exerted on an object submerged in a fluid, and it is equal to the weight of the fluid displaced by the object.
Given:
Mass of the stone (m): 10 kg
Density of the stone (ρ): 10000 kg/m^3
To determine the weight of the stone when it is immersed in water, we need to find the weight of the stone in air and subtract the buoyant force.
1. Calculate the weight of the stone in air:
Weight = mass * acceleration due to gravity
Weight = m * g
Weight = 10 kg * 9.8 m/s^2
Weight = 98 N (Newton)
2. Calculate the volume of the stone:
Density = mass / volume
Volume = mass / density
Volume = 10 kg / 10000 kg/m^3
Volume = 0.001 m^3
3. Calculate the buoyant force:
Buoyant force = weight of the fluid displaced
Buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity
For water, the density is approximately 1000 kg/m^3
Buoyant force = 1000 kg/m^3 * 0.001 m^3 * 9.8 m/s^2
Buoyant force = 9.8 N
4. Determine the weight of the stone when immersed in water:
Weight in water = Weight in air - Buoyant force
Weight in water = 98 N - 9.8 N
Weight in water = 88.2 N
Therefore, the weight of the stone when it is totally immersed in water is 88.2 N.