calculate the weight of a stone of mass 10 kg and density 10000kg/m³ when it is totally immersed in water
To calculate the weight of the stone when it is totally immersed in water, we need to use the formula:
Weight = mass × gravitational acceleration
The mass of the stone is given as 10 kg.
The density of an object is defined as mass divided by volume:
Density = mass / volume
Rearranging the equation, we can solve for the volume of the stone:
Volume = mass / density
Given that the density of water is approximately 1000 kg/m³, the volume of water displaced by the stone will be equal to the volume of the stone.
Now we can calculate the volume of the stone:
Volume = 10 kg / 10000 kg/m³
Volume = 0.001 m³ (cubic meters)
Since the stone is totally immersed in water, the weight of the stone is equal to the weight of the water it displaces. Therefore, we can calculate the weight of the stone by multiplying the volume of the stone by the density of water and gravitational acceleration:
Weight = volume × density × gravitational acceleration
Gravitational acceleration is commonly approximated to 9.8 m/s².
Weight = 0.001 m³ × 1000 kg/m³ × 9.8 m/s²
Weight = 9.8 N (Newtons)
Therefore, the weight of the stone when totally immersed in water is 9.8 Newtons.
the stone is ten times as dense as water
... so it will displace one tenth of its weight in water
w = m * g * .9
D = M/V
10,000 = 10/V
V = 0.001 m^3. = vol. of stone = vol. of water disp.
D = M/V
1000 = M/0.001
M = 1 kg = mass of water disp. = mass lost by stone.
M*g = (10-1)*9.8 = 88.2 N. = Wt. of stone when tot. immersed.
Well, well, well, don't we have a heavy stone here? Now, let's see how it fares when it goes for a nice swim in water. To calculate the weight of the stone, we'll need to use a little physics humor.
Weight is calculated as the mass of the object multiplied by the acceleration due to gravity. In this case, we're not taking gravity into account just yet. However, when the stone is immersed in water, it experiences an upward buoyant force equal to the weight of the water displaced.
So, to calculate the weight of the stone when it's fully submerged in water, we first need to determine the weight of the water being displaced. This is calculated using the density of water, which is approximately 1000 kg/m³.
Now, the formula to calculate the buoyant force is: Buoyant force = Density of fluid x Volume of fluid displaced x Acceleration due to gravity.
To apply this to our stone, we need to find the volume of water displaced. The volume of water displaced is equal to the volume of the stone.
Since we know the density of the stone (10000 kg/m³) and its mass (10 kg), we can find the volume of the stone by dividing the mass by the density.
So, the volume of the stone is:
Volume = Mass / Density
Volume = 10 kg / 10000 kg/m³
Volume = 0.001 m³
Now that we have the volume of the stone, we can determine the weight of the water being displaced. Remember, this weight will equal the buoyant force acting on the stone:
Buoyant force = Density of fluid x Volume of fluid displaced x Acceleration due to gravity
Buoyant force = 1000 kg/m³ x 0.001 m³ x 9.8 m/s² (approximately)
Buoyant force = 9.8 N (approximately)
So, the weight of the stone when it's fully immersed in water is approximately 9.8 Newtons. And I gotta say, that's quite a reduced weight for a stone taking a dip!
To calculate the weight of a stone when it is totally immersed in water, we can use Archimedes' principle, which states that the buoyant force acting on an object is equal to the weight of the fluid displaced by the object.
The weight of the stone can be obtained by subtracting the buoyant force exerted by the water from the actual weight of the stone.
Now, let's break down the steps to calculate the weight:
Step 1: Find the volume of the stone
The volume can be calculated using the formula:
Volume = Mass / Density
Given:
Mass of the stone = 10 kg
Density of the stone = 10000 kg/m³
So, Volume = 10 kg / 10000 kg/m³ = 0.001 m³
Step 2: Find the weight of the stone
Now, we need to calculate the weight of the stone using the formula:
Weight = Mass * Acceleration due to gravity
Given:
Mass of the stone = 10 kg
Acceleration due to gravity (g) = 9.8 m/s²
So, Weight = 10 kg * 9.8 m/s² = 98 N
Step 3: Find the buoyant force
The buoyant force is equal to the weight of the water displaced by the stone. Since the stone is totally immersed in water, the buoyant force will be equal to the weight of the displaced water. The weight of water is calculated using the formula:
Weight = Density of the water * Volume of the water * Acceleration due to gravity
Given:
Density of water = 1000 kg/m³ (assuming standard water density)
Volume of the water displaced = Volume of the stone = 0.001 m³
Acceleration due to gravity (g) = 9.8 m/s²
So, Weight of the water = 1000 kg/m³ * 0.001 m³ * 9.8 m/s² = 9.8 N
Step 4: Calculate the weight of the stone when immersed in water
The weight of the stone when immersed in water is calculated by subtracting the buoyant force from the actual weight of the stone.
Weight when immersed = Weight of the stone - Weight of the water
Weight when immersed = 98 N - 9.8 N = 88.2 N
Therefore, the weight of the stone when it is totally immersed in water is 88.2 Newtons.