A ball has a diameter of 3.86 cm and average density of 0.0836 g/cm3. What force is required to hold it completely submerged under water?
force=bouyancy-weight=4/3 PI (3.86/2)^3(1.0-.0836)
That is the mass (in grams) required.
Weight in Newtons=gramsabove/1000*9.8N/kg
To find the force required to hold the ball completely submerged under water, we can use Archimedes' principle. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The weight of the fluid displaced is given by the formula:
Weight of fluid displaced = Volume of the object × Density of the fluid × Acceleration due to gravity
First, let's calculate the volume of the ball. The ball is a sphere, and the formula to calculate the volume of a sphere is:
Volume = (4/3) × π × (radius)³
Since we are given the diameter of the ball, we can calculate the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 3.86 cm / 2 = 1.93 cm
Now, we can calculate the volume of the ball:
Volume = (4/3) × π × (1.93 cm)³
Next, we need to calculate the weight of the fluid displaced. The density of the fluid is given in the problem as 0.0836 g/cm³. The acceleration due to gravity can be approximated as 9.8 m/s².
However, we need to have consistent units, so let's convert the values to a common unit. Converting the density to kg/m³:
Density of the fluid = 0.0836 g/cm³ = 836 kg/m³ (since 1 g/cm³ = 1000 kg/m³)
Converting the radius to meters:
Radius = 1.93 cm = 0.0193 m (since 1 cm = 0.01 m)
Now we can calculate the weight of the fluid displaced:
Weight of fluid displaced = Volume × Density of the fluid × Acceleration due to gravity
Finally, we can calculate the force required to hold the ball submerged by using the formula:
Force = Weight of fluid displaced
Remembering that weight = mass × acceleration due to gravity, we can calculate the force:
Force = (Weight of fluid displaced) × (Acceleration due to gravity) = (Volume × Density of the fluid × Acceleration due to gravity) × (Acceleration due to gravity)
Plugging in the values we calculated, we can find the force required to hold the ball completely submerged under water.
To calculate the force required to hold the ball completely submerged under water, we need to use Archimedes' principle. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The first step is to find the volume of the ball. The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * (radius)^3
Since we are given the diameter, we need to divide it by 2 to get the radius:
Radius = diameter / 2 = 3.86 cm / 2 = 1.93 cm
Now we can calculate the volume:
Volume = (4/3) * π * (1.93 cm)^3
Next, we need to convert the volume to cubic centimeters (cm³) since the density is given in g/cm³:
Volume = (4/3) * π * (1.93 cm)^3 = 2.899 cm³
The next step is to calculate the weight of the water displaced by the ball. The weight can be calculated using the formula:
Weight = Density * Volume
Weight = 0.0836 g/cm³ * 2.899 cm³
Now we need to convert the weight to newtons (N). Since 1 g = 0.0098 N (approximately):
Weight = 0.0836 g/cm³ * 2.899 cm³ * 0.0098 N/g
Finally, we can calculate the force required to hold the ball completely submerged under water. This force is equal to the weight of the water displaced, so:
Force = Weight = 0.0836 g/cm³ * 2.899 cm³ * 0.0098 N/g
Using a calculator, we can compute this expression to find the force required to hold the ball completely submerged under water.