A ball has a diameter of 3.70 cm and average density of 0.0841 g/cm3. What force is required to hold it completely submerged under water?
I need to find the magnitude in N
Thank you!
Let the unknown required force be F.
F + M*g = buoyant force
= (volume)*(water density)*g
Volume = (pi/6)*D^3 = 26.52 cm^3
M = Mass = 2.23 g
That is an extremely light ball. More like a balloon.
The buoyancy force is much larger than the weight.
Solve for F
To find the force required to hold the ball completely submerged under water, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The buoyant force can be calculated using the equation:
Buoyant force = (density of fluid) * (volume of displaced fluid) * (acceleration due to gravity)
In this case, the fluid is water, which has a density of approximately 1 g/cm3.
To find the volume of displaced fluid, we need to calculate the volume of the ball. The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * (radius)^3
Since the diameter of the ball is given as 3.70 cm, the radius is half of that, which is 1.85 cm.
Using these values, we can calculate the volume of the ball and then find the force required to hold it submerged under water.
1. Calculate the volume of the ball:
Volume = (4/3) * π * (1.85 cm)^3
2. Calculate the buoyant force:
Buoyant force = (density of water) * (volume of ball) * (acceleration due to gravity)
3. Convert the mass of the ball to kilogram and multiply it by the acceleration due to gravity (9.8 m/s^2) to get the weight of the ball in newtons.
The resulting force will be the magnitude in newtons required to hold the ball completely submerged under water.
To find the force required to hold the ball completely submerged under water, you can use Archimedes' principle. According to this principle, the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object.
Here are the steps to calculate the force:
Step 1: Find the volume of the ball.
The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
where r is the radius of the sphere. The radius can be calculated by dividing the diameter by 2.
Given the diameter of the ball is 3.70 cm,
r = 3.70 cm / 2 = 1.85 cm = 0.0185 m
Now, calculate the volume of the ball:
V = (4/3) * π * (0.0185)^3
Step 2: Calculate the mass of the ball.
The mass can be calculated using the density and volume formula:
m = density * volume
Given the density of the ball is 0.0841 g/cm^3, which can be converted to kg/m^3 by multiplying by 1000,
density = 0.0841 g/cm^3 * 1000 kg/m^3 = 84.1 kg/m^3
Now, calculate the mass of the ball:
m = 84.1 kg/m^3 * V
Step 3: Calculate the weight of the ball.
The weight is equal to the mass multiplied by the acceleration due to gravity, g = 9.8 m/s^2
weight = m * g
Step 4: Calculate the buoyant force.
The buoyant force is equal to the weight of the fluid displaced by the ball, which is equal to the weight of the ball.
Step 5: Convert the weight of the ball to force.
The weight is a force, so there is no need for conversion.
Therefore, the magnitude of the force required to hold the ball completely submerged under water is equal to the weight of the ball, which we found in step 3.