Calculate the Buoyancy Force on a Billiard Ball Submerged in Water

How can we calculate the buoyancy force on a billiard ball completely submerged in water?

1. What is the formula to calculate the volume of a sphere?

2. What is the density of water?

3. How do we calculate the weight of the fluid displaced by the billiard ball?

4. What is the relationship between the weight of the fluid displaced and the buoyant force?

Calculating the Buoyancy Force on a Billiard Ball

1. The formula to calculate the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

2. The density of water is approximately 1 g/cm³.

3. To calculate the weight of the fluid displaced, we multiply the volume of water displaced by the density of water.

4. The buoyant force on the billiard ball is equal to the weight of the fluid displaced.

When a billiard ball is completely submerged in water, we can determine the buoyancy force acting on it by using Archimedes' principle. This principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

1. First, we calculate the volume of the billiard ball using the formula V = (4/3)πr³, where the radius (r) of the ball is given as 2.9 cm. By substituting the radius into the formula, we find the volume to be approximately 93.69 cm³.

2. Since the ball is submerged in water, the fluid being displaced is water, which has a density of around 1 g/cm³.

3. To calculate the weight of the fluid displaced, we multiply the volume of water displaced (93.69 cm³) by the density of water (1 g/cm³) to find that the weight is equal to 93.69 grams.

4. Finally, the buoyant force acting on the billiard ball is equal to the weight of the fluid displaced, which in this case is approximately 93.69 grams.