# The Diameter of Contact Between a Basketball and the Floor

What is the diameter of contact between a basketball and the floor when a basketball player pushes down with a force of 50 N?

The diameter of contact between a basketball and the floor can be calculated based on the force applied by the player and the pressure inside the basketball. In this scenario, the player pushes down with a force of 50 N on a basketball inflated to a gauge pressure of 8 psi (equivalent to 55.16 kPa). To find the diameter, we need to determine the contact area between the ball and the floor.

## Calculating the Contact Area

**Step 1:**Convert pressure from psi to kPa To calculate the contact area, we first convert the pressure from psi to kPa: P = 8 psi * 6.89476 kPa/psi = 55.16 kPa

**Step 2:**Use the formula for contact area Next, we apply the formula for contact area between two objects under a given force: A = F / P Where A is the contact area, F is the force applied (50 N in this case), and P is the pressure between the two objects (55.16 kPa). Plugging in the values: A = 50 N / 55.16 kPa = 0.91 square meters

## Calculating the Diameter

To find the diameter of contact, we make the assumption that the contact area is circular.**Step 3:**Use the formula for the area of a circle Using the formula A = πr^2, where A is the contact area and r is the radius of the circular contact area: r = sqrt(0.91/π) = 0.54 meters

**Step 4:**Calculate the diameter Finally, we find the diameter by multiplying the radius by 2: d = 2 * 0.54 meters = 1.08 meters Therefore, the diameter of contact between the basketball and the floor is approximately 1.08 meters when a basketball player exerts a force of 50 N.