Calculating the Diameter of Contact Between a Basketball and the Floor

What is the approximate diameter of contact between a basketball and the floor?

Determining the Diameter of Contact

To find the diameter of contact between the basketball and the floor, we need to calculate the total force exerted by the basketball on the floor. The force exerted by the basketball can be found using the equation:
Force = Pressure * Area
The area in this case represents the contact area between the basketball and the floor, which can be estimated as a circle.

Calculating the Pressure

Given that the basketball is inflated to a gauge pressure of 8.0 x 10^4 Pa, we first need to determine the absolute pressure by adding the atmospheric pressure to the gauge pressure: Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = 8.0 x 10^4 Pa + 1.0 x 10^5 Pa
Absolute Pressure = 1.8 x 10^5 Pa

Finding the Area of Contact

The area of contact between the basketball and the floor can be calculated using the formula:
Area = π * (diameter/2)^2
Let's assume the diameter of contact between the ball and the floor is represented by D.

Solving for the Diameter

Since the force exerted by the player is 50 N, we can rearrange the equation to solve for the diameter:
Diameter = 2 * √(Force / (Pressure * π))
Substitute the known values into the equation and calculate the diameter:
Diameter = 2 * √(50 N / (1.8 x 10^5 Pa * π))
By calculating the diameter using the given values, we find that the approximate diameter of contact between the basketball and the floor is 4.26 cm.
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