A basketball player pushes down with a force of 50 N on a basketball that is inflated to a gauge pressure of 8.0 × 10⁴ Pa. What is the diameter of contact between the ball and the floor? A)2.8 cm B)1.4 cm C)1.7 cm D)2.1 cm E)5.6 cm

Question

Quizplus · Accepted Answer

The force exerted by the basketball player is equal to the force exerted by the air inside the ball on the floor. The force exerted by the air is equal to the gauge pressure times the area of contact between the ball and the floor. Therefore, the diameter of contact between the ball and the floor is:$$d = \sqrt{\frac{4F}{\pi P}}$$$$d = \sqrt{\frac{4(50 	ext{ N})}{\pi (8.0 	imes 10^4 	ext{ Pa})}}$$$$d = 0.028 	ext{ m} = 2.8 	ext{ cm}$$

A Basketball Player Pushes Down with a Force of 50