A basketball player pushes down with a force of 50 N on a basketball that is inflated to a gauge pressure of 8.0 x 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

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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. The area of contact is equal to the area of a circle with diameter d. Therefore, we have:$$F = P_g * A$$$$F = P_g * \pi * d^2 / 4$$$$d = \sqrt{4F / (\pi * P_g)}$$$$d = \sqrt{4 * 50 N / (\pi * 8.0 x 10^4 Pa)}$$$$d = 0.028 m = 2.8 cm$$

A Basketball Player Pushes Down with a Force of 50