You have been asked to predict how the pressure inside a basketball changes as a player dribbles the ball. For a first model, assume the basketball can be modeled as a sphere of constant radius r containing pressurized air and the air can be modeled as an ideal gas. ... during a dribble, a section of the sphere deforms and is compressed a distance h by the floor without wrinkling or changing r. The result is a new spherical shape missing a segment (see figure). This missing segment is called a spherical cap and has a volume cap = (1/3) [h² (3r – h)]. Before Dribble Pinitial 150 kPa T = 27°C 2r r = 12 cm During Dribble Pdribble = ???? T = 27°C a) Calculate the mass of air, in kg, inside the basketball before the dribble. b) If the sphere is compressed a distance h = 3 cm during the dribble, determine the ratio P dribble/Pinitial. If necessary, assume the temperature of the air does not change and the mass inside the basketball is constant. c) If the mass of air inside the basketball, m = pV, is a constant, show that dp/dt = - − (p/¥)(d\/dt) where p is the uniform density of the air inside the basketball and Vis the volume of the air. Note p and both depend on time.

You have been asked to predict how the pressure inside a basketball changes as a player dribbles the ball. For a first model, assume the basketball can be modeled as a sphere of constant radius r containing pressurized air and the air can be modeled as an ideal gas. ... during a dribble, a section of the sphere deforms and is compressed a distance h by the floor without wrinkling or changing r. The result is a new spherical shape missing a segment (see figure). This missing segment is called a spherical cap and has a volume cap = (1/3) [h² (3r – h)]. Before Dribble Pinitial 150 kPa T = 27°C 2r r = 12 cm During Dribble Pdribble = ???? T = 27°C a) Calculate the mass of air, in kg, inside the basketball before the dribble. b) If the sphere is compressed a distance h = 3 cm during the dribble, determine the ratio P dribble/Pinitial. If necessary, assume the temperature of the air does not change and the mass inside the basketball is constant. c) If the mass of air inside the basketball, m = pV, is a constant, show that dp/dt = - − (p/¥)(d\/dt) where p is the uniform density of the air inside the basketball and Vis the volume of the air. Note p and both depend on time.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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