Exam (79).pdf - Question Two identical pool balls with a 2.37-in diameter may move freely on a pool table Ball B is at rest and ball A has an initial

Exam (79).pdf - Question Two identical pool balls with a...

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Question: Two identical pool balls with a 2.37-in. diameter may move freely on a pool table. Ball B is at rest, and ball A has an initial velocity of v = v 0 i . ( a ) Knowing that b = 2 in. and e = 0.7, determine the velocity of each ball after impact. ( b ) Show that if e = 1, the final velocities of the balls form a right angle for all values of b . Fig. P13.165 Answer : Draw the velocity diagram, impact phases of ball A and ball B as shown in figures.
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From figure 1, calculate the angle between the horizontal and the normal direction of the impact. Here, is the diameter of the balls and is the horizontal distance between the two balls. Substitute for and for . (a)
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From the figure, using the principle of impulse and momentum, calculate the velocity of the balls A and B in the tangential direction. Ball A – Here, is the mass of the ball, is the velocity of the ball before the impact, is the force on the ball, is the velocity of ball A in the tangential direction, is the initial velocity of ball A and is the final velocity of ball A . Substitute for . …… (1) Ball B – Here, is the initial velocity of ball B
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  • Velocity, initial velocity, Ball B

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