(a) Explanation Given information: The velocity ( v 0 ) of ball before the impact is 4 m / s . The velocity ( v A ) of ball after the impact is 1.92 m / s . The distance a is 1.65 m . Calculation: Calculate the velocity ( v A ) 0 of ball A before impact. ( v A ) 0 = v 0 i (1) Substitute 4 m / s for v 0 in Equation (1). ( v A ) 0 = 4 i Since the ball at B is initially at rest, the velocity of ball B before impact is, ( v B ) 0 = 0 Since the ball at C is initially at rest, the velocity of ball C before impact is, ( v C ) 0 = 0 Calculate the velocity of ball A after impact using the relation: ( v A ) = − v A j (2) Substitute 1.92 m / s for ( v A ) in Equation (2). ( v A ) = − 1.92 j Calculate the velocity of ball B after impact using the relation: v B = ( v B ) x i + ( v B ) y j Here, ( v B ) x is velocity of ball B along x direction and ( v B ) y velocity of ball B along y direction. Calculate the velocity of ball C after impact using the relation: ( v C ) = v c i According to the linear momentum is conserved. v 0 = v A + v B + v C (3) Here, v A is velocity of ball A after impact, v B is velocity of ball B after impact, and velocity of ball C after impact. Substitute − 1.92 j for v A , ( v B ) x i + ( v B ) y j for v B , and v c i for v C in Equation (3). v 0 = − 1.92 j + ( v B ) x i + ( v B ) y j + v c i Write the i components vectors as follows: 4 = 0 + ( v B ) x + v C ( v B ) x = 4 − v C Write the j components vectors as follows: 0 = − 1.92 + ( v B ) y + 0 ( v B ) y = 1.92 Find the velocity of ball C using the conservation of energy as follows: 1 2 v 0 2 = 1 2 v A 2 + 1 2 v B 2 + 1 2 v C 2 1 2 v 0 2 = 1 2 v A 2 + ( 1 2 ( v B ) x + 1 2 ( v B ) y ) 2 + 1 2 v C 2 (4) Substitute 4 m / s for v 0 , 1 (b) To determine Find the hitting point C ′ on the side of the table.

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 14.2, Problem 14.51P

(a)

To determine

Find the velocities of ball B and C.

(b)

To determine

Find the hitting point C′ on the side of the table.

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Chapter 14.2, Problem 14.50P

Chapter 14.2, Problem 14.52P

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In a game of billiards, ball A is given an initial velocity v0 along the longitudinal axis of the table. It hits ball B and then ball C , which are both at rest. Balls A and c are observed to hit the sides of the table squarely at A, and C, respectively, and ball B is observed to hit the side obliquely at B, .Knowing that v0 = 4 m/s, vA = 1.92 m/s, and a= 1.65 m, determine (a) the velocities vB and vC of balls B and C , (b) the point C, where ball C hits the side of the table. Assume frictionless surfaces and perfectly elastic impacts (i.e., conservation of energy).

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Chapter 14 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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Find the velocities of ball B and C .

Solution Summary: The author calculates the velocity of ball B and C using the relation: (v_A)0=4i.