(a) Explanation Given information: The velocity of the block A ( v A ) is 3 ft/s . Assume the block are perfectly plastic after the impact, that is e = 0 . The coefficient of kinetic friction between all surfaces ( μ k ) is 0.20. The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Show the impact diagram of blocks A and block B as in Figure (1). The expression for the conservation of momentum for the impact between A and B as follows: m v A + m v B + m v C = m v ′ A + m v ′ B + m v ′ C v A + v B + v C = v ′ A + v ′ B + v ′ C Since the block B and C are at rest. Substitute 3 ft/s for v A , 0 for v B , 0 for v C , and 0 for v ′ C . 3 + 0 + 0 = v ′ A + v ′ B + 0 v ′ A + v ′ B = 3 (1) The expression for the coefficient of restitution for the impact between A and B as follows: ( v A − v B ) e = v ′ B − v ′ A Substitute 3 ft/s for v A , 0 for v B , and 0 for e . ( 3 − 0 ) 0 = v ′ B − v ′ A v ′ B − v ′ A = 0 (2) Solve the equation (1) and (2). v ′ A = 1.5 m/s v ′ B = 1.5 m/s Consider the block C . Show the impulse momentum diagram for the block C as Figure (2). The expression for the initial momentum ( P 1 ) for the block C as follows: P 1 = W C g v C The expression for the impulsive force ( Imp ) for the block C as follows: Imp = μ k W C t The expression for the final momentum ( P 2 ) for the block C as follows: P 2 = W C g v The expression for the impulse momentum for the block C as follows: P 1 + Imp = P 2 Substitute W C g v C for P 1 , μ k W C t for Imp and W C g v for P 2 . W C g v C + μ k W C t = W C g v v C g + μ k t = 1 g v Substitute 0 for v C , 0 (b) To determine Find the total distance traveled by each block during that time.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.4, Problem 13.181P

(a)

To determine

Find the time required (t) for the three blocks to reach the same velocity.

(b)

To determine

Find the total distance traveled by each block during that time.

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Chapter 13.4, Problem 13.180P

Chapter 13.4, Problem 13.182P

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Find the time required ( t ) for the three blocks to reach the same velocity.

Solution Summary: The author calculates the time required for the three blocks to reach the same velocity. The coefficient of kinetic friction between all surfaces is 0.20.