(a) Explanation Given information: The mass of the block A ( m A ) is 5kg . The mass of the block B ( m B ) is 6kg . The mass of the collar C ( m C ) is 3kg . The vertical height of collar and block A ( x ) is 1.7 m . The coefficient of restitution ( e ) is 0. The acceleration due to gravity ( g ) is 9.81 m/s 2 . Calculation: Show the diagram of the blocks with the velocity acting as Figure (1). Consider the position 1. The velocity of the block A ( v A ) 1 and B ( v B ) 1 in the position 1 is zero. The kinetic energy of the blocks in the position1 ( T 1 ) is zero. The potential energy of the blocks in the position 1 ( V 1 ) is zero. Consider the position 2. Due to kinematic, the velocity in the block A ( v A ) and block B ( v B ) is equal. Calculate the kinetic energy of the blocks in the position 2 ( T 2 ) using the formula: T 2 = 1 2 m A ( v A ) 2 + 1 2 m B v B 2 Substitute v A for v B . T 2 = 1 2 m A ( v A ) 2 + 1 2 m B v A 2 Substitute 5kg for m A and 6kg for m B . T 2 = 1 2 × 5 × ( v A ) 2 + 1 2 × 6 × v A 2 = 5.5 v A 2 Calculate the potential energy of the blocks in the position 2 ( V 2 ) using the formula: V 2 = m A g x − m B g x Substitute 5kg for m A , 6kg for m B , 9.81 m/s 2 for g , and 1.7 m for x . V 2 = ( 5 × 9.81 × 1.7 ) − ( 6 × 9.81 × 1.7 ) = − 16.677 kg ⋅ m The expression for the conservation of energy from position 1 to position 2 as follows: T 1 + V 1 = T 2 + V 2 Substitute 0 for T 1 , 0 for V 1 , 5 (b) To determine Find the distance the blocks and collar ( d ) move after the impact before coming to stop. (c) To determine Find the value of ( x ) at the end of one complete cycle.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 13, Problem 13.198RP

(a)

To determine

Find the velocity of the blocks (v′A), (v′B), and collar immediately after A hits C (v′C).

(b)

To determine

Find the distance the blocks and collar (d) move after the impact before coming to stop.

(c)

To determine

Find the value of (x) at the end of one complete cycle.

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Chapter 13, Problem 13.197RP

Chapter 13, Problem 13.199RP

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Find the velocity of the blocks ( v ′ A ) , ( v ′ B ) , and collar immediately after A hits C ( v ′ C ) .

Solution Summary: The author shows the diagram of the blocks with the velocity acting as Figure (1).

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Find the velocity of the blocks (v′A), (v′B), and collar immediately after A hits C (v′C).

Find the distance the blocks and collar (d) move after the impact before coming to stop.

Find the value of (x) at the end of one complete cycle.

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Chapter 13 Solutions