Explanation Given information: Mass of block is 1 k g . Mass of sphere is 0.5 k g . Initial velocity of the block is 2 m / s . Co-efficient of kinetic friction μ k between block and surface is 0.6 . Co-efficient of restitution between block and sphere is e = 0.8 . The total linear momentum of two particles is conserved. Therefore m A v A + m B v B = m A v A 1 + m B v B 1 The co-efficient of restitution is defined as v B 1 − v A 1 = e ( v A − v B ) The principle of conservation of energy is defined as, “When a particle moves under the action of conservation of forces, the sum of kinetic energy and potential energy of that particle remains constant.” T 1 + V 1 = T 2 + V 2 Calculation: Apply conservation of linear momentum ← m A v A + m B v B = m A v A 1 + m B v B 1 Substitute 0 + ( 1 k g ) ( 2 m / s ) = ( 0.5 k g ) v A 1 + ( 1 k g ) v B 1 Therefore 4 = v A 1 + 2 v B 1 → ( 1 ) Apply co-efficient of restitution equation To determine (b) Distance x traveled by the block

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 13.4, Problem 13.175P

To determine

(a)

Maximum height h reached by the sphere

To determine

(b)

Distance x traveled by the block

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Chapter 13.4, Problem 13.174P

Chapter 13.4, Problem 13.176P

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(a) Maximum height h reached by the sphere

Solution Summary: The author explains the principle of conservation of energy. The total linear momentum of two particles is conserved.