Explanation Given information: h A = 0.8 i n e = 0.9 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: For ball A. Apply conservation of energy. T 1 + V 1 = T 2 + V 2 At position 1. T 1 = 0 V 1 = m A g h A At position 2. T 2 = 1 2 m A v A 2 V 2 = 0 Therefore. 1 2 m A v A 2 = m A g h A Solve to find the velocity of ball A. v A = 2 g h A = 2 ( 32.2 f t / s 2 ) ( 8 12 f t ) = 6.552 f t / s For the impact. Find the angle. θ = sin − 1 ( r 2 r ) = 30 ° Apply linear momentum conservation: In x direction: 0 + 0 = m B v B 1 + m A ( v A 1 ) n cos θ + m A ( v A 1 ) t sin θ → ( 1 ) The balls are identical, therefore: m A = m B Therefore. v B 1 + ( v A 1 ) n cos θ + ( v A 1 ) t sin θ = 0 → ( 1 ) For ball A, apply linear momentum conservation: In t direction: − m A v A sin θ = m A ( v A 1 ) t Therefore: ( v A 1 ) t = − v A sin θ → ( 2 ) By substituting: ( v A 1 ) t = − v A sin θ = − ( 6

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

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Chapter 13.4, Problem 13.185P

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The vertical displacement hB of ball B.

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Chapter 13.4, Problem 13.184P

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The vertical displacement h B of ball B.

Solution Summary: The author explains the principle of conservation of energy and the co-efficient of restitution.

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