Explanation Given information: The rock A falls a distance ( y ) is 20 m . The coefficient of restitution between the ball and wall ( e ) is 0.2. The inclined slope ( α ) is 40 ° . The acceleration due to gravity ( g ) is 9.81 m/s 2 . Calculation: Show the free body diagram of the rock falling with the velocity acting as in Figure (1). Consider the position (1). The initial kinetic energy of the rock falling ( T 1 ) is zero as it rest initially. The expression for the gravitational potential energy of the rock falling ( V g 1 ) as follows: V g 1 = m g y The elastic potential energy of the rock ( V e 1 ) is zero. The work done ( U 1 − 3 N C ) for non-conservative force of the rock is zero. Consider the position 2. The expression for the final kinetic energy of the rock ( T 2 ) as follows: T 2 = 1 2 m v B 2 The final gravitational potential energy and elastic potential energy of the rock ( V g 2 ) and ( V e 2 ) is zero respectively. The expression for the work energy on the rock falling as follows: T 1 + V g 1 + V e 1 + U 1 − 3 N C = T 2 + V g 2 + V e 2 Substitute 0 for T 1 , m g y for V g 1 , 0 for V e 1 , 0 for U 1 − 3 N C , 1 2 m v B 2 for T 2 , 0 for V g 2 and 0 for V e 2 . 0 + m g y + 0 + 0 = 1 2 m v B 2 + 0 + 0 g y = v B 2 2 v B = 2 g y Substitute 9.81 m/s 2 for g and 20 m for y . v B = 2 × 9.81 × 20 = 19.8091 m Calculate the velocity of the rock in n direction using the relation: ( v B ) n = − v B cos α Substitute 19.8091 m for v B and 40 ° for α . ( v B ) n = − 19.8091 cos 40 ° = − 15.17 m/s Calculate the velocity of the rock in t direction using the relation: ( v B ) t = v B sin α Substitute 19.8091 m for v B and 40 ° for α . ( v B ) t = 19.8091 sin 40 ° = 12.733 m/s Calculate the velocity of the rock in tangent t -direction after impact using the relation: ( v ′ B ) t = ( v B ) t = − v B sin α Substitute 19.8091 m for v B and 40 ° for α . ( v ′ B ) t = ( v B ) t = − 19

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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 13.172P

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Find the velocity of the rock (v′B) after the impact.

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Chapter 13.4, Problem 13.171P

Chapter 13.4, Problem 13.173P

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Find the velocity of the rock ( v ′ B ) after the impact.

Solution Summary: The author shows the free body diagram of the rock falling with the velocity acting as in Figure (1).

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Find the velocity of the rock (v′B) after the impact.

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