Explanation Given: The mass of the disks A is m A = 4 kg . The mass of the disks B is m B = 2 kg . The initial velocity of the disk A is ( v A ) 1 = 15 m/s . The initial velocity of the disk B is ( v B ) 1 = 8 m/s . The coefficient of the restitution is e = 0.8 . Draw the free body diagram of the disks as shown in Figure (1). Write the principle of conservation of linear momentum. ∑ m v 1 = ∑ m v 2 (I) Here, m is the mass, v is the velocity and the suffixes 1 , 2 indicates the initial and final stages. Refer Figure (1). Here, the impact occurs along y − a x i s . Write the formula for coefficient of restitution ( e ) . e = ( v B ) 2 y − ( v A ) 2 y ( v A ) 1 y − ( v B ) 1 y (II) Here, v is the velocity, the suffixes A , B indicates the disks A and B and the suffixes x , y indicates the axes, 1 , 2 indicates the initial and final stages. Conclusion: From Figure (1). The line of impact is along y − a x i s . The velocity of the disk A along the line of impact is ( v A ) 1 = − 15 m/s ( v A ) 1 x = − 15 ( 4 5 ) = − 12 m/s ( v A ) 1 y = − 15 ( 3 5 ) = − 9 m/s Here, the negative direction indicates, the disk A moves in opposite direction to the disk B (facing each other). The velocity of the disk B along the line of impact is ( v B ) 1 = 8 m/s ( v B ) 1 x = 0 m/s ( v B ) 1 y = 8 m/s According law conservation of linear momentum: Consider when the disk A and disk B collides. At Initial: Calculate the initial momentum. ∑ m v 1 = m A ( v A ) 1 y + m B ( v B ) 1 y Substitute 4 kg for m A , 2 kg for m B , − 9 m/s for ( v A ) 1 y and 8 m/s for ( v B ) 1 y . ∑ m v 1 = ( 4 kg ) × ( − 9 ) m/s + ( 2 kg ) ( 8 m/s ) = − 36 + 16 = − 20 N ⋅ s Calculate the final momentum. ∑ m v 2 = m A ( v A ) 2 y + m B ( v B ) 2 y Substitute 4 kg for m A , 2 kg for m B ∑ m v 2 = 4 kg ( v A ) 2 y + 2 kg ( v B ) 2 y = 4 ( v A ) 2 y + 2 ( v B ) 2 y = 2 [ 2 ( v A ) 2 y + ( v B ) 2 y ] Calculate the velocity of the disks after collision. Substitute − 20 N ⋅ s for ∑ m v 1 and 2 [ 2 ( v A ) 2 y + ( v B ) 2 y ] for ∑ m v 2 in Equation (I). − 20 N ⋅ s = 2 [ 2 ( v A ) 2 y + ( v B ) 2 y ] 2 ( v A ) 2 y + ( v B ) 2 y = − 20 2 2 ( v A ) 2 y + ( v B ) 2 y = − 10 (III) Calculate the coefficient of restitution ( e )

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 15.4, Problem 89P

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The velocity of each disks just after the collision and direction of the disk B .

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Chapter 15.4, Problem 88P

Chapter 15.4, Problem 90P

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The velocity of each disks just after the collision and direction of the disk B .

Solution Summary: The author calculates the velocity of each disk after the collision and the direction of the disk B.

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The velocity of each disks just after the collision and direction of the disk B .

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