Explanation Given: The radius of the inner rim, r i = 25 mm or 0 .025 m . The radius of the outer rim, r o = 50 mm or 0 .05 m . The velocity of cord C F , υ F = 2 m / s . The acceleration of cord C F , a F = 3 m / s . Show the position vector from C to I C as in Figure (1). Show the angular acceleration of the gear at point s C and D as in Figure (2). Show the acceleration of point A as in Figure (3). Conclusion: Express the angular velocity of cord C F . ω F = υ F r i + r o (I) Substitute 2 m / s for υ F , 0 .025 m for r i and 0 .05 m for r o in Equation (I). ω F = 2 0.025 + 0.05 = 2 0.075 = 26.67 rad / s Express the normal component of acceleration of point C . ( a C ) n = ( ω F ) 2 r i (II) Substitute 26.67 rad / s for ω F and 0 .025 m for r i in Equation (II). ( a C ) n = ( 26.67 ) 2 ( 0.025 ) = 17.78 m / s 2 Express the normal component of acceleration of point D . ( a D ) n = ( ω F ) 2 r o (III) Substitute 26.67 rad / s for ω F and 0 .05 m for r o in Equation (III). ( a D ) n = ( 26.67 ) 2 ( 0.05 ) = 35.56 m / s 2 Write the expression for position vector from C to D . r C / D = [ − r i + ( − r o ) ] j (IV) Substitute 0 .025 m for r i and 0 .05 m for r o in Equation (IV). r C / D = [ − 0.025 + ( − 0.05 ) ] j = { − 0.075 j } m Express the angular acceleration of the pulley. a C = a D + α × r C / D − ω F 2 r C / D − ( a F i ) + [ ( a C ) n j ] = − [ ( a D ) n j ] + ( − α k ) × r C / D − ω F 2 r C / D (V) Substitute 3 m / s 2 for a F , 17.78 m / s 2 for ( a C ) n , 35.56 m / s 2 for ( a D ) n and { − 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.7, Problem 118P

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The angular acceleration α of the pulley and the acceleration aA of the block.

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Chapter 16.7, Problem 117P

Chapter 16.7, Problem 119P

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Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The angular acceleration α of the pulley and the acceleration a A of the block.

Solution Summary: The author shows the position vector from C to IC, and the angular acceleration of the gear at point s.

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The angular acceleration α of the pulley and the acceleration aA of the block.

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Chapter 16 Solutions