(a) Explanation Given information: The weight of the cylinder B is W B = 6 lb . The weight of the wedge A is W A = 4 lb . The radius of the cylinder is r = 3 in . . Calculation: Consider the acceleration due to gravity as g = 32.2 ft / s 2 . Calculate the mass ( m ) as shown below. m = W g (1) For the cylinder. Substitute 6 lb for W and 32.2 ft / s 2 for g in Equation (1). m B = 6 32.2 = 0.1863 lb ⋅ s 2 / ft For the wedge. Substitute 4 lb for W and 32.2 ft / s 2 for g in Equation (1). m A = 4 32.2 = 0.1242 lb ⋅ s 2 / ft Calculate the mass moment of inertia ( I ¯ ) for the disk as shown below. I ¯ = 1 2 m B r 2 Substitute 0.1863 lb ⋅ s 2 / ft for m B and 3 in . for r . I ¯ = 1 2 × 0.1863 lb ⋅ s 2 / ft × ( 3 in . × 1 ft 12 in . ) 2 = 0.00582 lb ⋅ ft ⋅ s 2 Sketch the Kinematics diagram as shown in Figure 1. Refer to Figure 1. Calculate the acceleration ( a B / A ) as shown below. a B / A = r α Substitute 3 in . for r . a B / A = ( 3 in . × 1 ft 12 in . ) α = 0.25 α Sketch the Free Body Diagram of the cylinder and the wedge as shown in Figure 2. Refer to Figure 2. Apply the Equilibrium of forces along x direction as shown below. ∑ F x = m a x ( W A + W B ) sin 20 ° = ( m A + m B ) a A − m B a B / A cos 20 ° Substitute 6 lb for W B , 4 lb for W A , 0 (b) To determine Find the angular acceleration of the cylinder.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 16.2, Problem 16.148P

(a)

To determine

Find the acceleration of the wedge.

(b)

To determine

Find the angular acceleration of the cylinder.

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Chapter 16.2, Problem 16.147P

Chapter 16.2, Problem 16.149P

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Chapter 16 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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Find the acceleration of the wedge.

Solution Summary: The author calculates the acceleration due to gravity as m=Wg for the cylinder and 4lb for W.

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Find the acceleration of the wedge.

Find the angular acceleration of the cylinder.

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Chapter 16 Solutions