(a) Explanation Given information: The force applied to a tape wrapped around the body indicated ( P ) is 3 N . The mass of the thin hoop ( m ) is 2.4 kg . The radius of the tape is r . Calculation: Consider the acceleration due to gravity ( g ) as 9.81 m / s 2 . Calculate the mass moment of inertia of the tape ( I ¯ ) : I ¯ = m r 2 Substitute 2.4 kg for m . I ¯ = 2.4 × r 2 = 2.4 r 2 Show the free body diagram of the tape as in Figure 1. Here, h is the distance between gravity and force P , a is the acceleration of the tape AB , and α is the angular acceleration of tape AB . Refer to Figure 1. Calculate the horizontal forces by applying the equation of equilibrium: Sum of the horizontal forces is equal to 0. ∑ F x = 0 P − m a = 0 P = m a Substitute 3 N for P and 2.4 kg for m . 3 = 2.4 × a a = 3 2.4 a = 1.25 m / s 2 Calculate the moment about point G by applying the equation of equilibrium: ∑ M G = I G α ( P × r ) = I ¯ α Substitute 3 N for P and 2 (b) To determine Find the acceleration of the point B ( a B ) .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 16.1, Problem 16.50P

(a)

To determine

Find the acceleration of the point A (aA).

(b)

To determine

Find the acceleration of the point B (aB).

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Chapter 16.1, Problem 16.49P

Chapter 16.1, Problem 16.51P

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Chapter 16 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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Find the acceleration of the point A ( a A ) .

Solution Summary: The author shows the free body diagram of the tape as in Figure 1. Calculate the horizontal forces by applying the equation of equilibrium.