(a) Explanation Given information: The mass ( m A ) of block A is 20 kg. The mass ( m B ) of block B is 25 kg. The length of cable ( r ) is 0.8 m. The angle of cable ( θ ) with horizontal is 30 ° . Calculation: Consider r and θ re the polar coordinates of block A and y B is the position coordinate (positive downward, origin at the pulley). The motion of block B is rectilinear. Write total length of cable connecting block A and block B . r + y B = constant (1) Differentiate Equation (1) with respect to t to write velocity of the blocks. r ˙ + v B = 0 (2) Here r ˙ is the velocity of cable and v B is the velocity of the block B . Differentiate Equation (2) with respect to t to write acceleration of the blocks. r ¨ + a B = 0 r ¨ = − a B (3) Here, r ¨ is the acceleration of cable and a B is the acceleration of block B . Sketch the free body diagram of block A as shown in Figure (1). Refer Figure (1), Consider equilibrium along x -axis: Σ F x = m A a A T cos θ = m A a A T = m A a A cos θ (4) Sketch the free body diagram of block B as shown in Figure (2). Refer Figure (2), Consider equilibrium along y -axis: Σ F y = m B a B m B g − T = m B a B − T = m B a B − m B a B (5) Add Equation (4) and (5). T − T = m A a A cos θ + m B a B − m B a B m B g = m A a A sec θ + m B a B (6) Sketch the polar coordinate of acceleration of block A with triangle construction as shown in Figure (3). Refer Figure (3), The tangential velocity of block A ( θ ˙ ) is zero initially. Write the equation of radial coordinate of acceleration A . a r = r ¨ − r θ ˙ 2 − a A cos θ = r ¨ − r θ ˙ 2 Substitute 0 for θ ˙ (b) To determine Find the initial acceleration of block A . (c) To determine Find the initial acceleration of block B .

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 12.1, Problem 12.71P

(a)

To determine

The initial tension in the cable.

(b)

To determine

Find the initial acceleration of block A.

(c)

To determine

Find the initial acceleration of block B.

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Chapter 12.1, Problem 12.70P

Chapter 12.1, Problem 12.72P

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