(a) Explanation Given Information: The velocity ( v A ) of block A is 8 in ./s . The acceleration ( a A ) of block A is 6 in ./s 2 . The angle ( θ ) of block is 15 ° . The angle ( β ) of block A is 25 ° . Calculation: Show the distance of cable as in Figure (1): Write the express for total lengths of cables. 2 x A + x B / A = constant (1) Here, x A is length of the cable A and x B / A is position of the cable B with respective to block A . Differentiate the Equation (1) with respective to time ( t ). 2 d x A d t + d x B / A d t = 0 Denotes d x A d t as v A and d x B / A d t as v B / A . Since, rate of change of any coordinate with respect to time is equal to the velocity. 2 v A + v B / A = 0 (2) Calculate the velocity ( v B / A ) of block B with respective to block A : Substitute 8 in ./s for v A in equation (2). ( 2 × 8 ) + v B / A = 0 v B / A = − 16 in ./s | v B / A | = 16 in ./s Differentiate the equation (2) with respective to time ( t ). 2 d v A d t + d v B / A d t = 0 Denotes d v A d t as a A and d v B / A d t as a B / A . Since, rate of change of velocity with respect to time is equal to the acceleration. 2 a A + a B / A = 0 (3) Calculate the velocity ( a B / A ) of block B with respective to block A : Substitute 6 in ./s 2 for a A in Equation (3). 2 ( 6 ) + a B / A = 0 a B / A = − 12 | a B / A | = 12 in (b) To determine The acceleration ( a B ) of block B .

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977206

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

Publisher: McGraw-Hill Education

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Chapter 11.4, Problem 11.124P

(a)

To determine

The velocity (vB) of block B.

(b)

To determine

The acceleration (aB) of block B.

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Chapter 11.4, Problem 11.123P

Chapter 11.4, Problem 11.125P

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Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

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The velocity ( v B ) of block B .

Solution Summary: The author calculates the distance of cable as in Figure (1): Write the express for total lengths of cables.