(a) Explanation The below figure represent the free body diagram of the system. Figure-(1) Write the expression of speed of the truck in the vector form. v ¯ B = v B ( cos θ i − sin θ j ) (I) Here, the inclination angle is θ , the speed of the truck is v B . Write the expression of acceleration of the truck in the vector form. a ¯ B = − a B ( cos θ i − sin θ j ) (II) Here, the acceleration of the truck is a B . Write the expression of acceleration of the end A of the ladder with respect to the truck. a A / B = a A − a ¯ B (III) Here, the acceleration of the end A of the ladder with respect to the ground is a A . Write the expression of the acceleration of the end A of the ladder with respect to the ground. a A = a ¯ B + ω ˙ k × r i + ω k × ( ω k × r i ) + 2 ω k × b ˙ i + b ¨ i (IV) Here, the angular acceleration of the extension part is ω ˙ , the distance between A and B is r , the angular velocity of the extension part is ω , the relative velocity is b ˙ and the relative acceleration is b ¨ . Write the expression of the distance between A and B . r = b L + b (V) Here, the length of the ladder is b L and the length of the extension is b . Conclusion: Substitute 35 mi / hr for v B and 30 ° for θ in Equation (I). v ¯ B = ( 35 mi / hr ) { ( cos 30 ° ) i − ( sin 30 ° ) j } = { ( 35 mi / hr ) ( 5280 ft 1 mi ) ( 1 hr 3600 sec ) } { ( cos 30 ° ) i − ( sin 30 ° ) j } = ( 51.33 ft / s ) ( 0.87 i − 0.5 j ) = ( 44.66 ft / s ) i − ( 25.67 ft / s ) j Substitute 10 ft / s for a B and 30 ° for θ in Equation (II). a ¯ B = − ( 10 ft / s 2 ) { ( cos 30 ° ) i − ( sin 30 ° ) j } a 2 + b 2 = − ( 10 ft / s 2 ) ( 0.87 i − 0.5 j ) = − ( 8.7 ft / s 2 ) i + ( 5 ft / s 2 ) j Substitute 20 ft for b L and 5 ft for b in Equation (V). r = ( 20 ft ) + ( 5 ft ) = 25 ft Substitute − ( 8.7 ft / s 2 ) i + ( 5 ft / s 2 ) j for a ¯ B , 0 for ω ˙ , 25 ft for r , 10 deg / sec for ω , 2 ft / s for b ˙ and − 1 ft / s 2 for b ¨ in Equation (IV). a A = [ { − ( 8.7 ft / s 2 ) i + ( 5 ft / s 2 ) j } + 0 × r + ( 10 deg / s ) × { ( 10 deg / s ) × ( 25 ft ) } + 2 ( 10 deg / s ) × ( 2 ft / s ) i + ( − 1 ft / s 2 ) i ] = [ − ( 8 (b) To determine The acceleration of the end A of the ladder with respect to the ground.

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 5.7, Problem 167P

(a)

To determine

The acceleration of the end A of the ladder with respect to the truck.

(b)

To determine

The acceleration of the end A of the ladder with respect to the ground.

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Chapter 5.7, Problem 165P

Chapter 5.7, Problem 168P

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Chapter 5 Solutions

Engineering Mechanics: Dynamics

Ch. 5.2 - Prob. 1P Ch. 5.2 - The circular sector rotates about a fixed axis...Ch. 5.2 - Prob. 3P Ch. 5.2 - Prob. 4P Ch. 5.2 - When switched on, the grinding machine accelerates...Ch. 5.2 - The small cart is released from rest in position 1...Ch. 5.2 - The flywheel has a diameter of 600 mm and rotates...Ch. 5.2 - Prob. 8P Ch. 5.2 - Prob. 9P Ch. 5.2 - The angular acceleration of a body which is...

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