(a) Explanation Show the displace diagram of spring as in Figure (1). Express the length of the A D by using sine rule theory. A D sin θ / 2 = O A sin 90 ° A D = [ O A sin 90 ° ] ( sin θ / 2 ) = O A ( sin θ / 2 ) (I) Express the length of the A A ' . A A ' = 2 A D (II) Express the length of the A ' C by using the cosine rule. A ' C = ( A A ' ) 2 + ( A C ) 2 − 2 ( A A ' ) ( A C ) cos [ 180 − θ 2 ] = ( A A ' ) 2 + ( A C ) 2 + 2 ( A A ' ) ( A C ) ( cos θ / 2 ) (III) Express the stretch of the spring. δ = A ' C − b 4 (IV) Express the mass of the bar by using the conservation of energy. T 1 + V 1 = T 2 + V 2 0 + 0 = 1 2 I o ω 2 2 + 1 2 k δ 2 − m g b 2 sin θ 1 2 I o ω 2 2 + 1 2 k δ 2 − m g b 2 sin θ = 0 (V) Here, moment of inertia of the bar is I o , the angular velocity of the bar is ω 2 , mass of the bar is m and acceleration due to gravity is g . Conclusion: Substitute 3 b 4 for O A in Equation (I). A D = 3 b 4 ( sin θ / 2 ) Substitute 3 b 4 ( sin θ / 2 ) for A D in Equation (II). A A ' = 2 [ 3 b 4 ( sin θ / 2 ) ] = 3 b 2 ( sin θ / 2 ) Substitute 3 b 2 ( sin θ / 2 ) for A A ' and b 4 for A C in Equation (III) (b) To determine Determine the angular velocity of the bar.

8th Edition

ISBN: 9781118885840

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

Publisher: WILEY

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Chapter 6.6, Problem 133P

(a)

To determine

Determine the mass of the bar.

(b)

To determine

Determine the angular velocity of the bar.

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Chapter 6.6, Problem 131P

Chapter 6.6, Problem 134P

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