Explanation Show the free body diagram as in Figure (1). Consider the upper arm and draw the free body diagram for the upper arm as in Figure (2). Refer Figure (1) and consider the following geometrical relations. y = l sin θ d y = l cos θ d θ Here, the vertical movement of the cab is y , angle made by the upper arm with horizontal and man is θ and length of the upper arm A B is l . Write the work energy equation for the upper arm. d U = d T Here, the work done is d U and change in potential energy is d T . The work done is equal to the sum of work done by the force and torque. p d y − m g ( 2 d y ) + M B d θ = d [ 1 2 m v 2 ] ( p − 2 m g ) l cos θ ⋅ d θ + M B ⋅ d θ = m a d ( 2 y ) ( p − 2 m g ) l cos θ ⋅ d θ + M B ⋅ d θ = 2 m a ⋅ l cos θ ⋅ d θ ( p − 2 m g ) l cos θ ⋅ d θ + M B ⋅ d θ = 2 m a ⋅ l cos θ (I) Here, mass of man and cab is m , torque applied at joint M B , velocity is v , the force is p and acceleration due to gravity is g . Consider the forces acting along y direction. ∑ F y = m a p − m g = m a p = m g + m a (II) Substitute Equation (II) in Equation (I). [ ( m g + m a ) − 2 m g ] l cos θ + M B ⋅ d θ = 2 m a ⋅ l cos θ M B = m g l cos θ [ a g + 1 ] (III) Conclusion: Substitute 200 kg for m , 6 m for l , 1

8th Edition

ISBN: 9781118885840

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

Publisher: WILEY

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Chapter 6.7, Problem 164P

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Determine the torque required by arm AB at B and torque applied to BC at C.

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Chapter 6.7, Problem 163P

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Determine the torque required by arm A B at B and torque applied to B C at C .

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Determine the torque required by arm AB at B and torque applied to BC at C.

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