Determine the required magnitude of force P to maintain equilibrium of the linkage at θ = 60°. Each link has a mass of 20 kg.
The required magnitude of force P to maintain equilibrium.
Answer to Problem 1FP
The required magnitude of force P to maintain equilibrium is
Explanation of Solution
Given information:
The mass of each link
The given angle
Show the free body diagram of the forces acting on the link as in Figure (1).
Observation:
The weight W and the horizontal component of P do positive work, when the position coordinates
Virtual displacement:
Write the position coordinate about x axis at point C.
Here, the length of the link AB is
Write the position coordinate about y axis about the center of the link.
Determine the weight of the link W.
Here, the acceleration due to gravity is g.
Virtual work equation:
Write the virtual work equation to determine the magnitude of force P.
Here, the angle of force
Conclusion:
Differentiate Equation (I) with respect to
Substitute 1.5 m for
Differentiate Equation (II) with respect to
Substitute 1.5 m for
Substitute 20 kg for m and
Substitute 196.2 N for W,
Here, the value of
Modify the Equation,
Thus, the required magnitude of force P to maintain equilibrium is
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