The crane can be adjusted for any angle 00 ≤ θ ≤ 900 any extension 0 ≤ x ≤ 5 m. For a suspended mass of 120 kg, determine the moment developed at A as a function of x and θ. What values of both x and θ develop the maximum possible moment at A? Compute this moment. Neglect the size of the pulley at B.
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Let us write an equation to calculate the moment using \theta and x as variables around point A.
Moment is the force multiplied by the perpendicular distance from the point we are referencing. Thus, in this question, the distance changes based upon the values of x. In addition, the angle also determines the length, as a small angle would allow for a longer perpendicular distance between the force that pulls on the crane and point A.
Simplifying our equation gives us:
The maximum moment will develop if \theta = 0^0 and x=5 m. Substituting these values gives us:
M_A=14715 N\cdotm (clockwise)
Maximum moment = 14715 N\cdotm (clockwise)