Cuesta College, San Luis Obispo, CA
A boom crane is supported by a vertical piston. (Calculate all torques with respect to the pivot, located at the base of the boom, approximated here as a uniform beam.) The magnitude of the force applied by the piston is _________ the magnitude of the weight of the boom.(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)
Correct answer (highlight to unhide): (C)
The weight of the boom acts at its center of gravity, straight downwards. The perpendicular lever arm for the weight force w extends from the pivot to perpendicularly intercept the weight force line of action, such that this will be a horizontal line of length ℓw.
The piston force acts straight upwards, and the perpendicular lever arm for the piston force Fpiston also extends from the pivot to perpendicularly intercept the piston force line of action, such that this will be also be a horizontal line of slightly shorter length ℓpiston.
Since the boom is in static equilibrium ("is supported") and does not rotate, then the net torque on it is equal to zero (Στ = 0), such that the clockwise torque of the weight force on the boom must equal the counterclockwise torque of the piston force on the boom:
(cw) τw = (ccw) τpiston.
Substituting in the perpendicular lever arms for these torques:
w·ℓw = Fpiston·ℓpiston,
and since ℓw > ℓpiston, then w < Fpiston, and thus the force applied by the piston is greater than the magnitude of the weight of the boom.
Sections 70854, 70855, 73320
Exam code: quiz05b0oM
(A) : 7 students
(B) : 24 students
(C) : 24 students
(D) : 0 students
Success level: 42%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.74
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