Question

The tower crane is used to hoist a 2.0mg- load upward at constant velocity. The 1.7Mg- jib BD and 0.6-Mg jib BC have centers of mass at G1 and G2, respectively.

Determine the required mass of the counterweight C so that the resultant moment produced by the load and the weight of the tower crane jibs about point A is zero.
The center of mass for the counterweight is located at G3.

Answer 1

This is a classic problem in statics. The counterweight is placed so that the tower crane would be stable, or the total moment is zero. There are four sources of torques: the load, the jib BD, the jib BC, and the counter weight. Staring with the total moment equals zero, and taking clockwise moments as positive. The units of moment here is Mg * m.

M = 0
(2.0)(12.5) + (1.7)(9.5) - (0.6)(4) - (C)(7.5) = 0
7.5C = 38.75
C = 5.17 Mg

Therefore, the counterweight must be 5.17 Mg.


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