A tower crane(Figure 1) must always be carefully balanced so that there is no ne

Question

A tower crane(Figure 1) must always be carefully balanced so that there is no net torque tending to tip it. A particular crane at a building site is about to lift a m = 3200 kg air-conditioning unit. The crane's dimensions are shown in the figure.(Figure 2) The length the beam is L = 8.3 m and maximum distance from the pivot is xmax = 3.0 m .

Where must the crane's M = 9000 kgcounterweight be placed when the load is lifted from the ground? (Note that the counterweight is usually moved automatically via sensors and motors to precisely compensate for the load.)

Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent. Ignore the mass of the beam.

Explanation / Answer

if the system is in equilibrium, the net torque is zero.

Mgd = mg (8.3)

hence, the distance is,

d = m(8.3)/M = 3200*8.3/9000 = 2.95 m

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the load is calculated as follows:

Mg(3.0) = (8.3)mg

m = M*3/8.3

= 9000*3/8.3

= 3253 kg

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