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 = 3100 kg air-conditioning unit. The crane's dimensions are shown in the figure.(Figure 2) The length the beam isL = 8.0 m and maximum distance from the pivot is xmax= 3.6 m .

A)Where must the crane's M = 9900 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.)

B)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

torque = R x F { R is perpendicular distance from hinge , F is force }

Force due to Mass M = Mg = 9900 * 9.81 = 97119 N

Force due to MaSS m = mg = 3100*9.81 = 30411 N

A.) the torue produce due to Mass M about hinge is greater than the torque produce by mass m about hinge to lift the load,

so,

R* Mg = L*mg

R = 8 * 30411/ 97119 N

R = 2.505 m { R is distance of Mass M placed from hinge }

B.)maximum load can be lifted

x*Mg = L*m1g

m1 = 3.6 * 97119 N /(8 * 9.81 )

m1 = 4455 Kg

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