The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A

Question

The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A rigid uniform horizontal bar of mass m1 = 100.0 kg and length L = 5.400 m is supported by two vertical massless strings. String A is attached at a distance d = 1.100 m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 2000 kg is supported by the crane at a distance x = 5.200 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.807 m/s2 for the magnitude of the acceleration due to gravity.

A) Find TA, the tension in string A.

B) Find TB, the magnitude of the tension in string B.

Explanation / Answer

Sum torque about string B
Ta*d-m1*g*L/2-m2*g*x=0
solve for Ta

Ta=g*(m1*L/2+m2*x)/d
plug in the numbers
Ta=9.81*(100*5.4/2+2000*5.2)/1 .10
95157 N

for Tb, sum forces in the y
95157-Tb-g*2100=0
solve for Tb

Tb=95157-9.81*2100
74556 N

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