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 = 80.00 kg and length L = 5.700 m is supported by two vertical massless strings. String A is attached at a distance d = 1.400 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 = 3000 kg is supported by the crane at a distance x = 5.500 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.

Find TA , the tension in string A

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

solving for Ta

Ta=g*(m1*L/2+m2*x)/d
pluging in the numbers
Ta=9.807*(80*5.7/2+3000*5.5)/1.4

TA= 117180N

for Tb, sum forces in the y
117180-Tb-g*3080=0
solving for Tb

Tb=117180-9.807*3080

TB =86974 N

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