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 = 75.00 kg and length L = 5.900 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 = 3500 kg is supported by the crane at a distance x = 5.700 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

Taking equilibrium of torque about point A where string A is attached to bar

- (m1 g)(L/2 - d) - (m2g) (x - d) + TB (d) = 0

- (75 x 9.8 ) (5.9/2 - 1.4) - (3500 x 9.8) (5.7 - 1.4) + TB (1.4) = 0

TB = 106164 N

Taking equilibrium of force

TA = TB + m1 g + m2 g

TA = 106164 + 75 x 9.8 + 3500 x 9.8 = 141199

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