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 = 95.00kg and length L = 5.200mis supported by two vertical massless strings. String A is attached at a distance d = 1.900m 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 = 3000kg is supported by the crane at a distance x = 5.000m from the left end of the bar.

Throughout this problem, positive torque is counterclockwise and use 9.807m/s2 for the magnitude of the acceleration due to gravity.

Part A

Find TA, the tension in string A.

Express your answer in newtons using four significant figures.

Part B

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

Express your answer in newtons using four significant figures.

Explanation / Answer

A.

If the system is in static equilibrium, the net torque exerted on the system must be zero.

Equate the net torque about B to zero and solve for tension in string A.

        TA(d) - m1g [L / 2] - m2gx = 0

Then, the tension in the string A is,

TA = [0.5m1gL + m2gx] / d = [0.5*95*9.8*5.2 + 3000*9.8*5] / 1.9 = 78642.4 N = 7.86x104 N

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B.

Equate the net torque about A to zero and solve for tension in string B.

        TB(d) - m1g [(L / 2) - d] - m2g(x-d) = 0

Then, the tension in the string A is,

TB = [m1 [(L / 2) - d] + m2(x-d)]g / d

      = [95*[(5.2/2 - 1.9)] + 3000* (5-1.9)]*9.8 / 1.9

      = 48311.42 N

      = 4.83x104 N

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