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 = 5.800 m is supported by two vertical massless strings. String A is attached at a distance d = 1.300 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 = 5.600 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.

Express your answer in newtons using four significant figures.

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

Express your answer in newtons using four significant figures.

Explanation / Answer

As bar is in rotational equilibrium,taking torque at left end

Torque due to T(B) =0

Torque due to T(A) =T(A)*1.3 counterclockwise

Torque due to weight of bar = 80*9.807*5.8/2=2275.224 N clockwise

Torque due to weight of object =3000*9.807*5.8=170641.8 N clockwise

counterclockwise torque =clockwise torque

T(A)*1.3 = 172917.024

T(A) = 133013.095 N

T(B) + m1g +m2g =T(A)

T(B)= 133013.095 -3500*9.807

T(B) = 98688.595 N

(1) T(A) the tension in string A.is 133013.095 N or 133 kN

(2) T(B) the magnitude of the tension in string B is 98688.595 N or 986.9 kN

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