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 m_1 = 100.0 kg and length 5.100 m is supported by two vertical massless strings. String A is attached at a distance d = 1.500 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 = 4.900 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.807 m/s^2 for the magnitude Find T_A, the tension in string A. Express your answer in newtons using four significant figures. Find T_B, the magnitude of the tension in string B. Express your answer in newtons using four significant figures.

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

given :

m1 = 100 kg

L = 5.1 m = L/2 = 2.55

m2 = 3000 kg

x = 4.9 m

d = 1.5 m

Ta=9.807*(100*2.55+3000*4.9)/1.5

Ta = 97775.79 N = 97780 N

for Tb, sum forces in the y

97775.79 -Tb - g*3100=0

solve for Tb

Tb = 97775.79 - 9.807*3100

Tb = 67374.09 = 67370 N

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