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 = 100 kg and length L = 5.50 m is supported by two vertical massless strings. String A is attached at a distance d = 1.60 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 = 5.30 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.80 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

The problems can ve solved as follows -

Part One:

Here, sum torques about left end

-TA*d + m1 g L/2 + m2 g x = 0

=> -TA*1.6 + 100*9.8*5.5/2 + 3500*9.8*5.3=0

=> -TA*1.6 + 2695 + 181790 = 0

=> TA = 184485 / 1.6 = 115303.12 N

Part Second:

(b) Again, sum forces in the y

TA - TB - m1 g - m2 g = 0

=> TB = TA - m1g - m2g = 115303.12 - 100*9.8 - 3500*9.8

= 80023.12 N

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