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 = 100.0 kg and length L = 5.800 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 = 3500 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.

Part A: Find TA, the tension in string A.

1.300x105

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

?

There is a Part C, but I wont be able to answer it until I answer Part B.

Explanation / Answer

Use net torque equation to find requried parameters

Write equation for um 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
plug in the numbers
Ta= { 9.81 ( 100 x 5.8 /2 ) + 3500 x 5.6 ) } / 1.5 m

= 1.29948x105 N

Round off the result to 4 significant digits
Ta = 1.300x105 N

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For Tb, sum forces in the y -direction
1.29948x105 N -Tb- g ( 3500 + 100 kg ) = 0
Solve for Tb
Tb=1.29948x105 N - 9.81 ( 3600 kg )
= 9.4632x104  N

Round off the result to 4 significant digits

Tb = 9.463 x104  N

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