Question

I did an experiment studying torque using a crane boom. For this experiment I need to analyze the sources of error. One source of error I came up with was the accuracy of leveling the string in the experiment but are there any others that anyone could think of? The experiment consisted of finding the center of mass of the crane boom and analyzing the forces on it.

Answer 1

For an equilibrium condition, we have

F_y = 0     ;       F_x = 0       ;          _cw = _ccw

The forces acting on the y-direction is given by,

F_y = V + T_y - w_B - w_L = 0

Or      V + T_y = w_B + w_L                                                                              { eq.1 }

The forces acting on the x-direction is given by,

F_x = H - T_x = 0

H = T_x = T cos                                                                                            { eq.2 }

There are two unknown terms namely as, H and T. At the point A in above figure, where the forces V and H are acting for the axis of rotation to pass through.

The forces w_B & w_L are the forces that produce the clockwise torques about the axis at A, while T_y produces the counterclockwise torque.

using a condition,    _cw = _ccw

w_B (L / 2) + w_L (L) = T_y (L)

w_B (L / 2) + w_L (L) = T sin (L)

T sin = (w_B / 2) + w_L

The tension in the cable is given as :

T = (w_B / 2) + w_L / sin                                                                         { eq.3 }