If the system is perfectly balanced then calculate the magnitude of the tension

Question

If the system is perfectly balanced then calculate the magnitude of the tension in both strings. (Express your answer using only the variables ml, d, L, m2 , x and or g.   

Calculate the numerical answer to part (a) using the following values: ml =80kg, L=5.0m, d= 1.0m, m2= 25 kg, x=4.5m

PROBLEM 3: A rigid, uniform horizontal bar of mass mi and length L is supported by two vertical massless strings. String A is attached at a distance of d from the left edge of the bar, and is connected to the ceiling. String B is attached to the left edge of the bar and is connected to the floor. An object of mass m2 is supported by the bar at a distance of x from the left edge of the bar. Let the axis of rotation be at the center of mass of the bar throughout this problem.

Explanation / Answer

Ta * d - ml*g*L/2 - m2*g*x) = 0

Ta = (1/2*ml*L + m2*x) )*g/d

For Tb, sum the vertical forces:

Tb = Ta - (ml + m2) * g

part b )

Ta = 3062.5 N

Tb = 2033.5 N

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