A rigid, uniform horizontal bar of mass m l and length L is supported by two ver

Question

A rigid, uniform horizontal bar of mass ml and length L is supported by two vertical massless strings. String A is attached at a distance of 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.

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

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

Explanation / Answer

Net torque is Zero

(TB*L/2) -[TA*((L/2) -d)] - [m2*g*((L/2)-(L-x))] = 0

(TB*L/2) - TA*L/2-(m2*g*(L/2)) = -TA*d - m2*g*(L-x),......(1)

and net force is also 0

TA = TB + m2*g + ml*g....(2)

Solve (1) and (2) to het TA and TB

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