A rigid, uniform horizontal bar of mass mt and length L is supported by two vert

Question

A rigid, uniform horizontal bar of mass mt 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. (a) If the system is perfectly balanced then calculate the magnitude of the tension In both strings. (Express your answer using only the variables m_l, L, d, m_2, x, and/or g)

Explanation / Answer

a)

taking torque about left end

TA (d) = (ml x + m2L/2)g

TA = (m2L/2+mlx)g/d

for equilibrium

TA = TB + mlg +m2g

TB = (m2L/2+mlx)g/d - mlg -m2g

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