Question: In figure the bar is uniform and weighing 500N. How large must W be if $T_1$ and $T_2$ are to be equ...

Question

In figure the bar is uniform and weighing 500N. How large must W be if $T_1$ and $T_2$ are to be equal?

Answer 1

Solution

To have equal tensions the overall centre of mass must lie midway between the rope–attachments. The uniform bar (500 N) has its c.g. exactly halfway between the supports. Since the extra weight W is hung 0.2L off this midpoint (0.7L instead of 0.5L from the left end), it must be 3 times as big as 500 N’s “moment portion” to “pull” the centre back, leading (by the moment–balance equation) to W = 1500 N.