M2 Moments question

A uniform rod AB has length 8m and mass 12kg. A particle of mass 8kg rests at B. The rod is supported at a point C (the pivot) and is in horizontal equilibrium. Find the length of AC. 2013-12-27 14.00.58.jpg

Not too sure where to start. Would trying to find BC help? AC would then be 8 - BC. I tried 8g * 3x = 12g * 2x. Is that the right idea?

Reply 1

noodledoodle

there is no need to find BC although you can.
As for how to solve it, I'll give you a clue, you can ignore the entire portion from A to the middle of the rod up to the final step.

Reply 2

TSR561

Original post by noodledoodle

there is no need to find BC although you can.
As for how to solve it, I'll give you a clue, you can ignore the entire portion from A to the middle of the rod up to the final step.

Yep, I'm working with that knowledge as well. But all I get is 24gx = 24gx, which obviously doesn't help in the slightest.

Reply 3

noodledoodle

instead of using only x, try labeling the two parts as x and y instead to make things clearer.

You can form 2 simultaneous equations, the first being x+y=4

by substitution you will be able to form a third equation and solve for both y and x

Reply 4

TSR561

Original post by noodledoodle

I spent close to 20 minutes trying to figure out the link between BC and C to the CoM of the rod. 4 metres. Of course. I'm an idiot. Thanks a lot :smile: