00:01
Alright, so we're given a problem with a hanging sign that is hung by a light rod, so we're not to worry about the mass of the rod.
00:12
The sign has a force of gravity of fg, and it is hung by also attached with a hinge right here, as well as on a with a string.
00:25
So let's first identify a point.
00:28
We're going to analyze some torques.
00:30
So i'm gonna choose usually choose the point you know the least about or the point that you care at least about so let's use the point on hinge on the wall and so let's talk about the torques acting on that hinge so there i'm just gonna ring it out here there is a torque from the sign right we can assume it's acting from the center of the sign which is a distance d plus l from the wall are from the pivot point and then you also have your uh you have your tension pulling diagonally at some angle theta and again we can put that into components into its two components and we really only care about the vertical because this horizontal component is not regarding any torque about our pivot point and so this you know if we call that t this it'll be t rights for gregn's sign of theta, whatever theta is.
01:41
And then because we know it's in equilibrium, we know that those two torques are equivalent, or they cancel up to zero.
01:50
So we know that the force of gravity from the sign times the distance away, d plus l, the magnitude of that is going to be equal to the magnitude of t sine theta.
02:06
And so if we just solve for t, which is what the question is asking us to find, determine the tension in the cable...