00:01
Problem 11 .17, we have a beam attached to a wall by a hinge, and it's supported by a cable.
00:14
The beam is nine meters long.
00:18
The maximum tension that the cable can support before it breaks is one kilenoon.
00:25
And so what we'd like to do is draw a free -body diagram of the forces acting on the beam.
00:31
We want to find what the maximum weight of the beam can be before the, cable will break and then we want to find the x and y components of the force that the hinge is exerting on the beam and then we want to know whether the vertical component of that is positive or negative so or another way of putting it is it directed upwards or downwards because whether it's positive or negative will depend on whether we put our y -axis going up or down so to begin with our tree body so we have our beam halfway along it, the weight will be acting.
01:41
A bit to the left of that will be the tension in the cable, which has its x and y components.
01:56
And then the force from the hinge will have component we'll call h sub x, and then we'll have the y axis going downwards.
02:12
Or we'll say that the h sub y is downwards.
02:17
And if we're wrong about this, then we just get a negative number and then we know it's actually pointing the other way.
02:25
And as usual, we're going to call the counterclockwise the direction of positive rotation.
02:33
And another thing we should do before we go too much further to figure out actually, you know, what is the distance between the hinge and where the cable attaches, which we can call l.
02:48
And so this is fairly straightforward because we know that l squared plus 16 meters squared is equal to 25 meters squared.
03:05
25 minus 16 is 9, and so l is 3 meters...