00:04
So the diagram for number 37 looks like this.
00:11
It's just a bar teetering on its center, which is b.
00:20
L length l here and length l here.
00:24
This is point c.
00:26
This is point a.
00:30
There is a force at point a.
00:35
And then there's also a spring that is a length l away.
00:43
So i'm going to go like this.
00:47
Just draw a line here, call that l, and then there's a spring.
00:57
Oops, i don't need to draw the spring.
01:09
F sub s is in this direction.
01:16
Finally, if i make this horizontal, let me try that again.
01:22
Make that horizontal and call this theta.
01:30
Okay, well, first of all, the unstretched length of the string is when theta is zero.
01:41
So when it's unstretched, it's really gonna look like this with l and l.
01:53
And so, the unstretched length of the string is the square, root of l squared plus l squared, which would be the square root of 2 times l.
02:22
So that's the unstretched length of the spring.
02:30
All right.
02:33
Now, i need the y value at point a, which is going to be.
02:48
Negative l, not cosine, sign.
02:58
I also need the y position at point c, which is gonna be positive l, sine theta.
03:08
And i need the x position at point c, which is gonna be positive l, cosine theta.
03:18
So i'm gonna call this y, and i'm gonna call this.
03:24
All right, let's go ahead and do the derivatives.
03:33
Delta y at a is negative l cosine theta.
03:40
Delta y at c is l cosine theta.
03:48
Delta x at c is negative l sine theta.
03:55
Derivative of cosine is opposite of sine.
03:59
I also need to know the direction of the spring force.
04:06
So the spring force in the x direction is negative.
04:28
Let me see.
04:28
I'm having a brain freeze right now.
04:34
Let me think about what's going on here.
04:54
This is 90.
05:06
Oh, okay.
05:23
It's an isosceles triangle.
05:25
And so this angle here is going to be 90 plus theta.
05:33
So we need to take 180 minus 90 plus theta and divide it amongst the two other angles.
05:52
So 180 minus 90 plus theta is going to be 90 minus theta over 2.
06:06
And so this angle here is 90 minus theta over 2.
06:20
Let me just make sure i got that rate again.
06:22
90 plus theta, take 180 minus that is going to give us 90 minus theta and then divided it amongst 2.
06:34
So 90 minus theta over 2.
06:36
Okay.
06:37
So this right here, the angle that's right next to it, or rather, let's not go to there first, let's go to this whole angle there there.
07:25
So this is 90 here.
07:27
That whole blue angle is 90 minus theta.
07:34
So if i take that blue angle and i subtract away the black angle, 90 minus theta over 2, that's going to give me this little green angle.
07:52
So the little green angle is going to be 90 minus theta minus half of 90 minus theta is just going to be half of 90 minus theta.
08:17
That's interesting.
08:23
Something minus half of itself is only half of itself.
08:28
So that green one also has to be 90 minus theta over 2.
08:40
Okay.
08:43
It seems unusual, but i'm going to go with it.
08:45
90 minus theta over 2.
08:48
All right.
08:49
So, f sub s, did i start writing this? in the x direction is going to be f sub s times the sign of 90 minus theta over 2.
09:32
S in the y direction is going to be f sub s times the cosine of 90 minus theta over 2.
09:48
Okay.
10:00
Let's go ahead and do the virtual work equation.
10:11
So, negative p times delta y at a.
10:28
Okay.
10:33
Delta y at c.
10:40
And actually i need the vertical f of s.
10:47
And wait a minute.
10:48
I want to make sure i have my signs correctly.
10:51
Correct.
10:52
F sub s in the x direction is negative.
10:55
And f sub x, s in the y direction is also negative.
11:00
So these are all negative.
11:03
Plus y direction, negative f sub s cosine of 90 minus theta over 2.
11:20
And then delta yc is l cosine theta.
11:30
I forgot to write my delta theta's, my delta theta's, my delta theta's.
11:38
Come on.
11:41
Delta, theta.
11:43
Don't really have room for them anyway.
11:46
Okay.
11:47
And then we've got negative f sub s, sign 90 minus theta, over two times negative negative l, sine theta, delta theta.
12:16
Okay...