00:01
We have this person that weighs 169 pounds, and they have two crutches, each at 18 degrees from the vertical.
00:10
So we want to find the coefficient of friction between the crutch and the ground, as well as the compressive force that is resisted by the crutch.
00:23
So the first thing to do is see how much force is how much of the weight is held by the crutch.
00:27
We're told that of the 169 pounds, one half of it is supported by the crutches, but there's two crutches, so we need to divide by two again.
00:37
That works out to 42 .25 pounds vertically for each crutch.
00:43
So if we draw our crutch at some angle or extend the triangle out for the angle, we'll need that later.
00:56
We have some component vertically, 42 .25.
01:03
Some component in the extraction.
01:09
With these members like this, like a crutch or any bar, where there's only forces on the end, it's called a two -force member, which means the total force has to exist along the axis of the beam.
01:23
And we can break that into components.
01:25
And we know the vertical component is 42 .25, which means the same vertical component exists down below, as well as the same horizontal component, we'll call it fx.
01:41
Now, as we talked about, this component is the component of the total vertical.
01:49
So we can solve this by trigonometry.
01:54
We know the force and the angle, and we want to find this f of x.
02:04
So we can use the tangent because we have the two short sides, or the tangent of 18 degrees is equal to the opposite fx over the adjacent 42 .25.
02:22
And so we can evaluate for fx is 18 degrees.
02:37
And that works out to 13 .73.
02:44
So 13 .73 pounds.
02:50
And that has to be resisted at the other side by the friction, which, we can call fx or typically script f...