00:01
Here we're going to use conservation of energy to find the coefficients of sliding friction on a slide.
00:07
And we don't know much about this slide other than the person going down it winds up with half the speed she would expect if there were no friction on the slide.
00:20
So we don't know either how long the slide is or how high it is or what her mass is.
00:27
But we do know that the inclination angle is 34 degrees.
00:32
So i am going to be using conservation of energy, in particular the work energy theorem.
00:42
The work done by a non -conservative force is equal to change in kinetic energy plus change in potential energy.
00:55
And all we have is gravitational potential energy.
01:00
No springs.
01:02
And i'm going to set that up for two cases.
01:05
I'm going to first of all set it up with no friction.
01:12
And here i'm going to use the notation that vff is her final speed with friction.
01:19
And just plain old vf is speed without friction.
01:26
And so there's no friction, makes the left -hand side zero.
01:31
We are going to take the difference between one half mv final squared, and we're going to assume an initial speed of zero up at the top of the slide.
01:47
Okay, so we'll subtract zero, plus gravitational potential energy final is zero at the bottom, minus initial mg.
02:03
Height.
02:09
And solving that, we see that the mass cancels.
02:13
Yep, that happens a lot.
02:16
And vf squared is equal to 2g.
02:21
And i'm going to use a little bit of trigonometry to get h is equal to d sine of 34 degrees.
02:36
So that is her expected speed without friction...