00:01
All right, let's say we have a block sliding down a ramp that is frictionless, but then after it slides down the ramp and encounters a rough patch, which has a coefficient of friction of 0 .61, so somewhere right about here.
00:16
And we want to find the height of the ramp such that the block speed after crossing the rough patch is 3.
00:26
Point or sorry this the width of this i should say is 0 .15 meters we want to find the height such that the speed of the block after leaving this section is 3 .7 meters per second and we're also given the mass of the block we don't need it to solve many of this but i'll write it to be complete 2 .25 kilograms so what we're going to have is the potential energy the block initially starts with is we'll say mgh where h is the height of our ramp this is going to be equal to the kinetic energy at the bottom of the ramp because there's no friction involved.
00:59
And so after it passes over this rough patch, it's going to lose a certain amount of energy we'll call delta w.
01:07
This is the work due to friction.
01:09
And then the remaining kinetic energy it has is going to be the difference between the initial potential energy and that work due to friction if we write it like this.
01:20
All right.
01:21
So you can see what happens if the work due to friction is zero.
01:24
It would just mean our potential energy.
01:25
Is equal to our kinetic energy, which is what we would expect to have.
01:30
All right.
01:31
So what's the work due to friction? the work is going to be the force of friction times the displacement.
01:37
I've already included the negative sign here...