00:01
In this video, we're going to be working with the concept of conservation of energy.
00:06
Okay, so conservation of mechanical energy says that for a closed system with no outside forces acting on it, mechanical energy is constant.
00:17
Okay, and that equals potential energy plus kinetic energy.
00:23
Okay, so this value will always be constant.
00:26
And what we have is a block.
00:28
It has a mass m, i'll call that m sub b.
00:31
Of 0 .15 kilograms.
00:36
Okay, it's approaching a ramp that's inclined at an angle of theta equals 20 degrees with the horizontal.
00:43
Okay, and it has an initial velocity upon approach vb equals 2 .15 meters per second.
00:53
Okay, and what we wanna find is how far up the ramp this block will go.
00:58
So let me draw you a picture.
00:59
Okay, so we have our mb.
01:03
It's moving with some initial velocity vb along a flat horizontal surface and it's approaching a ramp.
01:12
Okay, and that's angled at theta.
01:15
Okay, so we want to find the height that we reach, okay, before we come to a stop.
01:21
I know that there's a coefficient of friction between the block and the ramp uk and that equals 0 .12.
01:31
Okay, so using this information, we can find, find the height that the block reaches and we can find how far it goes up the ramp and i'll call that distance d and i'm going to call this horizontal surface i'm going to call this y equals zero so how do we find this initial velocity well initially we're at an elevation of zero and we're moving with some velocity so all of my energy is going to be kinetic so my initial energy is one half m v squared initial and that's going to equal my final energy, which is going to be all potential energy.
02:06
When we reach our highest point, our velocity is momentarily zero.
02:10
So that's going to be our potential energy, mgh, plus we have another term.
02:16
That's the work that the frictional force does as we travel a distance d up the ramp.
02:21
So that's going to be plus our force of friction times d...