00:01
Okay, so we have a ramp and then there is a section near the bottom that has friction.
00:11
So the coefficient of kinetic friction here is 0 .35.
00:18
Now we have a box that starts off at the top of the ramp at rest.
00:24
So our initial velocity is 0 meters per second.
00:28
And then we let it go and it goes down to the bottom and goes through this spot with friction.
00:35
But initially it does not have friction.
00:37
So we call this point a, this is point b, and this is point c.
00:42
So we can figure out the different velocities and energies at these different spots using conservation of energy.
00:50
So we're also told that the mass of the box is 5 kilograms.
00:55
And that this distance between b and c where the friction is, is 6 meters.
01:02
And then our height, our initial height of the box is 3 meters.
01:07
So in the first part we want to find the velocity when it gets to the bottom of the ramp.
01:14
So when it gets to the bottom of the ramp it's going to have the same velocity until it gets to the friction part.
01:22
So we can look at the velocity at point b to find out the velocity at the bottom of the ramp.
01:30
And using conservation of energy we can find that velocity.
01:35
We know that the energy initially at point a is mgh, so height at a.
01:42
And there's no kinetic energy because the velocity is 0.
01:46
And so the energy at point b is just kinetic energy.
01:50
And that's going to be 1 half m times the velocity at b squared.
01:56
So we can use this to solve for the velocity.
01:58
Our masses cancel out, we just divide both sides by m.
02:03
And then we can just solve for the velocity here.
02:05
So multiply both sides by 2 to get rid of the 1 half.
02:09
And take the square root.
02:11
Gives us vb is square root of 2gh.
02:18
That's going to be 2 times 9 .81 meters per second squared.
02:22
That's just the acceleration due to gravity times the height at a.
02:30
And that's going to give us a velocity of 7 .67 meters per second.
02:37
So that's our velocity at the bottom of the ramp.
02:41
And then in the second part, part b, we want to know if the box is going to make it to part c.
02:51
So is there enough energy in the box, is there enough kinetic energy to get through that frictional spot to get all the way to point c, which is 6 meters.
03:01
What we can do is figure out the kinetic energy that it has at point b.
03:06
And compare that to the work that would go into friction to get 6 meters through that friction...