00:02
All right.
00:02
So you have a roller coaster here that actually has friction on it.
00:06
So we're going to still use conservation of energy, but we're going to be able to figure out, well, what type of energy was lost? there's due to friction.
00:17
And we'll be able to compare that so we can find out what the friction average is, as well as what's the total mechanical energy, as well as what's the height of all of these things at different points.
00:30
So the key to this is this equation.
00:35
The work done at any moment by any force, force of friction, applied force in this first part, is going to be the force applied times distance.
00:48
So in part a, we need to figure out what is the total energy before and after the travel through this roller coaster.
00:58
So we're going to do all of the energy at first is done it by the work by this push force and this applied force.
01:12
Most likely it's a conveyor belt of some sort on the beginning of the roller coaster to get it going.
01:21
So we can do 8200 times six.
01:29
And we're assuming that this was done in the perpendicular to the direction.
01:34
So we don't need to worry about cosine of anything here because it looks like your drawing shows it on a flat surface.
01:42
So it's the conveyor belt added 49 ,200 joules of energy.
01:50
That's how much we have to start with.
01:53
Think of it like the conveyor belt was the battery and gave it a bunch of energy.
01:58
Now we have this amount of energy to make it all the way around the system of loops.
02:04
Hills and such.
02:08
Unfortunately, there's a friction force too, which is realistic.
02:12
There's got to be a little bit of friction.
02:13
So we need to compare that to this is the four, this is at point a.
02:20
Now we need to figure out what is our remaining energy when we get to the end and point d.
02:27
And that comes from this velocity at the d position.
02:33
Now we need to change this to meters per second.
02:36
So we need to need to multiply by 1 ,000 divided by 3 ,600 because there's 1 ,000 meters in a kilometer and 3 ,600 seconds in one hour.
02:50
So that will convert this to meters per second.
02:53
The reason that we have to do that is because we're using jewels and newtons.
03:00
And we need to stay in those same standard units of measurement for those equations that are using mutants and jewels to work, like the work function and the mechanical energy and the force the force times distance so i get 29 .17 i'm going to leave it with four digits for now so now i can find out the mechanical energy fine and this is going to be one half mv squared and the v that we're looking at is at point d so this should be one half times 100.
03:46
You wrote down 100 kilograms on your drawing.
03:48
It wasn't in the work problem itself.
03:51
So i assume that was given to you by your instructor independently and you used 100 kilograms.
03:58
Because without that, we can't figure out what the total energy has about.
04:04
So i'm going to use 100.
04:08
And we've got 29 .17 squared.
04:14
So let's see how much is left after this whole trip.
04:28
42 ,535.
04:31
So that's the, that is after the trip.
04:36
And so we lost some energy, right? so the way that we can find that average for friction force.
04:45
And i'm going to leave some of this for you to work out.
04:48
I'm going to set all this up though for you so that you can work through it and practice.
04:53
So we know that the work done.
04:57
Is force times distance.
04:59
So i'm going to do part b in blue here.
05:03
So work is equal to force of friction times the distance.
05:08
Well, we know what the work is, it's the change in energy.
05:13
So that's the other equation that we can look at.
05:15
The change in energy is the work done.
05:17
Well, the amount of energy that friction took away is the difference between the before and the after.
05:25
So if we say 49 ,200, minus 42 ,535.
05:34
I forgot my jewels on that.
05:36
I need that...