00:02
All right.
00:03
Looks like you have a question about how do we do incline plane problems and where do we go with the equations that we need? so what i did was i created a basic, how do you solve for an incline plane problem in general? and hopefully that will help you set up your problems here since you're reviewing, i assume for a final exam here pretty soon.
00:30
So i don't want to do the problems for you because we want you to get ready to go.
00:35
So i'm going to get everything set up and review how to do these types of problems.
00:40
Up on the top right, i've written down the primary equations that are utilized in this form of problem.
00:49
The main one is the second law of motion that the acceleration down a ramp or acceleration in general is found by taking the net force.
01:00
And dividing it by the mass of the object that's accelerating.
01:07
So the key on these problems is finding the net force and then dividing it by the mass of the object, and that'll tell you how fast it's accelerating down the ramp, or if it's even accelerating down the ramp, it may be sitting there.
01:22
I did notice that your instructor has put in a few extra sets of questions where it's relating how do you solve for acceleration in different ways when the net force is unknown.
01:40
These scenarios, you'll use those first unit equations that you learned to find acceleration or how far it traveled or how long it took for it to travel.
01:53
And i listed those out as well.
01:56
So this all comes down to, does it give you the time it takes for it to go down the ramp? did it give you a distance that it traveled down the ramp? those types of things will allow you to find acceleration in a different way.
02:10
Maybe you know the final velocity at the bottom of the ramp.
02:14
Now notice that i've shrunk these down a little bit because i've removed the initial velocity because it showed that it was always at rest here.
02:22
So you may not recognize them as those original equations because i've removed the initial velocity from them.
02:30
As long as it's not moving to start with, we can ignore that part of the equation.
02:36
Displacement x equals one half a t squared.
02:39
That would be if we know the time and we know the distance traveled and it's going at a constant acceleration.
02:47
Maybe we know the final velocity v, and we know how long it took to get to the bottom of the ramp.
02:53
That would be v equals at.
02:55
Or maybe we know the final velocity and how far it traveled down the ramp.
02:59
That would be this v equals square root of 2ax.
03:02
So it's all about what information was given in the problem to determine this.
03:08
So if times and distances or final velocities are given, it's one of those bottom three to find the a.
03:15
And then we can use that to find the net force.
03:18
So it's like reverse engineering the problem.
03:21
But if we are given all the forces involved, then we can use a equals net force to divide by m.
03:28
At the bottom here, i've drawn a force diagram of the scenario that we have.
03:34
We have a mass that's being pushed down a ramp at, then the ramp is at an angle and the coefficient of kinetic friction is given in the problem.
03:46
So i drew a force diagram of that just to kind of review what is all happening here and how do we find the net force.
03:55
Another thing that i like to do is i like to redraw these into an orientation that's easier for me to understand.
04:04
So i'm going to pretend that i live in a world where i live on the same angle as the ramp itself.
04:11
So when i look at the mass, it looks like it's on level ground.
04:14
And only gravity is messed up in that scenario rather than these three other vectors.
04:20
So i'll show you what i mean by that.
04:23
I'm going to draw my redraw in blue.
04:28
Now, this would not be an acceptable answer to drawing a force diagram.
04:33
What the acceptable answer is already drawn in black.
04:37
But this is just for my use.
04:40
So i'm going to redraw it in terms of that my vectors on the plane of the ramp are in the x and y.
04:57
And i'm going to break down the fg into its components.
05:03
So this is what i mean by that.
05:06
So normal force is now up here.
05:10
The pushing, pushing forces over here to the right.
05:14
The friction force is here.
05:16
And then i've broke, i'm going to break down gravity into fg parallel for the parallel part of the force through to gravity.
05:27
And then fg perpendicular, the part of the force that's perpendicular to the ramp.
05:33
So that redraw is going to help me because one thing that i will always know about fg parallel is that it's the sign of the angle times the total mass times gravity.
05:48
I should put that in as mass times gravity instead.
05:53
So i always be able to find fg parallel that way.
05:56
And i could find fg perpendicular using cosine theta mg.
06:02
And that, unless we have another force acting on it, is going to be equal to the normal force as well.
06:10
So that's another thing that we can say is true.
06:15
So so far we've just kind of given you like a general idea of how to solve an incline plane problem and regardless of what information was given.
06:29
So this hopefully will help.
06:30
I'm going to just make up an example that similar to your first one.
06:35
I'm going and then i'm going to solve it here.
06:39
So i'm going to need a little bit more space on minds...