00:01
So in this problem, we have a floor that is frictionless, so friction is equal to zero.
00:08
And a chair sitting on top of it, not very creative right now, so we'll just say it's a box.
00:13
We know this chair, though, is 12 kilograms.
00:17
And we are pulling on the chair with a force of 40 newtons, directed at an angle upwards.
00:22
And so we're pulling, pointed somewhat upwards.
00:26
We know it's 40 newtons, and it is 37 degrees relative to the force.
00:37
So we want to find with the normal forces.
00:41
So imagine the floor wasn't here, then this chair would want to fall down.
00:45
And so to keep the chair from falling down, the floor is exerting a normal force on the chair to keep it from falling through.
00:53
And that's what we want to find.
00:54
When we need to find forces like this, we should draw a free body diagram.
00:57
So our body is a chair.
00:58
We want to free it from the external reactions.
01:01
And we can simplify its geometry to just a point because we don't really care otherwise what it is.
01:06
Now on this body, when it's free, any external reactions are replaced with forces, and we also need to put any other forces on here.
01:14
So we have our force f that we're applying, which we know is equal to 40 newtons.
01:22
Now the chair has a certain weight.
01:24
Its weight is equal to its mass times the excerity due to gravity.
01:27
And then we have the normal force we have been talking about, which we should label.
01:36
And then to complete the free body diagram, we should draw an axis.
01:39
So we have x and y by convention and we also should label that our force is 37 degrees so that should complete it now we can use newton's second law to find the normal force in general newton cycle law the sum of forces on the body is equal to its mass times acceleration strictly this is a vector but what we can do is break it into components and say for example the sum of forces in the y direction is equal to the mass times acceleration in the y now we notice that the chair is sitting stationary on the ground.
02:16
So if there's no friction and there's a force, because we can see that our force here is going to have components, fy and fx, there's a force pulling the chair and no friction, so the box where the chair is going to move.
02:32
So it's going to have some x velocity and also an exertion of the x from the force and f equals i mean in second law.
02:41
But in the y, the box is staying on the ground, which means we have both vy is equal to 0 and ay equal to 0.
02:53
So our acceleration is 0, and therefore the sum of forces on this body should add to 0 in the y direction.
02:59
So now we just add up everything in the y direction.
03:02
We have the normal force...