Physics question, forces, vectors

[short]

Hey guys,

I am trying to understand the picture I uploaded (from Wikipedia) because it closely relates to what we are doing in my physics class. In the picture the different forces are calculated with sin and cos.

In the diagram it shows that the normal force acting on the box is m*g*cos(20).

This is where I am hung up, why is it cos? I thought if anything it should be sin(20) because we are finding the vertical component to the Normal force vector.

In my book it says the perpendicular force (the normal force is indeed perpendicular to the x-axis, right?) is equal to A * sin(theta), not cos.

Why when finding the normal force in the picture is it cos and not sin?

Thank you

[Falco Girgis]

Ugh, I completely remember that shit from physics. I honestly couldn't help you, though. That was something that everybody screwed up, because the normal "just is cos." I've never been offered a good explanation.

In the game development world (which is what I'm acquainted with), we aren't using sin/cos to calculate these kinds of things, it's direction unit-vector based instead--which is a million times more intuitive.

[avansc]

quite simple actually,

so you know what you mg is. and you are trying to find N. well you can draw N in the opposite dir. or mg. that will give you a triangle

then you know cos = adj/hyp

so

cos(theta) = N/mg

thus mg.cos(theta) = N

ps: tilt your head to the right... make sense now?

[K-Bal]

Just imagine what happens if theta is 0 or pi/2.

If it's zero all the force lies on the plane and you have no force down the slope (the slope has become a flat plane). Cos(theta) becomes 1 and sin(theta) becomes 0, exactly what you would expect from a logical point of view.

If it's pi/2 your block will fall all the way down. The ground has become perpendicular to your gravity force so it cannot influence the block anymore. Cos(theta) has become 0 and sin(theta) has become 1.

The values between 0 and pi/2 can be derived with geometry and you will find out that it is exactly cos and sin, just like avansc explained.

[short]

Yes,

actually it does. Thank you avansc

edit: you must have posted when I was replying. Yeah, I think I got my head around it, thank you k-bal

[Falco Girgis]

Holy shit, I always thought of it as being the other triangle in PH111.

[short]

Awesome!!

At least I'm not the only one to learn something from this thread

[K-Bal]

Holy shit, I always thought of it as being the other triangle in PH111.

We are all no perfect human beings :D

[dandymcgee]

In picture form:

Option2_Freebodydiagram2_pn.png (65.77 KiB) Viewed 801 times

The orange line is the magnitude of the Normal Force, and the top angle of the new green triangle is equivalent to theta due to the fact that both triangles are similar. Since Fn is adjacent to this newly discovered theta, you would use cosine to solve for it.