Weight on an Incline: Understanding Angles

[pooface]

There is not really a homework problem. I just want to understand the concept here.

See the image attached. How is it that in the free body diagram of the image shown the angle theta is from FN to the perpendicular Force applied by box to the horizontal? It is hard to describe in words. I just want to know how am I placing my angles and X,Y in a free body diagram of this setup.

I always thought the X axis was Cos and Y was Sin but when my professor solved the problem, FN, which is vertical, was determined by FN cos(theta)

I don't understand.

 

[mgb_phys]

The two thetas are equal from similair triangles.
Rather than trying to remmber which is cos and sin think what happens as the angle gets small, which force goes to zero ,that equals sin which goes to zero as theta is small,and which gets larger, that is cos goes to one as theta gets small.

 

[m2003]

The angle theta in the free body diagram is measured from the normal force (FN) to the perpendicular force applied by the box to the horizontal. This is because the normal force is the force that is perpendicular to the surface of the incline and is therefore the reference point for measuring the angle. The X and Y axes in a free body diagram can be chosen arbitrarily, but it is common to choose the X axis parallel to the surface of the incline and the Y axis perpendicular to it. In this case, FN cos(theta) is used to determine the vertical component of the normal force, which is necessary for solving the problem. It is important to note that the X and Y axes can be chosen differently as long as they are consistent throughout the problem.