Calculating Normal Force: Adding/Subtracting?

[barthayn]

Homework Statement

How to know when one is suppose to add or subtract to get the normal force of an object.

Homework Equations

F_N = F_g, F_N = F sin(-)

The Attempt at a Solution

I believe to get the normal force of a 2 kg object when it is being pulled upwards by a force of 45 Newtons at an angle of 40 degrees is:
F_N = 45 N sin(40) - 19.6 N
F_N = 9.32 N

or is it:

F_N = 45 N sin(40)
F_N = 28.9 N

Which one is correct? How do I know when to add or subject the normal force and gravitational force?

 

[mizzy]

I usually draw the FBD and look at my positive and negative values.

Fn is perpendicualr to the slope of the incline, therefore it's equal to the y component of mg.

 

[barthayn]

I usually draw the FBD and look at my positive and negative values.

Fn is perpendicualr to the slope of the incline, therefore it's equal to the y component of mg.

How is it the normal force equal to the force of gravity? That is impossible with an incline. It is only possible if the mass is on a flat surface. However, I see your point of labeling the FBD. Therefore, my example that I used, the mass was being pulled upwards because the normal force was higher than the force of gravity?

 

[rl.bhat]

If you push a cart with a force making an angle θ with the horizontal on the horizontal surface, then the normal force = mg + Fsinθ.
If you pull the cart in the above case, the normal force = mg - Fsinθ.
In your problem two forces are acting on the body.Net normal force is the sum of the components of two forces perpendicular to the surface of the inclined plane. 45 N is acting parallel to the inclined plane. So it has no vertical component with respect to the inclined plane. Hence the normal reaction is mg*cos(θ)