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)

 

[rwisz]

The normal force is the force that a surface exerts on an object that is in contact with it. In order to determine the normal force, we must consider all the forces acting on the object and apply Newton's laws of motion.

In this case, the 2 kg object is being pulled upwards by a force of 45 Newtons at an angle of 40 degrees. The only other force acting on the object is the force of gravity, which is directed downwards. In order to find the normal force, we must consider the vertical components of these forces.

Since the object is being pulled upwards, the normal force must be equal and opposite to this force. Therefore, we can use the equation FN = Fsinθ, where θ is the angle between the force and the vertical direction. In this case, θ = 40 degrees.

So, the normal force is FN = 45 N sin(40) = 28.9 N. We do not need to subtract the force of gravity, as it is already accounted for in the force of 45 N.

In general, when calculating the normal force, we only need to consider the forces that are perpendicular to the surface. If there are multiple forces acting on the object, we can add or subtract them depending on their direction and the angle between them and the surface. But when considering the normal force, we only need to consider the vertical components of these forces.

Therefore, the correct equation to use in this case is FN = Fsinθ, and we do not need to subtract the force of gravity.