Working with Newton's Third Law and friction

[ramseycharles0]

Homework Statement

If the mass (m) of the box is 20 kg and the ramp is 30 deg, what is the normal force (𝒏 ⃑)?
What is it’s acceleration down the ramp?

Relevant Equations

F=ma

I know that the normal force and Fg are unbalanced in this case, but I don't get how to set up the equilibrium equations with that. I struggle with determining what you set the equations equal to when its either balanced or unbalanced forces you're dealing with.

 

[phinds]

Do you know how to deal with vectors?

 

[haruspex]

Homework Statement:: If the mass (m) of the box is 20 kg and the ramp is 30 deg, what is the normal force (𝒏 ⃑)?
What is it’s acceleration down the ramp?
Homework Equations:: F=ma

I know that the normal force and Fg are unbalanced in this case, but I don't get how to set up the equilibrium equations with that. I struggle with determining what you set the equations equal to when its either balanced or unbalanced forces you're dealing with.

Whether balanced or unbalanced, the basic equation is the same. In any direction you care to choose, the sum of force components in that direction determines the acceleration: ΣF=ma.
In the balanced case, a=0; that is the only difference.
So pick a direction. Usual choices are vertical, horizontal, parallel to the plane or normal to the plane.
Depending on exactly what you know and what you need to find, some choices may lead to a quicker solution than others, but you can always solve it by choosing any two of those four.
The key thing you need to be able to do is figure out the component of a given force in a given direction. Do you know how to do that?