Two dimensional forces  Forces and Newton's Laws
Two dimensional forces
Lessons
Notes:
In this lesson, we will learn:
 How to solve force problems when force is applied at an angle
 How to solve force problems with inclines
Notes:
 When looking at forces in two dimensions, a force can point along the x or y axis, or at any angle in between. The net force acting on an object is found by adding all the forces acting on that object using vector addition.
 When solving for net force it can be helpful to break angled forces into x and y components so that the forces is the x and y directions can be added separately.
 When an object is on a slope, it tends to be pulled down the slope by gravity. We can understand why gravity pulls the object down the slope if we break the force of gravity into two components: one that is parallel to the slope, and one that is perpendicular.
 We can redefine the x direction to be parallel to the slope and the y direction to be perpendicular to the slope for a particular problem. Essentially, we "tilt" the axes to line up with the slope. The components can then be solved like normal x and y components.
 $\vec{F}_{x}$ represents the amount of $\vec{F}_{g}$ which is pulling the object down the slope.
 $\vec{F}_{y}$ represents the amount of $\vec{F}_{g}$ pushing into the slope. It is balanced by the normal force from the slope pushing back on the box.
$\Sigma \vec{F} = \vec{F}_{net} = m\vec{a}$
$\Sigma \vec{F}:$ sum of all forces, in newtons (N)
$\vec{F}_{net}:$ net force, in newtons (N)
$m:$ mass, in kilograms (kg)
$\vec{a}:$ acceleration, in meters per second squared $(m/s^{2})$
x and y Components of Force
$\vec{F}_{x or y} = \vec{F}\sin(\theta)$ (For the component opposite to $\theta$)
$\vec{F}_{x or y} = \vec{F}\cos(\theta)$ (For the component adjacent to $\theta$)

a)
How to solve force problems when force is applied at an angle

b)
How to solve force problems with inclines


2.
Forces on an incline