Object on an Inclined Plane Simulation

Objects on inclined planes have component vectors which are altered by the angle of elevation. Hence, we modify $$F_{net}=ma$$ into the following subset of equations in order to model the new forces acting on the object.

$$F_{net_x} = ma_x$$ $$F_a+F_{g_x} - F_f = ma_x$$ $$F_a + mg \sin \theta - \mu mg \cos \theta = ma_x$$ Fa is force applied, Fg is weight, Ff is friction force.

$$\tan \theta = {\mu}_{static}$$

When does the object begin to move?

As you may have noticed, there is an angle at which the object begins to move which is independent from its mass. This is known as the critical angle, which we can find using the formula on the right.