Solving Incline Plane Problems

Incline plane problems are an extension to Pully Problems. The significant difference is the gravity (and thus normal force) of the object is indirectly offset by the incline. Take a look at this diagram.

The relevant formulas are:

$g = 9.8$ $\frac{m}{s^2}$
$W_1 = m_1g$
$W_2 = m_2g$
$F_n = W_1\cos\theta$¹⁾
$F_g = W_1\sin\theta$²⁾

To solve for the acceleration of the system we use the tension acceleration formula: $a = \frac{F_g - W_2}{m_1 + m_2}$³⁾

Example

¹⁾

If friction is involved, you have to find the normal force with the friction equation

²⁾

$F_g$ is unlabeled, it is the force opposing tension on object 1

³⁾

to include friction, subtract $F_r$ from the numerator aswell