3.4.1.1
On an inclined plane, weight resolves parallel and perpendicular to the slope
Scalars & Vectors — AQA A-Level Physics
- The weight W acts vertically downwards.
- The component parallel to the slope is W sin(theta) -- this is the force pulling the object down the slope.
- The component perpendicular to the slope is W cos(theta) -- this equals the normal reaction force R if there is no motion perpendicular to the slope.
- If there is no friction, the object accelerates down the slope due to W sin(theta).
$$F_{\parallel} = W \sin \theta$$
- $F_parallel$: component of weight parallel to slope (N)
- $W$: weight of object (N)
- $θ$: angle of incline to the horizontal (degrees)
$$\begin{aligned}
F_{\perp} &= W \cos \theta \\
&= R
\end{aligned}$$
- $F_perp$: component of weight perpendicular to slope (N)
- $R$: normal reaction force (N)
- $θ$: angle of incline to the horizontal (degrees)
Examiner Tips and Tricks
- On a slope, the angle theta appears between the slope and the horizontal, but also between the weight vector and the line perpendicular to the slope.
- Draw the triangle carefully to avoid mixing up sin and cos.
Related:Kinematics