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Inclined plane

On an inclined plane the weight splits into two components: one along the plane pulling the body down the slope, and one perpendicular to the plane balanced by the normal force. The steeper the plane, the more of the weight acts along the motion and the less the body presses on the surface.

N = mg\cos\theta

normal force

F_{\parallel} = mg\sin\theta

weight component along the plane

Symbols

$\theta$	incline angle	°
$N$	normal force	N
$F_{\parallel}$	weight component along the plane	N

Example

An 8.0 kg block sits on an incline with $\theta = 20^\circ$ . $F_\parallel = 8.0\cdot 9.81\cdot\sin 20^\circ \approx 26.9$ N, and $N = 8.0\cdot 9.81\cdot\cos 20^\circ \approx 73.8$ N.

Place the acceleration axis along the plane – then you avoid splitting the normal force and friction into x- and y-components.

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Part of Foundations of Physics: Forces and Newton's laws.