The Inclined Plane

Normal Force

the surface pushes back

The ramp pushes out perpendicular to its surface exactly hard enough to cancel the block's press into it.

Example

The ramp pushes out perpendicular to its surface exactly hard enough to cancel the block's press into it. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The block presses into the ramp

From the last lesson, the block presses into the surface with 8 newtons.

W⊥=8 NW_\perp = \hl{8}\ \text{N}
The press into the surfaceA block on a ramp with one arrow pressing into the surface.minto-slope

The surface pushes straight back

The block does not sink into the ramp, so the surface must push out just as hard, perpendicular to the slope. That push is the normal force, equal to the press: 8 newtons.

N=W⊥=8 NN = W_\perp = \hl{8}\ \text{N}
Normal force balances the pressThe into-surface press and an equal arrow pushing out of the surface, perpendicular to the slope.minto-slopeN

Every press gets an equal normal force

Try smaller and larger presses into the surface. As long as the block is not sinking into the ramp, the normal force matches the press and the leftover into-surface force is zero.

W⊥NW⊥−N4 N4 N0 N8 N8 N0 N12 N12 N0 N\begin{array}{c|c|c}W_\perp & N & W_\perp - N \\ \hline 4\ \text{N} & 4\ \text{N} & 0\ \text{N} \\ 8\ \text{N} & 8\ \text{N} & 0\ \text{N} \\ 12\ \text{N} & 12\ \text{N} & 0\ \text{N}\end{array}
mechanics The normal force simply equals the into-slope press, 8 N, because nothing moves perpendicular to the surface.