Inclined Plane
An inclined plane is a flat sloped surface, such as a ramp, that lets a load be raised with less force applied over a longer distance.
Definition
An inclined plane is a ramp, a flat surface that is tilted, and pushing something up a ramp is easier than lifting it straight up. Set at an angle to the horizontal, it reduces the force needed to raise an object by spreading the work over a longer distance, with ideal mechanical advantage equal to the length of the slope divided by its height; wedges and screws are inclined planes in disguise. On a frictionless incline of angle $\theta$, the component of gravity along the slope is $mg\sin\theta$, the normal force is $mg\cos\theta$, and the ideal mechanical advantage is $L/h = 1/\sin\theta$. With kinetic friction $\mu_k$, the force needed to push a block up at constant speed is $F = mg(\sin\theta + \mu_k\cos\theta)$, and the block slides down on its own only if $\tan\theta > \mu_s$. Galileo used inclines to slow free fall enough to measure it.
Example
Movers use a ramp to roll a heavy refrigerator into a truck instead of lifting it, and wheelchair ramps work the same way. A ramp $6\ \text{m}$ long that rises $1.5\ \text{m}$ has a mechanical advantage of $6 / 1.5 = 4$, so pushing a $600\ \text{N}$ crate up it takes $150\ \text{N}$ without friction, and the work is $150 \times 6 = 900\ \text{J}$, equal to $600 \times 1.5$. For a $20\ \text{kg}$ box on a $25^\circ$ incline with $\mu_k = 0.15$, gravity along the slope is $20 \times 9.8 \times \sin 25^\circ \approx 82.8\ \text{N}$ and the normal force is $196\cos 25^\circ \approx 177.6\ \text{N}$, so friction is about $26.6\ \text{N}$. Pushing up at constant speed requires $82.8 + 26.6 \approx 109\ \text{N}$; without the ramp it would take $196\ \text{N}$.
Key Insight
A longer, gentler ramp needs less push than a short, steep one; you trade extra distance for a lighter load. Mountain roads zigzag for this reason, since switchbacks make the road longer so that the slope, and the force a car engine must supply, stays manageable. Every object on an incline accelerates at $g\sin\theta$ regardless of mass, which is a slowed-down version of free fall. That is exactly why Galileo could time rolling balls with a water clock and discover that distance grows with time squared.