Inclined Plane
The ramp: the oldest trick, the most elegant physics
Summary
The weight of an object on an inclined plane splits into two parts: one that pulls it down the slope (W∥) and one that presses it into the surface (W⊥). As the ramp gets steeper, the part pulling down grows; past a certain angle friction can no longer hold the object and it starts to slide. Drag the top of the ramp, change the surface and try pushing the block.
In depth
The inclined plane is one of the six classical simple machines, along with the lever, the pulley, the wheel and axle, the wedge and the screw. The weight W = mg of an object of mass m on a surface inclined at angle θ splits into a component parallel to the surface, W∥ = mg·sinθ, and a component perpendicular to it, W⊥ = mg·cosθ. The surface pushes on the object with a normal force of N = mg·cosθ. Static friction can be at most μs·N, so when tanθ > μs the object slides on its own. The acceleration of a sliding object is a = g(sinθ − μk·cosθ) and does not depend on its mass. On a frictionless ramp the force needed to push the object up is mg·sinθ: you gain in force but lose in distance, and the work done stays the same.
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