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Why does a longer ramp require less force to lift the same load?
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simple machine
Six simple machines for transforming energy into work.
An inclined plane is a simple machine that reduces the effort needed to lift a load by distributing the work over a longer distance.
The force required to move an object up a frictionless slope is calculated as:
In this formula, represents the weight of the object and is the angle of the incline relative to the horizontal.1
As the ramp becomes longer for a given height, the angle decreases. Because the sine of a smaller angle is a smaller value, the required force decreases accordingly. Conversely, a steeper slope (a larger angle) requires more force, approaching the full weight of the object as the slope becomes vertical. By increasing the length of the ramp, you trade distance for a reduction in the force necessary to move the load.1