Frictionless Inclined Plane
If there is no friction between the object being moved and the plane, the device is called an ideal inclined plane. This condition might be approached if the object is rolling, like a barrel, or supported on wheels or casters. Due to conservation of energy, for a frictionless inclined plane the work done on the load lifting it, Wout, is equal to the work done by the input force, Win
Work is defined as the force multiplied by the distance it moves. The work done on the load is just equal to its weight multiplied by the vertical distance it rises, which is the "rise" of the inclined plane
The input work is equal to the force Fi on the object times the diagonal length of the inclined plane.
Substituting these values into the conservation of energy equation above and rearranging
To express the mechanical advantage by the angle θ of the plane, it can be seen from the diagram (above) that
So
So the mechanical advantage of a frictionless inclined plane is equal to the reciprocal of the sine of the slope angle. The input force Fi from this equation is the force needed to hold the load motionless on the inclined plane, or push it up at a constant velocity. If the input force is greater than this, the load will accelerate up the plane; if the force is less, it will accelerate down the plane.
Read more about this topic: Inclined Plane
Famous quotes containing the words inclined and/or plane:
“Sometimes we are inclined to class those who are once-and-a-half-witted with the half- witted, because we appreciate only a third part of their wit.”
—Henry David Thoreau (1817–1862)
“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the plane of subjects to enfranchised slaves.”
—Anna Howard Shaw (1847–1919)