page_title: Inclined plane
section_title: Mechanical advantage using power
hierarchical_section_title: Inclined plane / Mechanical advantage using power
caption_attribution_description: Français&#160;: Système de poulie du plan incliné actionné par une machine à vapeur à Liverpool.
context_page_description: An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six classical simple machines defined by Renaissance scientists. Inclined planes are widely used to move heavy loads over vertical obstacles; examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade.
  Moving an object up an inclined plane requires less force than lifting it straight up, at a cost of an increase in the distance moved. The mechanical advantage of an inclined plane, the factor by which the force is reduced, is equal to the ratio of the length of the sloped surface to the height it spans. Due to conservation of energy, the same amount of mechanical energy is required to lift a given object by a given vertical distance, disregarding losses from friction, but the inclined plane allows the same work to be done with a smaller force exerted over a greater distance.
context_section_description: The mechanical advantage of an inclined plane is the ratio of the weight of the load on the ramp to the force required to pull it up the ramp.  If energy is not dissipated or stored in the movement of the load, then this mechanical advantage can be computed from the dimensions of the ramp.
  In order to show this, let the position r of a rail car on along the ramp with an angle, θ, above the horizontal be given by
  where R is the distance along the ramp.  The velocity of the car up the ramp is now
  Because there are no losses, the power used by force F to move the load up the ramp equals the power out, which is the vertical lift of the weight W of the load.
  The input power pulling the car up the ramp is given by
  and the power out is
  Equate the power in to the power out to obtain the mechanical advantage as
  The mechanical advantage of an inclined can also be calculated from the ratio of length of the ramp L to its height H, because the sine of the angle of the ramp is given by
  therefore,
  Example: If the height of a ramp is H = 1 meter and its length is L = 5 meters, then the mechanical advantage is
  which means that a 20 lb force will lift a 100 lb load.
  The Liverpool Minard inclined plane has the dimensions 1804 meters by 37.50 meters, which provides a mechanical advantage of
  so a 100 lb tension force on the cable will lift a 4810 lb load.  The grade of this incline is 2%, which means the angle θ is small enough that sinθ=tanθ.
caption: Layout of the cable drive system for the Liverpool Minard inclined plane.
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