Frictionless plane
In his 1638 The Two New Sciences,[1] Galileo presented a formula that predicted the motion of an object moving down an inclined plane.
[3] However, Galileo's equations do not contemplate friction, and therefore do not perfectly predict the results of an actual experiment.
Despite their nonexistence, they have considerable value in the design of engines, motors, roadways, and even tow-truck beds, to name a few examples.
[6] The effect of friction on an object moving down an inclined plane can be calculated as where
[7] Unless the inclined plane is in a vacuum, a (usually) small amount of potential energy is also lost to air drag.
N = normal force that is perpendicular to the plane
m = mass of object
g = acceleration due to gravity
θ ( theta ) = angle of elevation of the plane, measured from the horizontal