The frictionless plane is a concept from the writings of

Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

. In his 1638 '' The Two New Sciences'', Galileo presented a formula that predicted the motion of an object moving down an

inclined plane An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle from the vertical direction, 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 clas ...

. His formula was based upon his past experimentation with free-falling bodies. However, his model was not based upon experimentation with objects moving down an inclined plane, but from his conceptual modeling of the forces acting upon the object. Galileo understood the mechanics of the inclined plane as the combination of horizontal and vertical vectors; the result of

gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...

acting upon the object, diverted by the

slope In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is use ...

of the plane. However, Galileo's equations do not contemplate

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...

, and therefore do not perfectly predict the results of an actual

experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...

. This is because some energy is always lost when one mass applies a non-zero

normal force In mechanics, the normal force F_n is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1. In this instance ''normal'' is used in the geometric sense and means perpendicular, as oppose ...

to another. Therefore, the observed

speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quanti ...

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

and distance traveled should be less than Galileo predicts. This energy is lost in forms like sound and heat. However, from Galileo's predictions of an object moving down an inclined plane in a frictionless environment, he created the theoretical foundation for extremely fruitful real-world experimental prediction. Frictionless planes do not exist in the real world. However, if they did, one can be almost certain that objects on them would behave exactly as Galileo predicts. Despite their nonexistence, they have considerable value in the design of engines, motors, roadways, and even tow-truck beds, to name a few examples. The effect of friction on an object moving down an inclined plane can be calculated as :

F_\mathrm = \mu_\mathrm F_\mathrm,

where

F_\mathrm

is the force of friction exerted by the object and the inclined plane on each other, parallel to the surface of the plane,

F_\mathrm

is the

exerted by the object and the plane on each other, directed perpendicular to the plane, and

\mu_\mathrm{k}

is the coefficient of

kinetic friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...

. Koyré, pp. 84–86. Unless the inclined plane is in a

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...

, a (usually) small amount of

potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...

is also lost to

air drag In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding ...

References

Abstraction Physics education

See also

References