Inclined plane
An inclined plane is a simple machine. It allows one to use less force to move an object.
Examples of inclined planes are ramps, sloping roads and hills, plows, chisels, hatchets, carpenter's planes, and wedges. The typical example of an inclined plane is a sloped surface; for example a roadway to bridge at a different height.
Another simple machine based on the inclined plane is the blade, in which two inclined planes placed back to back allow the two parts of the cut object to move apart using less force than would be needed to pull them apart in opposite directions.
Calculation of forces acting on an object on an inclined planes
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
f = frictional force of the inclined plane
To calculate the forces on an object placed on an inclined plane, consider the three forces acting on it.
- The normal force (N) exerted on the body by the plane due to the attraction of gravity i.e. mg cos θ
- the force due to gravity (mg, acting vertically downwards) and
- the frictional force (f) acting parallel to the plane.
We can break the force from gravity into two vectors, one perpendicular to the plane and one parallel to the plane. Since there is no movement perpendicular to the plane, the component of the gravitational force in this direction (mg cos θ) must be equal and opposite to normal force exerted by the plane, N. Therefore, [math]\displaystyle{ N=mgcos\theta }[/math].
If the component of the force from gravity parallel to the surface (mg sin θ) is greater than the static frictional force fs – then the body will slide down the inclined plane with acceleration (g sin θ − fk/m), where fk is the force of friction – otherwise it will remain stationary.
When the angle of the slope (θ) is zero, sin θ is also zero, so the body will not move.
Inclined Plane Media
Wheelchair ramp, Hotel Montescot, Chartres, France
Demonstration inclined plane used in education, Museo Galileo, Florence.
Diagram, known as the Epitaph of Stevinus, by Flemish engineer Simon Stevin in 1586 to illustrate his ingenious derivation of the mechanical advantage of an inclined plane using a string of beads. He proved that the mechanical advantage of the inclined plane (the ratio of the weight of the load to the force required to push it up the plane) was equal to the ratio of the length of the plane ("Run") to the
The inclined plane's geometry is based on a right triangle. The horizontal length is sometimes called Run, the vertical change in height Rise.
Instrumented inclined plane used for physics education, around 1900. The lefthand weight provides the load force Fw. The righthand weight provides the input force Fi pulling the roller up the plane.
Key: Fn = N = Normal force that is perpendicular to the plane, Fi = f = input force, Fw = mg = weight of the load, where m = mass, g = gravity
Layout of the cable drive system for the Liverpool Minard inclined plane.
