# ⓘ 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 a ..

## ⓘ 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, carpenters 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.

## 1. Calculation of forces acting on an object on an inclined planes

To calculate the forces on an object placed on an inclined plane, consider the three forces acting on it.

• the force due to gravity mg, acting vertically downwards and
• The normal force N exerted on the body by the plane due to the attraction of gravity i.e. mg cos θ
• 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, N = m g c o s θ {\displaystyle N=mgcos\theta }.

If the component of the force from gravity parallel to the surface mg sin θ is greater than the static frictional force f s – then the body will slide down the inclined plane with acceleration g sin θ − f k / m, where f k 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.