Calculation of forces acting on an object on an inclined plane

Key:
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. Air resistance may be neglected for most calculations, except at high speeds.

1. The normal force (N) exerted by the plane onto the body,
2. the force due to gravity (mg - acting vertically downwards) and
3. the frictional force (f) acting parallel to the plane.

We can decompose the gravitational force 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 (mgcosθ) must be equal and opposite to normal force exerted by the plane, N. If the remaining component of the gravitational force parallel to the surface (mgsinθ) is greater than the static frictional force f_s - then the body will slide down the inclined plane with acceleration (gsinθ - f_k/m), where f_k is the kinetic friction force - otherwise it will remain stationary.

When the slope angle (θ) is zero, sinθ is also zero so the body does not move.

External links

• An interactive simulation of Physics inclined plane