## Tuesday, December 8, 2015

### Motion of a body on a Rough Inclined Plane an Introduction

A body on a rough inclined plane tend to move downward by default when gravitational force is sufficient to move it downward.When the body is on inclined plane,its weight acts vertically downward and it is not normal to the surface of contact.

Let us consider a body of mass m is on a inclined plane of certain inclination with horizontal.Its weight can be resolved into components as horizontal and vertical components.If a perpendicular is drawn from the normal towards weight of the body,the angle between weight and this perpendicular is similar to angle of inclination and it is proved using simple geometry principles as shown the video presented below.

Hence the COS component of the weight acts normal to the surface and this part of weight of the body is the force applied by the lower surface of the upper body on the upper surface of the lower body.The reaction to this acts by the lower surface on the upper surface it is called normal reaction.

The SIN component of the weight acts along the direction of the inclined plane and it tries to pull the body down along the inclined plane.Automatically frictional force comes into action against this component of weight which is trying to move the body down the plane.

We know that static frictional force is self adjusting force and hence with the increase of angle of inclination,SIN component keeps increasing and static frictional force also keeps increasing.At a certain stage and at a particular angle of inclination,the static frictional force reaches its limiting and maximum value and it further remains constant.

The component of weight along the plane then dominates the body and body starts sliding down. This particular angle of inclination where it happens is called angle of repose and it depends on the roughness of the surface.

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