Time taken to Slide Down on Rough Inclined Plane against Friction

A body on rough inclined plane takes some time to reach the bottom of a rough inclined plane and it depends on length of inclined plane,angle of inclination and coefficient of friction.We know that, when the body is on a inclined plane,weight does not act in the perpendicular direction of the inclined plane.It is just because,weight always towards the center of the earth due to gravitational force. But inclined plane is making some angle with vertical.So to know the part of weight acting along the plane and part of the weight perpendicular to the plane, we shall divide the weight into components using vector resolution.

Once we resolve weight into components, we can understand that SIN component of weight acts along the direction of the plane and it tries pull the body in downward direction.The body can move only when this component of weight is more than limiting frictional force.For this thing to happen, we can increase the angle of inclination and a particular angle of inclination, frictional force is dominated and body starts sliding down.

Let us start a body of mass M from the top of the inclined plane and let it is started from the state of rest.It means its initial velocity is zero.As the part of weight is pulling it down against friction, body starts sliding down. As it is shown in the previous post, we can find Acceleration of a body sliding down on a rough inclined plane.

Now we know acceleration of the body,initial velocity,distance travelled by the body is noting but length of inclined plane.By substituting all this values in the equation of motion as shown below in the video, we can calculate, time taken by the body to come down along the inclined plane.

If the surface is smooth, we can equate coefficient of friction to zero and measure the time taken by the body to slide down on the smooth inclined plane.