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Derive the expression for the acceleration of a body sliding down are rough inclined plane

Derive the expression for the acceleration of a body sliding down are rough inclined plane

Grade:11

1 Answers

RAHUL ROHILLA
askIITians Faculty 873 Points
3 years ago

A body on a rough inclined plane slides down with a certain acceleration when angle of inclination is greater than angle of repose. A body will be able to come down on a rough inclined plane only when SIN component of weight of the body is able todominatemaximum static frictional force.If the component of the weight of the body is less than limiting friction, then body remains in the state of rest and static frictional force self adjusts it self to the applied force.For the body to slide down along the rough inclined plane, the angle of inclination shall be a minimum value and thisparticularangle is called "angle of repose".
If the angle of inclination is more than angle of repose, the part of the weight is more than maximum frictional force and the body starts sliding down with anacceleration.It is because the body has a resultant force in the down ward direction.
To find theresultantforce, force along the direction of motion is treated as positive and force against the motion shall be treated asnegative.
The force along the motion is SIN component of weight and force against the motion is the maximum frictional force.Frictional force can be written as the product of coefficient of friction and normal reaction.Here normal reaction is the difference between COS component of the weight of the body.
Basing on this, we can write effectiveaccelerationof theaccelerationof the body sliding down on a rough inclined plane. If the surface is smooth,its coefficient of friction is zero and we can write the modified equation for theacceleration.

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