# Friction

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Friction, Angle of Repose, difference between sliding friction and rolling friction

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9/8/2009
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```							Friction
When a body moves over the surface of another body, a force acts between the surfaces of the two bodies, which opposes the motion of the moving body, this force opposing the motion is called friction. It is of different types. As soon as an external force is applied on a body, a force of friction starts acting between the surfaces of contact. If the magnitude of force is less than the frictional force, the body remains at rest. In that case the frictional force acting between the two bodies is called Static friction.

When on applying the external force, the body is just about to start its motion, then its state is called the state of limiting equilibrium and the force of friction acting during this period is called limiting friction. Now on increasing the external force, the magnitude of force will become greater than the frictional and the body starts moving on the surface, the force of friction acting during this period is called Kinetic friction.

Laws of friction:1) Friction acts in the direction opposite to the direction of motion of the body. 2) Friction depends upon the nature of two surfaces. 3) Friction does not depend upon shape or area of two surfaces. 4) Due to the weight of a body, a downward force W acts on the surface. According to the Newton’s 3rd law the surface exert an equal and opposite force in upward direction. This force is called the Normal Reaction force R.

Frictional force f

Normal Reaction force R

f = μ R, Here μ is the coefficient of friction.

Angle of Friction:The angle between the resultant of f and R and R is called the angle of friction

Angle of Repose:When a body is in limiting equilibrium on an inclined plane, the angle between the inclined plane and horizontal is called the angle of repose. Mass of the body = m Mgcosθ will act normal to the inclined plane Mgsinθ will act parallel to the inclined plane, in equilibrium

Mgsinθ = f Mgcosθ = R

f / R = Mgsinθ / Mgcosθ f / R = tanθ But μ = f / R Hence μ = tanθ Coefficient of friction = tangent of the angle of Repose Again μ = tanλ tanθ = tanλ Or θ=λ

Angle of friction = angle of repose Body sliding down an inclined plane:If the angle of repose is large then forces acting on the body will be 1) Mg = weight of the body in vertically downward direction. 2) Mgcosθ = normal to the inclined plane. 3) Mgsinθ = parallel to the inclined plane. 4) R = normal reaction force perpendicular to the inclined plane. 5) f = frictional force opposite to the direction of motion.

Thus the resultant force parallel to the inclined plane Mgsinθ - f = Ma

f = μR = Mgcosθ Mgsinθ – μMgcosθ = Ma Acceleration = a = gsinθ – μcosθg If frictional force = μ = 0 Then a = gsinθ

Body moving up on an inclined plane:If the angle of repose is large then forces acting on the body will be 1) Mg = weight of the body in vertically downward direction. 2) Mgcosθ = normal to the inclined plane. 3) Mgsinθ = parallel to the inclined plane. 4) R = normal reaction force perpendicular to the inclined plane. 5) f = frictional force opposite to the direction of motion.

Thus the resultant force parallel to the inclined plane Mgsinθ + f = Ma f = μR = Mgcosθ Mgsinθ + μMgcosθ = Ma Acceleration = a = gsinθ + μcosθg If frictional force = μ = 0 Then a = gsinθ

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