CBSE Class 11 Physics Friction Notes

FRICTION

Friction - The property by virtue of which the relative motion between two surfaces in contact is opposed is known as friction.

Frictional Forces - Tangential forces developed between the two surfaces in contact, so as to oppose their relative motion are known as frictional forces or commonly friction.

Types of Frictional Forces - Frictional forces are of three types :-

1. Static frictional force

2. Kinetic frictional force

3. Rolling frictional force

Static Frictional Force - Frictional force acting between the two surfaces in contact which are relatively at rest, so as to oppose their relative motion, when they tend to move relatively under the effect of any external force is known as static frictional force. Static frictional force is a self adjusting force and its value lies between its minimum value up to its maximum value.

Minimum value of static frictional force - Minimum value of static frictional force is zero in the condition when the bodies are relatively at rest and no external force is acting to move them relatively.

f_s(min) = 0

Maximum value of static frictional force - Maximum value of static frictional force is μsN (where μs is the coefficient of static friction for the given pair of surface and N is the normal reaction acting between the two surfaces in contact) in the condition when the bodies are just about to move relatively under the effect of external applied force.

 f_s(max) = μ_sN

 Therefore, f_s(min) ≤ fs ≤ f_s(max)

  or, 0 ≤ fs ≤ μ_sN

Kinetic Frictional Force - Frictional force acting between the two surfaces in contact which are moving relatively, so as to oppose their relative motion, is known as kinetic frictional force. It’s magnitude is almost constant and is equal to μ_kN where μ_k is the coefficient of kinetic friction for the given pair of surface and N is the normal reaction acting between the two surfaces in contact. It is always less than maximum value of static frictional force.

f_k = μ_kN

Since, f_k < f_s(max) = μ_sN

Therefore, μ_kN < μ_sN

or, μ_k < μ_s

Limiting Frictional Force – The maximum value of static frictional force is the maximum frictional force which can act between the two surfaces in contact and hence it is also known as limiting frictional force.

Laws of Limiting Frictional Force –

1. Static friction depends upon the nature of the surfaces in contact.

2. It comes into action only when any external force is applied to move the two bodies relatively, with their surfaces in contact.

3. Static friction opposes the impending motion.

4. It is a self adjusting force.

5. The limiting frictional force is independent of the area of contact between the two surfaces.

Cause of Friction

Old View - The surfaces which appear to be smooth as seen through our naked eyes are actually rough at the microscopic level. During contact, the projections of one surface penetrate into the depressions of other and vice versa. Due to which the two surfaces in contact form a saw tooth joint opposing their relative motion. When external force is applied so as to move them relatively this joint opposes their relative motion. As we go on increasing the external applied force the opposition of saw tooth joint also goes on increasing up to the maximum value known as limiting frictional force (μ_sN) after which the joint suddenly breaks and the surfaces start moving relatively. After this the opposition offered by the saw tooth joint slightly decreases and comes to rest at almost constant value (μ_kN)

Modern View – According to modern theory the cause of friction is the atomic and molecular forces of attraction between the two surfaces at their actual point of contact. When any body comes in contact with any other body then due to their roughness at the microscopic level they come in actual contact at several points. At these points the atoms and molecules come very close to each other and intermolecular force of attraction start acting between them which opposes their relative motion.

Contact Force - The forces acting between the two bodies due to the mutual contact of their surfaces are known as contact forces. The resultant of all the contact forces acting between the bodies is known as resultant contact force. Example

friction (f) and normal reaction (N) are contact forces and their resultant (Fc) is the resultant is the resultant contact force.

Fc = √ f² + N²

Since maximum value of frictional force is Limiting frictional force (μsN) Therefore maximum value of contact force is

Angle of Friction – The angle between the resultant contact force (of normal reaction and friction) and the normal reaction is known as the angle of friction.

Angle of Repose – The angle of the inclined plane at which a body placed on it just begins to slide is known as angle of repose. 

Perpendicular to the plane
N = mgCosθ (since body is at rest)

Parallel to the plane when body is at rest mgSinθ θ
mgSinθ = fs

When body is just about to slide

mgSinθ = f_s(max) = μ_sN = μ_smgCosθ
or, Tanθ = μs
or, θ = Tan^-1μs

Note - Angle of repose is equal to the maximum value of angle of friction

Rolling Frictional Force - Frictional force which opposes the rolling of bodies (like cylinder, sphere, ring etc.) over any surface is called rolling frictional force. Rolling frictional force acting between any rolling body and the surface is almost constant and is given by μrN. Where μr is coefficient of rolling friction and N is the normal reaction between the rolling body and the surface.

f_r = μ_rN
Note – Rolling frictional force is much smaller than maximum value of static and
kinetic frictional force.
f_r << f_k < f_s(max)
or, μ_rN << μ_kN < μ_sN
or, μ_r << μ_k < μ_s

Cause of Rolling Friction – When any body rolls over any surface it causes a little depression and a small hump is created just ahead of it. The hump offers resistance to the motion of the rolling body, this resistance is rolling frictional force. Due to this reason only, hard surfaces like cemented floor offers less resistance as compared to soft sandy floor because hump created on a hard floor is much smaller as compared to the soft floor.

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