5 Laws of Friction - Class 11 Physics - Laws of motion

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Laws of Friction (With Explanation and Equations)

1. Direction of Friction

Statement:
The limiting force of friction always acts opposite to the direction in which a body moves or tends to move.

Explanation:
When a body is pushed in one direction, friction always acts in the opposite direction to oppose the relative motion between the two surfaces.

Equation:

\[ \vec{f}\ \text{is opposite to}\ \vec{v} \]

or

\[ \vec{f}=-f\hat{v} \]

  • \(\vec{f}\) = Frictional force
  • \(\vec{v}\) = Velocity or direction of impending motion
  • \(\hat{v}\) = Unit vector along the direction of motion

2. Friction Acts Tangentially

Statement:
The force of friction acts tangentially (parallel) to the surfaces in contact.

Explanation:
Normal reaction acts perpendicular to the surface, whereas friction acts along the surface.

Equation:

\[ \vec{f}\perp\vec{R} \]

  • \(\vec{f}\) = Frictional force (parallel to the surface)
  • \(\vec{R}\) = Normal reaction (perpendicular to the surface)

3. Limiting Friction is Directly Proportional to Normal Reaction

Statement:
The magnitude of the limiting force of friction is directly proportional to the normal reaction between the two surfaces.

Equation:

\[ f\propto R \]

Therefore,

\[ f=\mu R \]

  • f = Limiting force of friction
  • R = Normal reaction
  • \(\mu\) = Coefficient of friction

Explanation:
If the normal reaction doubles, the limiting friction also doubles, provided the coefficient of friction remains constant.

4. Limiting Friction is Independent of the Area of Contact

Statement:
The limiting force of friction is independent of the apparent area of contact as long as the normal reaction remains constant.

Equation:

\[ f=\mu R \]

Explanation:
Since the area of contact (A) does not appear in the equation, changing the contact area does not change the limiting friction if the normal reaction remains the same.

5. Limiting Friction Depends on the Nature of the Surfaces

Statement:
The limiting force of friction depends on the nature (roughness or smoothness) of the surfaces in contact.

Equation:

\[ f=\mu R \]

For two different surfaces,

\[ \mu_1>\mu_2 \]

Hence,

\[ f_1=\mu_1R>f_2=\mu_2R \]

Explanation:
Rough surfaces have a larger coefficient of friction and therefore produce greater friction than smooth surfaces under the same normal reaction.

Summary Formula

The fundamental equation of limiting friction is

\[ \boxed{f=\mu R} \]

  • f = Limiting force of friction
  • \(\mu\) = Coefficient of friction
  • R = Normal reaction

This equation explains that limiting friction is directly proportional to the normal reaction, independent of the apparent area of contact, and depends on the nature of the surfaces through the coefficient of friction.

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