The Invisible Force | Friction | IIT-JEE | Class 10 | Class 12 | JEE Main | JEE Advanced | Anime

Описание: The chapter on Friction explores the tangential forces that arise between contacting surfaces to oppose relative motion or the tendency of such motion. It is a component of the contact force, which is the resultant of the friction force (acting along the surface) and the normal force (acting perpendicular to the surface).
The following sections provide a detailed explanation of the key concepts covered in this chapter:
1. Types of Friction
The sources categorise friction primarily into two types based on whether the objects are moving relative to each other:
• Static Friction (f
s
​
): This exists when there is a tendency for relative motion but the surfaces remain at rest relative to one another. It is a self-adjusting force, meaning it increases to exactly match the applied external force up to a certain limit.
• Limiting Friction (F
max
​
): This is the maximum value of static friction just before an object begins to slide. It is calculated using the formula f
s,max
​
=μ
s
​
N, where μ
s
​
is the coefficient of static friction and N is the normal reaction force.
• Kinetic Friction (f
k
​
): Once the limiting friction is exceeded, the object begins to slide, and kinetic friction takes over. Its value is generally constant and slightly lower than limiting friction, calculated as f
k
​
=μ
k
​
N.
2. Key Angles in Friction
• Angle of Friction: This is the angle between the normal force and the resultant contact force when motion is impending.
• Angle of Repose: The minimum angle of inclination for an inclined plane at which an object placed on it just begins to slide down under its own weight. Mathematically, the tangent of this angle equals the coefficient of static friction (tanθ=μ
s
​
).
3. Pushing vs Pulling
A common application discussed is why pulling an object at an angle is easier than pushing it. When pushing, a component of the force acts downwards, increasing the normal force and thereby increasing the maximum possible friction. Conversely, pulling at an angle has an upward component that reduces the normal force and the friction, making it easier to move the object.
4. Block-over-Block Systems
These problems involve two or more blocks stacked on each other, often with friction between them and sometimes with the ground.
• Moving Together: If the applied force is small enough, both blocks move with a common acceleration. This occurs as long as the friction required to keep the blocks together is less than the limiting friction at their interface.
• Slipping: If the external force exceeds a certain maximum value (F
max
​
), the friction can no longer hold them together, and the blocks begin to slide relative to each other with different accelerations.
5. Uniform Pure Rolling
Pure rolling is a specific type of motion where a body rolls without slipping. The primary condition is that the velocity of the point of contact must be zero relative to the surface.
• Condition: This is satisfied when the linear velocity (v) and angular velocity (ω) relate as v=Rω.
• Friction's Role: In uniform pure rolling, static friction is present to prevent slipping, but it does no work because there is no relative displacement at the point of contact.
6. Mechanical Energy and Loss
Friction often results in a loss of mechanical energy, which is dissipated as heat. In kinetic friction, energy is lost because there is displacement against the frictional force. However, in pure rolling, energy loss is negligible because the static friction does not perform work.