Static Friction — Revision Notes

⚡ 30-Second Revision

Definition: — Force opposing *tendency* of relative motion.
Nature: — Self-adjusting, $0 le f_s le f_{s,max}$.
Limiting Static Friction: — $f_{s,max} = mu_s N$.
Coefficient of Static Friction: — $mu_s = \frac{f_{s,max}}{N}$ (dimensionless, depends on surfaces).
Angle of Friction ($phi_s$): — $an phi_s = mu_s$.
Angle of Repose ($ heta_r$): — $an \theta_r = mu_s$ (max incline angle for no slide).
Direction: — Parallel to surfaces, opposite to impending motion.
Key Principle: — Object moves if applied force $>$ $f_{s,max}$.

2-Minute Revision

Static friction is the resistive force that prevents two surfaces from sliding relative to each other when an external force tries to initiate such motion. It's a 'self-adjusting' force, meaning its magnitude varies to exactly oppose the applied force, up to a certain maximum limit.

This maximum value is called limiting static friction, $f_{s,max}$, and is given by the formula $f_{s,max} = mu_s N$, where $mu_s$ is the coefficient of static friction and $N$ is the normal force. If the applied force is less than or equal to $f_{s,max}$, the object remains at rest, and the static friction force equals the applied force.

If the applied force exceeds $f_{s,max}$, the object begins to move, and kinetic friction takes over. The coefficient $mu_s$ depends only on the nature of the surfaces in contact. Important related concepts include the angle of friction and the angle of repose, both of which have a tangent equal to $mu_s$.

Remember, static friction opposes the *tendency* of relative motion, not always the overall motion of the object.

5-Minute Revision

Static friction is a crucial contact force that arises when two surfaces are in contact and there's an attempt to cause relative motion, but no actual sliding occurs. Its defining characteristic is its 'self-adjusting' nature: it will exert a force exactly equal and opposite to the applied external force, preventing motion, as long as the applied force does not exceed a critical threshold. This threshold is known as the limiting static friction, denoted as $f_{s,max}$.

The formula for limiting static friction is $f_{s,max} = mu_s N$, where $mu_s$ is the coefficient of static friction and $N$ is the normal force pressing the surfaces together. $mu_s$ is a dimensionless constant specific to the pair of surfaces.

If the applied force $F_{app}$ is less than or equal to $f_{s,max}$, the object remains stationary, and the static friction force $f_s$ is equal to $F_{app}$. If $F_{app}$ exceeds $f_{s,max}$, the object begins to slide, and the friction transitions to kinetic friction.

Two important concepts related to $mu_s$ are the angle of friction ($phi_s$) and the angle of repose ($heta_r$). The angle of friction is the angle the resultant contact force makes with the normal force when motion is impending, and $an phi_s = mu_s$. The angle of repose is the maximum angle of inclination of a plane at which an object placed on it will just begin to slide down, and similarly, $an \theta_r = mu_s$. These relationships are frequently tested.

Worked Example: A $2,\text{kg}$ block is on a horizontal surface with $mu_s = 0.4$. What is the minimum horizontal force required to move the block? (Take $g = 10,\text{m/s}^2$)

1
Normal Force: — $N = mg = 2,\text{kg} \times 10,\text{m/s}^2 = 20,\text{N}$.
2
Limiting Static Friction: — $f_{s,max} = mu_s N = 0.4 \times 20,\text{N} = 8,\text{N}$.
3
Minimum Force to Move: — The block will move if the applied force just exceeds $f_{s,max}$. So, the minimum force required is $8,\text{N}$.

Remember to always draw free-body diagrams, resolve forces carefully, and correctly identify the normal force, especially on inclined planes or when external forces have vertical components.

Prelims Revision Notes

Static friction ($f_s$) is a crucial force in NEET physics, acting to prevent relative motion between surfaces in contact. It is a self-adjusting force, meaning its magnitude varies from zero up to a maximum value, $f_{s,max}$, to exactly oppose the applied external force that tends to cause motion. The direction of static friction is always parallel to the surfaces and opposite to the *impending* (or threatened) relative motion.

The limiting static friction ($f_{s,max}$) is the maximum possible static friction that can be exerted before the object starts to slide. It is given by the formula: $f_{s,max} = mu_s N$, where $mu_s$ is the coefficient of static friction and $N$ is the normal force pressing the surfaces together.

$mu_s$ is a dimensionless constant that depends solely on the nature of the two surfaces in contact. A key point for NEET is that $mu_s$ is generally greater than the coefficient of kinetic friction ($mu_k$), implying it takes more force to start an object moving than to keep it moving.

For an object to remain at rest, the applied force $F_{app}$ must satisfy $F_{app} le f_{s,max}$. If $F_{app} > f_{s,max}$, the object will begin to move. When solving problems, always calculate $f_{s,max}$ first to determine if motion will occur.

Important Related Concepts:

Angle of Friction ($phi_s$): — This is the angle between the resultant contact force (normal force + friction force) and the normal force, when the object is on the verge of motion. The relationship is $an phi_s = mu_s$.
Angle of Repose ($ heta_r$): — For an object on an inclined plane, this is the maximum angle of inclination at which the object will just begin to slide down. The relationship is $an \theta_r = mu_s$. This means the angle of friction is numerically equal to the angle of repose.

Common Pitfalls to Avoid:

1
Assuming $f_s = mu_s N$ always. Remember, this is only the *maximum* value; $f_s$ can be any value from $0$ to $mu_s N$.
2
Incorrectly identifying the normal force $N$. It is not always equal to $mg$, especially on inclined planes or when external forces have vertical components.
3
Confusing the direction of friction. It opposes *relative* motion, not necessarily the overall motion of the body (e.g., static friction helps a car accelerate forward).

Mastering these concepts and practicing free-body diagrams for various scenarios (horizontal surfaces, inclined planes, blocks against walls, systems of blocks) is essential for scoring well on static friction questions in NEET.

Vyyuha Quick Recall

Static Friction Stays Still, Self-adjusting Strongly. Maximum is Mu-S Normal.