What is the inequality for friction?

F ≤ μR, where F is friction, R is normal reaction, μ is coefficient of friction.

F_MAX = μR, the maximum possible frictional force. When moving, F = F_MAX.

When is a surface smooth?

When μ = 0. No friction; ignore friction in the problem.

What is limiting equilibrium?

The object is on the point of moving. F = μR and the object is stationary but about to move.

When an object is stationary and the applied force is less than F_MAX, what is F?

F equals the applied force (or resultant of parallel forces), acting in the opposite direction to balance them.

When an object is moving, what is the friction?

F = μR, always. Direction is opposite to the direction of motion.

In which direction does friction act?

Parallel to the surface, opposite to the direction of motion or potential motion.

If applied force 40 N and F_MAX = 49 N, does the block move?

No. 40 < 49, so friction balances the applied force. F = 40 N, block stays at rest.

If applied force 60 N and F_MAX = 49 N, what happens?

Block accelerates. F = 49 N (opposing motion). Resultant = 60 - 49 = 11 N in direction of applied force.

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Coefficient of Friction

Summary

Friction is a force that resists motion between a surface and an object. The magnitude satisfies F ≤ μR, where μ is the coefficient of friction and R is the normal reaction. The maximum friction is F_MAX = μR. When stationary, friction balances other forces up to F_MAX; when moving, friction always equals μR opposing motion.

1. What is Friction?

Friction is a force between a surface and an object that resists motion across the surface.

On a horizontal surface with only gravity and normal reaction, there is no friction
When an additional force acts parallel to the surface, friction appears in the opposite direction
Friction always acts parallel to the surface
Friction opposes the resultant force that would cause motion
Up to a limiting value, friction prevents motion entirely
Beyond that limit, friction has constant magnitude opposing motion

2. Coefficient of Friction

The magnitude of friction satisfies:

$F \leq \mu R$

Where:

(F) = force of friction (N)
(R) = normal reaction force (N)
(\mu) = coefficient of friction (dimensionless)
Smooth surface: (\mu = 0) (no friction)
Rough surface: (\mu > 0)

The maximum possible friction: $F_{MAX} = \mu R$

3. Stationary Object – When F ≤ F_MAX

4. Stationary Object – When Resultant > F_MAX

If the object is stationary but the resultant of other parallel forces exceeds F_MAX:

The object begins to accelerate in the direction of the resultant
Friction = (F_{MAX}) = (\mu R), acting opposite to the motion

5. Moving Object

6. Force Diagram with Friction

7. Worked Example

8. Key Vocabulary

Coefficient of Friction

Q: If applied force 40 N and F_MAX = 49 N, does the block move?

No. 40 < 49, so friction balances the applied force. F = 40 N, block stays at rest.

Q: If applied force 60 N and F_MAX = 49 N, what happens?

Block accelerates. F = 49 N (opposing motion). Resultant = 60 - 49 = 11 N in direction of applied force.

Summary

1. What is Friction?

Friction is a force between a surface and an object that resists motion across the surface.

On a horizontal surface with only gravity and normal reaction, there is no friction
When an additional force acts parallel to the surface, friction appears in the opposite direction
Friction always acts parallel to the surface
Friction opposes the resultant force that would cause motion
Up to a limiting value, friction prevents motion entirely
Beyond that limit, friction has constant magnitude opposing motion

2. Coefficient of Friction

The magnitude of friction satisfies:

$F \leq \mu R$

Where:

(F) = force of friction (N)
(R) = normal reaction force (N)
(\mu) = coefficient of friction (dimensionless)
Smooth surface: (\mu = 0) (no friction)
Rough surface: (\mu > 0)

The maximum possible friction: $F_{MAX} = \mu R$

3. Stationary Object – When F ≤ F_MAX

If the object is stationary and the resultant of other parallel forces is ≤ F_MAX:

The object remains stationary
Friction exactly balances the other horizontal/parallel forces
(F) = resultant of other forces (equal and opposite)
If resultant = F_MAX, the object is in limiting equilibrium (on the point of moving)

4. Stationary Object – When Resultant > F_MAX

If the object is stationary but the resultant of other parallel forces exceeds F_MAX:

The object begins to accelerate in the direction of the resultant
Friction = (F_{MAX}) = (\mu R), acting opposite to the motion

5. Moving Object

When the object is in motion parallel to the surface:

Friction always equals (F_{MAX} = \mu R)
Direction is always opposite to the motion
This holds regardless of other forces

6. Force Diagram with Friction

Block on rough horizontal surface: (P) applied right, friction (F) left. If (P \leq \mu R), block stays at rest with (F = P). If (P > \mu R), block accelerates with (F = \mu R).

7. Worked Example

Box: mass 12 kg, μ = 0.7, horizontal force 80 N.

(R = mg = 12 \times 9.8 = 117.6) N

(F_{MAX} = \mu R = 0.7 \times 117.6 = 82.32) N

80 N < 82.32 N → friction balances the applied force. (F = 80) N (opposite to applied). Box does not move.

8. Key Vocabulary

Smooth: μ = 0, ignore friction
Rough: μ > 0, include friction
On the point of moving: Limiting equilibrium, (F = \mu R)