Friction Study Notes

LECTURE 05: FRICTION - B.F. Moshi 2025/2026

Introduction to Friction

• Whenever we attempt to slide one body over another, there exists a force that opposes this motion, known as friction.

Types of Friction

• Static Friction:
    - Definition: The friction that prevents the movement of an object at rest.

• Kinetic Friction:
    - Definition: The friction that acts on an object that is already moving.

Real-World Examples of Friction

1. Car Tires and Road: Friction between the tires of a car and the road surface.

2. Sneakers and Ground: Friction between the soles of sneakers and the ground.

3. Bicycle Brakes: Friction between the bicycle brakes and the wheels.

4. Train Wheels and Rails: Friction between the wheels of a train and the railway tracks.

Characteristics of Friction

• Friction is a force that stops or slows down movement.

• This force is a result of two surfaces rubbing against each other.

Types of Motion Associated with Friction

• Static Friction: Involves no motion.

• Sliding (Kinetic) Friction: Involves motion.

• Rolling Friction: Involves objects rolling over a surface.

Coefficient of Friction

• Definition: The coefficient of friction is a value representing the relationship between the force of friction between two objects and the normal force acting between those objects.

• Formula: $ext{Coefficient of Friction} <br>ightarrow rac{F_{friction}}{N}$

• In a practical context:
    - Static Friction Coefficient (μs) and Kinetic Friction Coefficient (μk).

Calculation of Friction Coefficient

• The coefficient of kinetic friction is calculated as the ratio of the force of friction to the normal force:

• $ext{Coefficient of Kinetic Friction: } ext{μ} = rac{F}{N}$

Portion of Lecture on Forces Involved in Friction

Sample Problem: Forces on a 6-kg Object

• Given:
    - Mass (m) = 6 kg
    - Frictional force (Ffrict) = 15 N

• Determine:
    - Gravitational force (Fgrav) = $F_{grav} = m imes g = 6 imes 9.8 = 58.8 ext{ N}$
    - Normal force (Fnorm) = 58.8 N (equal to gravitational force when vertical acceleration is zero)
    - Net force (Fnet) = 0 N (object moving at constant velocity)
    - Applied force (Fapp) = 15 N (matched to friction)

Application of Forces: Free Body Diagram of a Box

• Forces involved:
    - Applied force (F applied)
    - Static friction force
    - Normal force (Fnorm) and gravitational force (Fg)

Sliding vs Tipping Dynamics

Dynamics of Pushing a Box

1. When pushing starts, static friction counteracts the motion initially.

2. As the force increases:
      - Sliding: If the pushing force exceeds the maximum static friction force, the box begins to slip.
      - Tipping: If the force creates enough rotational movement, the box will tip over.

Conditions for Sliding and Tipping

• Condition to Slide: If the pushing force ($F_{push}$) exceeds the maximum static friction force ($F_{f(max)} = ext{μs} imes F_{norm}$), the box will slide.

• Condition to Tip: At rest, the normal force ($F_{norm}$) creates a point load that can cause tipping if sustained force creates an unmanageable couple with gravity.
    - Mathematical reference: rac{M_{push}}{f} > rac{Mg}{N}

Inclined Planes and Friction

Example Problem

• A 5 kg box is placed on a 42-degree incline with a 30 N frictional force acting against it. Calculate the sliding distance in 4 seconds.

• Steps to Solve:
    - Draw a free-body diagram to analyze forces along the plane.
    - Calculate gravitational force (down the ramp) & static or kinetic friction (up the ramp).
    - Apply Newton's second law: the sum of forces equals mass times acceleration.

Work & Energy Problem

• A block with initial speed of 1.0 m/s slides down a ramp: 5.8 m at an incline of 72 degrees in 1.1 seconds. Required: Calculate coefficient of friction, round to nearest hundredth.

Summary

• Understanding friction is crucial for dynamics, mechanical designs, and safety in vehicle operations. It is a pivotal concept in both theoretical and applied physics.