Unit 3.6 – Friction (Static & Kinetic)

What is Friction?

• Key Idea: Friction arises due to irregularities at the microscopic level between two surfaces. Even smooth surfaces have tiny bumps and grooves that interlock, creating resistance to motion.

Types of Friction

1. Static Friction

• Definition: The force that prevents an object from starting to move when a force is applied.
• Behavior: Static friction adjusts itself to exactly balance the applied force until it reaches its maximum value.
• Formula:
  $${𝑓}_{\text{static}}\le {𝜇}_{𝑠}\cdot 𝑁$$
  Where:
  • ${𝑓}_{\text{static}}$ = Static frictional force.
  • ${𝜇}_{𝑠}$ = Coefficient of static friction (depends on the materials in contact).
  • $𝑁$ = Normal force (perpendicular contact force).
• Example:
  • Pushing a heavy box that doesn’t move initially. The static friction increases as you push harder, up to a point where it can no longer resist, and the box starts moving.

2. Kinetic Friction

• Definition: The force that opposes the motion of an object already in motion.
• Behavior: Kinetic friction remains constant regardless of the applied force (as long as the object is moving).
• Formula:
  $${𝑓}_{\text{kinetic}}={𝜇}_{𝑘}\cdot 𝑁$$
  Where:
  • ${𝑓}_{\text{kinetic}}$ = Kinetic frictional force.
  • ${𝜇}_{𝑘}$ = Coefficient of kinetic friction (usually smaller than ${𝜇}_{𝑠}$).
  • $𝑁$ = Normal force.
• Example:
  • Sliding a book across a table. Once the book is moving, kinetic friction slows it down until it comes to rest.

Comparison Between Static and Kinetic Friction

Factors Affecting Friction

1. Nature of Surfaces: Rougher surfaces produce more friction, while smoother surfaces produce less.
   • Example: Ice has low friction, while sandpaper has high friction.
2. Normal Force: Friction increases with the normal force (e.g., heavier objects experience more friction).
   • Example: Pushing a heavy box is harder than pushing a light one.
3. Area of Contact: Friction does not depend on the area of contact (for rigid bodies).
   • Example: A box slides with the same friction whether it’s lying flat or standing upright.
4. Lubrication: Adding lubricants (like oil or grease) reduces friction by filling gaps between surfaces.

Advantages and Disadvantages of Friction

Advantages:

1. Enables walking and running by providing grip.
2. Helps vehicles stop using brakes.
3. Allows us to write on paper with a pen or pencil.
4. Essential for holding objects (e.g., gripping a glass).

Disadvantages:

1. Causes wear and tear of machine parts.
2. Reduces efficiency by converting useful energy into heat.
3. Increases effort required to move objects.

Real-Life Examples of Friction

1. Walking:
   • Static friction between your shoes and the ground prevents slipping and allows you to walk.
2. Braking in Cars:
   • Kinetic friction between the brake pads and wheels slows down the car.
3. Sliding a Box:
   • You need to overcome static friction to start moving the box, and then kinetic friction slows it down as it slides.
4. Rubbing Hands Together:
   • Friction generates heat, which warms your hands.
5. Rolling vs. Sliding:
   • Rolling friction (e.g., wheels) is much smaller than sliding friction, which is why wheels are used to reduce effort.

Examples to Understand Friction

Example 1:

• Solution: Using the formula for static friction:
  $${𝑓}_{\text{static}}={𝜇}_{𝑠}\cdot 𝑁$$
  The normal force ($𝑁$) is equal to the weight of the box:
  $$𝑁=𝑚\cdot 𝑔=10\cdot 9.8=98\text{N}\mathrm{.}$$
  Substituting values:
  $${𝑓}_{\text{static}}=0.5\cdot 98=49\text{N}\mathrm{.}$$
  The minimum force required to start moving the box is $49\text{N}$.

Example 2:

• Solution: Using the formula for kinetic friction:
  $${𝑓}_{\text{kinetic}}={𝜇}_{𝑘}\cdot 𝑁$$
  Substituting values:
  $${𝑓}_{\text{kinetic}}=0.4\cdot 98=39.2\text{N}\mathrm{.}$$
  The force required to keep the box moving at a constant velocity is $39.2\text{N}$.