In exploring the concepts of frictional forces and limiting equilibrium, this discussion aims to provide a thorough understanding of these essential mechanics topics, which are vital for students.

Understanding Frictional Forces

• Friction: A force that stops objects from moving easily against each other.
• Two Types:
  • Static Friction: Stops objects from starting to move.
  • Kinetic Friction: Slows down moving objects, usually less than static friction.
• Depends on: Surface types and the force pushing the surfaces together.

Image courtesy of Jackwestin

Coefficient of Friction (μ)

• What it is: A number showing how much friction surfaces produce.
• Formula: μ = Friction Force / Force pushing surfaces together.
• Key Point: Bigger μ means more friction.

Limiting Equilibrium

• The point where an object is about to move.
• Max Friction = μ times the force pushing surfaces together.

Example Problems

Problem 1: Calculating Limiting Friction

Question: Find the limiting friction for a 10 kg box on a surface, with a static friction coefficient of 0.5.

Solution:

• Normal Reaction (R): $R = \text{mass} \times \text{gravity} = 10 \text{ kg} \times 9.8 \text{ m/s}^2 = 98 \text{ N}$
• Limiting Friction (F): $F = \mu \times R = 0.5 \times 98 \text{ N} = 49 \text{ N}$
• Result: Limiting friction is $49 N$.
• Graph:

Problem 2: Limiting Equilibrium on an Incline

Question: Check if a 5 kg box on a 30° incline (static friction coefficient 0.3) is in limiting equilibrium.

Solution:

• Normal Reaction (R): $R = \text{mass} \times \text{gravity} \times \cos(\theta) = 5 \text{ kg} \times 9.8 \text{ m/s}^2 \times \cos(30°) \approx 42.43 \text{ N}$
• Parallel Force: $= \text{mass} \times \text{gravity} \times \sin(\theta) = 5 \text{ kg} \times 9.8 \text{ m/s}^2 \times \sin(30°) \approx 24.5 \text{ N}$
• Maximum Frictional Force (F): $F = \mu \times R = 0.3 \times 42.43 \text{ N} \approx 12.73 \text{ N}$
• Check: Parallel Force $24.5 N$ > Max Friction $12.73 N$, so not in limiting equilibrium.
• Result: The box is not in limiting equilibrium.
• Graph: