Friction

Why it matters

Friction is a fundamental concept in engineering mechanics that affects the design and analysis of various structures and machines. Understanding friction is crucial for civil engineers to ensure stability and safety in structures like bridges, roads, and buildings.

Key ideas

• Frictional Force: The resistance force that acts opposite to the direction of motion or intended motion of a body.
• Types of Friction:
  • Static Friction: The frictional force that prevents relative motion between two bodies in contact. It acts when the bodies are at rest.
  • Kinetic (Dynamic) Friction: The frictional force acting between moving surfaces.
• Coefficient of Friction (μ): A dimensionless scalar value that represents the frictional properties of the contacting surfaces. It varies based on the materials and surface conditions.
• Laws of Friction:
  1. Limiting static friction and sliding friction are modeled as proportional to normal force; actual static friction adjusts up to its limit.
  2. Frictional force is independent of the apparent area of contact.
  3. Kinetic friction is usually less than static friction.

Formulas

• Static Friction Bound: |F_s| ≤ μ_s·N
  • F: Frictional force (N)
  • μ: Coefficient of friction (dimensionless)
  • N: Normal force (N)
• Maximum Static Friction: F_s = μ_s·N
  • F_s: Maximum static frictional force (N)
  • μ_s: Coefficient of static friction (dimensionless)
• Kinetic Friction: F_k = μ_k·N
  • F_k: Kinetic frictional force (N)
  • μ_k: Coefficient of kinetic friction (dimensionless)

Worked example

Problem: A block weighing 100 N is placed on a horizontal surface. The coefficient of static friction between the block and the surface is 0.4. Determine the minimum horizontal force required to start moving the block.

Given:

• Weight of the block, W = 100 N
• Coefficient of static friction, μ_s = 0.4

Solution:

1. Calculate the normal force (N). Since the block is on a horizontal surface, N = W = 100 N.
2. Use the formula for maximum static friction: F_s = μ_s·N
3. Substitute the given values: F_s = 0.4 × 100 N
4. Calculate: F_s = 40 N

Answer: The minimum horizontal force required to start moving the block is 40 N.

Common mistakes

• Confusing static and kinetic friction coefficients.
• Ignoring the direction of frictional force, which opposes relative slip or its tendency at the contact.
• Miscalculating the normal force, especially on inclined planes.

For GATE CE

Questions on friction often involve calculating the frictional force, determining the coefficient of friction, or analyzing motion on inclined planes. Practice problems involving both static and kinetic friction, and ensure a clear understanding of the laws of friction.

Quick check

1. What is the unit of the coefficient of friction?
2. How does the frictional force change with an increase in normal force?
3. Which is generally larger: static friction or kinetic friction?

Answers: 1. Dimensionless, 2. The limiting value increases; actual static friction need not increase, 3. Maximum static friction is usually greater than kinetic friction for the same normal load.