5.1 Friction

Friction

Friction is a force that opposes motion between surfaces in contact. It shows up everywhere: it's what lets you walk without slipping, what lets car tires grip the road, and what gradually wears down moving parts in machines. Understanding how friction works is essential for applying Newton's laws to realistic situations where surfaces interact.

There are three main types of friction: static, kinetic, and rolling. Each follows its own rules and equations. This guide covers how each type works, the key formulas, and how to solve problems involving friction.

Principles and Effects of Friction

Friction acts parallel to the contact surface and opposite to the direction of motion (or attempted motion). At a microscopic level, even "smooth" surfaces have tiny bumps and ridges. When two surfaces press together, these irregularities interact in two main ways:

• Adhesion: molecules on each surface form weak bonds with each other
• Abrasion: surface irregularities physically interlock, resisting sliding

These interactions convert kinetic energy into thermal energy (heat). That's why rubbing your hands together warms them up, and why bearings and gears in machines can overheat during extended use.

Friction is not always a nuisance. Without it, you couldn't walk, run, or drive. Your shoes need friction with the ground to push you forward, and tires need friction with the road to accelerate, brake, and turn. On the other hand, friction in engines and machines reduces efficiency and causes parts to wear out over time.

Types of Friction Compared

Static friction ($f_s$) acts on objects that are not yet moving relative to the surface. It matches the applied force up to a maximum value. For example, if you push gently on a heavy box and it doesn't budge, static friction is exactly canceling your push.

• The maximum static friction force is: $f_{s,\max} = \mu_s N$
  • $\mu_s$ = coefficient of static friction (depends on the two materials)
  • $N$ = normal force (the perpendicular contact force from the surface)
• Below this maximum, static friction adjusts to match the applied force: $f_s \leq \mu_s N$
• Examples: a book sitting on a tilted table without sliding, a person standing on a slope

Kinetic friction ($f_k$) acts on objects that are already sliding across a surface. Unlike static friction, kinetic friction has a fixed magnitude for a given situation.

• The kinetic friction force is: $f_k = \mu_k N$
  • $\mu_k$ = coefficient of kinetic friction
• $\mu_k$ is almost always less than $\mu_s$ for the same pair of surfaces. That's why it takes more force to start pushing a box than to keep it sliding.
• Examples: a crate sliding across a floor, a skier gliding down a slope

Rolling friction ($f_r$) acts on objects that roll along a surface without slipping. It's caused by slight deformation of the object and/or surface at the contact point.

• Rolling friction is generally much smaller than static or kinetic friction, which is why wheels and ball bearings are so useful for reducing resistance.
• Examples: car tires on pavement, a bowling ball rolling down a lane

Problem-Solving with Friction Coefficients

Here's a step-by-step approach for friction problems:

1. Draw a free body diagram. Sketch the object and label every force: weight ($mg$), normal force ($N$), applied forces, and friction.

2. Identify the type of friction. Is the object stationary? Use static friction. Sliding? Use kinetic friction. Rolling? Use rolling friction.

3. Find the normal force ($N$). On a flat, horizontal surface with no vertical applied forces, $N = mg$. On an incline or with angled pushes/pulls, you'll need to calculate $N$ from the vertical force balance.

4. Calculate the friction force. Use the appropriate equation:

   • Static (maximum): $f_{s,\max} = \mu_s N$
   • Kinetic: $f_k = \mu_k N$

5. Apply Newton's second law along each axis:

   • If the object is at rest or moving at constant velocity: $\sum F = 0$
   • If the object is accelerating: $\sum F = ma$

6. Solve for the unknown. This might be the friction force, the acceleration, the minimum force needed to start motion, or the friction coefficient itself.

Analyzing Friction on Inclined Planes

Inclined plane problems deserve special attention because the normal force is not equal to the object's full weight.

For an object on a ramp tilted at angle $\theta$:

• The weight component along the incline (pulling the object downhill): $mg \sin\theta$
• The weight component perpendicular to the incline (pressing into the surface): $mg \cos\theta$
• The normal force balances the perpendicular component: $N = mg \cos\theta$

So the friction force on an incline becomes $f = \mu \cdot mg \cos\theta$. As the angle increases, the normal force decreases (less pressing into the surface), which means less friction available to prevent sliding. At the same time, the component pulling the object downhill increases. That's why steeper ramps are harder to stand on.