Normal Force, Frictional Forces

Normal force

Normal force is a contact force that is normal/perpendicular to the contacting surface to prevent objects from moving through each other. It results from interactions of the electrons at the surfaces of the objects, according to the Pauli exclusion principle.

On a horizontal surface, the normal force on an object is not always equal to the weight of the object. Here is an illustration of the normal force in an elevator. Based on Newton's second law, we can write down $G-N=ma$, and find out the normal force can be larger or smaller than the weight in various cases.

A scale that measures weight does not measure gravity directly, but the normal force. Therefore, if you measure your weight not on a flat surface, the reading from the scale will be smaller than your actual weight.

Frictional forces

Friction is a force that resists the relative motion of surfaces. It always converts kinetic energy into thermal energy. There are many types of friction:

• Dry friction: oppose relative lateral motion of solid surfaces
  • Static: surfaces are non-moving relative to each other
  • Kinetic: surfaces are moving relative to each other
• Fluid friction: between layers of a viscous fluid
• Skin friction: between a fluid surface and a solid surface
• Internal friction: resist deformation of a solid material

Empirical laws for static friction:

• It prevents the would-be relative motion between the surfaces
• Its maximal value is proportional to normal force
• It is independent of the collective motion of the surfaces

Empirical laws for kinetic friction between non-adhesive surfaces:

• It opposes the relative motion between the surfaces
• It is proportional to the normal force.
• It is independent of the collective motion of the surfaces
• It is independent of the area of contact
• It dissipates energy as heat and sound

Most land vehicles depend on friction as traction to accelerate, decelerate, and turn.

Coefficients of friction

When we consider dry, non-adhesive friction (contacting surfaces are solid and not stuck to each other), Coulomb model is used:

$$f_s\leq \mu_s N$$ $$f_k=\mu_kN$$

where $f_s$ is the static friction, $f_k$ is the kinetic friction, $\mu_s$ is the coefficient of static friction, $\mu_k$ is the coefficient of kinetic friction, $N$ is the normal force on the object.