Chapter 5: Using Newton’s Laws – Friction, Uniform Circular Motion, and Drag Forces

Using Newton’s Laws With Friction

Introduction to Friction

Friction is a fundamental force that arises whenever two solid surfaces are in contact and move (or attempt to move) relative to each other. The microscopic origins of friction are complex and not yet fully understood, but it is essential in everyday phenomena and engineering applications.

• Friction is always present between contacting surfaces.

• It is a contact force caused by the roughness and interactions at the microscopic level.

• The frictional force vector always acts parallel to the surface of contact.

Kinetic Friction

Kinetic friction occurs when two surfaces slide past each other. The force of kinetic friction is given by:

• Formula: $F_k = \mu_k F_N$

• $F_N$ is the normal force (perpendicular to the surface).

• $\mu_k$ is the coefficient of kinetic friction, which depends on the materials in contact.

• This equation is a magnitude equation, not a vector equation, because $F_k$ and $F_N$ do not have the same direction.

Static Friction

Static friction acts when two surfaces are at rest relative to each other. It prevents motion up to a maximum value:

• Formula: $F_s \leq \mu_s F_N$

• $\mu_s$ is the coefficient of static friction.

• Static friction adjusts as needed to prevent slipping, up to its maximum value.

• It is generally easier to keep an object sliding (kinetic friction) than to start it moving (static friction).

Nature of Friction Forces

• Kinetic friction ($f_k$ or $F_k$) opposes the motion of a moving object.

• Static friction ($f_s$ or $F_s$) prevents the motion of an object.

• Friction always opposes relative motion.

• Frictional forces are parallel to the surface and perpendicular to the normal force.

• Microscopic models of friction include roughness, sticking, scraping, and lubrication.

• In general, $\mu_s > \mu_k$.

Coefficients of Friction

The coefficients of friction depend on the materials in contact. The following table summarizes typical values:

Surfaces	Coefficient of Static Friction, $\mu_s$	Coefficient of Kinetic Friction, $\mu_k$
Wood on wood	0.4	0.2
Ice on ice	0.1	0.03
Metal on metal (lubricated)	0.15	0.07
Steel on steel (unlubricated)	0.7	0.6
Rubber on dry concrete	1.0	0.8
Rubber on wet concrete	0.7	0.5
Rubber on other solid surfaces	1–4	1
Teflon® on Teflon in air	0.04	0.04
Steel on steel in air	0.04	0.04
Lubricated ball bearings	<0.01	<0.01
Synovial joints (human limbs)	0.01	0.01

Additional info: Table values are approximate and intended only as a guide.

Friction Force vs. Applied Force

The relationship between frictional force and applied force is illustrated in the following graph:

• For small applied forces, static friction increases to match the applied force, preventing motion.

• Once the applied force exceeds $\mu_s F_N$, the object begins to slide and kinetic friction takes over, remaining constant at $\mu_k F_N$.

• Key equations:

  • $0 \leq F_s \leq \mu_s F_N$

  • $F_k = \mu_k F_N$

  • $\mu_s \geq \mu_k$

Example: Holding a Box Against a Wall

If you press a box against a rough wall, you can prevent it from slipping down by applying a horizontal force. The normal force points out from the wall, and the frictional force points up, counteracting gravity.

• Application: The horizontal force increases the normal force, which increases the maximum possible frictional force.

• Diagram: Shows forces acting on the box: friction upward, normal force perpendicular to wall, gravity downward, and applied force horizontally.

Example: Sled and Frog

• Kinetic friction opposes the motion of a sled sliding on snow.

• Static friction prevents a frog from slipping down a slope, pointing uphill to oppose slipping.

Additional info: These examples illustrate the direction and role of frictional forces in everyday situations.