Part 1 | Space, Time, and Motion

Equilibrium and Force Analysis

In classical mechanics, analyzing the forces acting on an object is essential for understanding its motion. When an object is at rest or moving with constant velocity, the net force acting on it is zero, indicating equilibrium.

• Newton's First Law: An object at rest or moving at constant velocity has zero net force ().

• Equilibrium Conditions:

  • Sum of forces in the x-direction:

  • Sum of forces in the y-direction:

• Free-Body Diagram: Shows all forces acting on an object, such as normal force (), applied force (), friction (), and weight ().

Example: A block on a surface with forces acting vertically and horizontally. If velocity is constant, and .

Part 15 | Static and Kinetic Friction

Factors Affecting Friction

Friction is a resistive force that opposes the relative motion between two surfaces in contact. It depends on certain physical properties but not on others.

• Affecting Factors:

  • Material/Surfaces: The nature of the surfaces in contact determines the coefficient of friction.

  • Normal Force (): The perpendicular force pressing the surfaces together.

• Not Affecting Factors:

  • Surface Area: The area of contact does not significantly affect friction for most macroscopic cases.

  • Speed: For dry friction, speed is not a major factor.

Friction Formula:

• Friction force is proportional to the normal force:

• General equation:

• is the coefficient of friction (static or kinetic )

Static vs. Kinetic Friction

Static friction prevents motion up to a maximum value, while kinetic friction acts during motion and is typically less than maximum static friction.

• Static Friction (): The force that must be overcome to start moving an object.

• Kinetic Friction (): The force opposing motion once the object is moving.

• Transition: When applied force exceeds maximum static friction, the object begins to move and kinetic friction takes over.

Example: Pushing a refrigerator with increasing force:

• At 50 N, 100 N, 150 N: Friction force matches applied force (static friction).

• At 200 N: Friction force is less than applied force, object accelerates (kinetic friction).

Graphical Representation of Friction

The relationship between applied force and friction force can be visualized:

• Static friction increases linearly with applied force up to a maximum.

• Once motion starts, kinetic friction remains approximately constant.

Microscopic Origin of Friction

Friction arises from microscopic interactions and roughness between surfaces. The direction of friction opposes the direction of motion or attempted motion.

• Contact Points: Microscopic peaks and valleys interlock, causing resistance.

• Direction: Always opposite to the direction of applied or attempted motion.

Coefficients of Friction: Table of Common Values

The coefficient of friction varies depending on the materials in contact. The following table summarizes typical values:

Additional info: Table values are approximate and may vary with conditions.

Problem Solving: Friction Applications

Friction problems often involve calculating the maximum static friction, determining if an object will move, and analyzing motion under kinetic friction.

• Maximum Static Friction:

• Kinetic Friction:

• Newton's Second Law:

Example: A dresser (45 kg) with and is pushed with 325 N. Calculate if it moves:

• Normal force: N

• Maximum static friction: N

• Since 325 N < 339.57 N, the dresser does not move.

Example: If the applied force exceeds , use kinetic friction to find acceleration:

• Net force:

• Acceleration:

Friction in Automotive Applications

Friction between tires and road determines acceleration and stopping distance.

• Static Friction: Prevents tires from slipping during acceleration.

• Kinetic Friction: Acts when tires skid during braking.

• Maximum Acceleration:

• Braking Acceleration:

Example: Car at rest, , m/s2:

• m/s2

Example: Car skidding to stop, :

• m/s2

Minimum Coefficient of Friction for Non-Slipping

To prevent sliding, the minimum coefficient of static friction must be sufficient to provide the required acceleration.

• Example: Crate in truck accelerating at m/s2:

Additional info: These principles are foundational for understanding friction in physics and engineering contexts.