Friction

Introduction to Friction

Friction is a fundamental force that arises when two surfaces are in contact. It acts to oppose the relative motion or attempted motion between the surfaces. No surface is perfectly smooth, and microscopic irregularities cause frictional forces to exist.

• Frictional force always acts parallel to the surfaces in contact and opposes motion.

• Even surfaces that appear smooth have microscopic bumps and valleys that impede motion.

• The direction of the frictional force is always opposite to the direction of motion or attempted motion.

Types of Friction

• Kinetic (Sliding) Friction: Occurs when there is actual motion between two objects. It always acts to oppose the direction of motion.

• Static Friction: Occurs when an object is at rest. It prevents the object from starting to move. To initiate motion, the applied force must overcome static friction.

Key Point: Static friction can vary from zero up to a maximum value, depending on the applied force. Once motion begins, kinetic friction takes over, which is usually less than the maximum static friction.

Mathematical Description of Friction

The force of friction is proportional to the normal force (the perpendicular force between the surfaces). The proportionality constant depends on the nature of the surfaces in contact.

• Kinetic Friction:

• Static Friction (maximum):

Where:

• = force of kinetic friction

• = force of static friction

• = coefficient of kinetic friction

• = coefficient of static friction

• = normal force

Important Note: The coefficient of static friction is always greater than the coefficient of kinetic friction ().

Coefficients of Friction: Typical Values

The coefficients of friction depend on the materials in contact. Below is a table summarizing typical values:

Additional info: Table values inferred and expanded for clarity.

Example: Object Pulled Across a Floor

An object is pulled along a horizontal surface by a force of 40.0 N applied at a 30.0° angle above the horizontal. The coefficient of kinetic friction is 0.30. Calculate the acceleration.

• Resolve the applied force into horizontal and vertical components:

• Horizontal:

• Vertical:

• Normal force:

• Kinetic friction:

• Net force:

• Acceleration:

Example Calculation:

• Given: , , , (assumed for calculation),

Additional info: Mass assumed for calculation; adjust as needed for specific problems.

Inclined Planes with Friction

When an object is placed on an inclined plane, friction acts parallel to the surface and opposes the motion down the slope. The normal force is reduced due to the angle of the incline.

• Normal force:

• Frictional force:

• Net force down the incline:

• Acceleration:

Example: A box slides down a 30° slope with . Find the acceleration.

• Plug in to find .

Circular Motion

Introduction to Circular Motion

Circular motion occurs when an object moves along a circular path. Unlike linear motion, the direction of velocity is constantly changing, even if the speed remains constant. This change in direction requires a net force directed toward the center of the circle.

• Centripetal force is the net force that causes circular motion, always directed toward the center of the circle.

• Velocity vectors are tangent to the circle at every point.

Centripetal Acceleration

Objects in uniform circular motion experience an acceleration toward the center of the circle, called centripetal acceleration ("center-seeking").

• The magnitude of centripetal acceleration is given by:

• Where is the speed of the object and is the radius of the circle.

• This acceleration is always perpendicular to the velocity vector and points toward the center of the circle.

Centripetal Force

The net force required to keep an object moving in a circle is called the centripetal force. It is not a new force, but the name given to the net force causing circular motion.

• The magnitude of the centripetal force is:

• Where is the mass of the object.

• Examples include tension in a string, gravitational force, or friction, depending on the context.

Example: Car on a Circular Track

A car of mass 1000 kg moves at 20 m/s around a curve of radius 50 m. What is the required centripetal force?

Additional info: Example added for clarity and application.