Advanced Dynamics: Resistive and Elastic Forces

Friction

A resistive force that arises from the interactions between two surfaces in contact, acting parallel to the surfaces and opposing relative motion.

Static Friction

Friction that acts when surfaces are not sliding relative to each other, matching the applied force to keep the object in equilibrium.

Kinetic Friction

Friction that acts when surfaces are sliding relative to each other, remaining relatively constant and usually weaker than static friction.

Coefficient of Friction

A unitless scalar that represents the ratio of the force of friction between two bodies and the normal force pressing them together.

Normal Force

The force exerted by a surface in a direction perpendicular to the surface.

Maximum Static Friction

The maximum force of static friction before an object begins to slide; represented as f{s,max} = bcs F_N.

Terminal Velocity

The constant velocity reached by an object when the drag force equals the gravitational force, resulting in zero net force.

Linear Drag

A type of drag force that is proportional to velocity, common for small objects at low speeds.

Quadratic Drag

A type of drag force that is proportional to the square of the velocity, common for larger objects moving quickly.

Hooke's Law

The principle stating that the force exerted by a spring is proportional to its displacement from the equilibrium position, expressed as bc{F}_s = -kbc{x}.

Spring Constant

A measure of a spring's stiffness, represented by k in Hooke's Law, with units of N/m.

Restoring Force

The force exerted by a spring that acts to return it to its equilibrium position.

Misconception: Normal Force

Assuming F_N = mg; the normal force can change based on surface angles and applied forces.

Misconception: Static Friction

Assuming static friction equals bcs FN; it is actually equal to the applied force up to its maximum value.

Misconception: Drag Acceleration

Thinking that acceleration remains constant for falling objects with drag; acceleration decreases as velocity increases.

Misconception: Hooke's Law Sign

Dropping the negative sign in bc{F} = -kbc{x}; the negative sign is essential for properly describing the force direction.

Inclined Plane

A flat surface tilted at an angle, where forces acting on an object can be resolved into components.

Newton's Second Law

The principle stating that the sum of the forces acting on an object equals the mass of that object times its acceleration.

Free Body Diagram

A graphic representation used to visualize the forces acting on an object, illustrating the direction and size of each force.

Friction Force Graph

A graph that illustrates the relationship between applied force and frictional force, showing a linear increase until the static limit is reached.

Equilibrium Position

The point at which the net force acting on an object is zero, resulting in no acceleration.

Plastic Deformation

A permanent deformation that occurs when a material is stretched beyond its elastic limit.

Velocity as a Function of Time

An expression showing how velocity changes over time, often derived using differential equations.

Asymptotic Behavior

A characteristic of a function as it approaches a limit, often used to describe how velocity approaches terminal velocity.

Dynamic Forces

Forces that change based on conditions like surface properties, velocity, and position, including friction, drag, and spring forces.

Gradient of Friction Force Graph

The slope in a friction force versus applied force graph represents how friction force changes with the applied force.