Unit 3 Notes: Energy Methods and Power in AP Physics 1

Energy (mechanics)

A property of a system that measures its ability to cause change (often motion or deformation); tracked to predict speeds, heights, and compressions.

System (energy methods)

The chosen collection of objects/interactions used for energy accounting; determines what counts as internal energy changes vs. external work.

Configurations and interactions

The idea that energy is associated with the arrangement of objects and their forces (e.g., Earth–object), not simply “stored in an object” alone.

Kinetic energy (K)

Energy of motion: K = (1/2)mv^2, where m is mass and v is speed.

Gravitational potential energy near Earth (Ug)

Energy due to height in a roughly constant gravitational field: Ug = mgh, where h is measured from a chosen zero level.

Spring (elastic) potential energy (Us)

Energy stored in an ideal spring due to stretch/compression: Us = (1/2)kx^2, where x is displacement from relaxed length.

Mechanical energy (Emech)

Sum of kinetic and tracked potential energies: Emech = K + Ug + Us.

Conservation of energy

Total energy of an isolated system cannot change; energy may be transferred or transformed but not created or destroyed.

Conservation of mechanical energy

K + U remains constant when only conservative forces do work within the system and there is no external work (Wext = 0).

Conservative force

A force for which work depends only on initial and final positions (not path) and for which a potential energy function can be defined (e.g., gravity, ideal spring).

Nonconservative force

A force (e.g., kinetic friction, air resistance, external push/pull) for which mechanical energy is generally not conserved; it transfers mechanical energy into other forms like thermal.

Work (W)

Energy transferred by a force acting through a displacement (the mechanism that moves energy into or out of a system).

Work–energy theorem

Net work changes kinetic energy: Wnet = ΔK.

General energy accounting equation

Ki + Ui + Wext = Kf + Uf, where Wext is work done on the system by external forces.

External work (Wext)

Work done on a system by forces from outside the system boundary (often friction, an applied push, or tension from an external agent).

Reference level for gravitational potential energy

The chosen “zero height” for h in Ug = mgh; consistency is required, and Ug can be positive, zero, or negative depending on that choice.

Kinetic friction force (fk)

A common model for kinetic friction magnitude: fk = μkN, where μk is the coefficient of kinetic friction and N is the normal force.

Work done by kinetic friction (Wf)

If friction is constant and opposes motion over distance d: Wf = −fk d (negative because it removes mechanical energy from the tracked forms).

Normal force on an incline (N)

For an object on a ramp at angle θ (no acceleration perpendicular to surface): N = mg cosθ.

Energy bar chart

A qualitative representation comparing amounts of K, Ug, Us (and sometimes thermal) at two moments to show energy transfers/transforms.

System schema / interaction diagram

A diagram identifying objects and interactions to decide which forces are internal (can be modeled with potential energy) versus external (modeled as work).

Average power (Pavg)

Rate of energy transfer over a time interval: Pavg = W/Δt.

Watt (W)

SI unit of power: 1 W = 1 joule per second (1 J/s).

Instantaneous power (force parallel to motion)

When the force component is along the velocity: P = Fv (more generally uses the component of force in the direction of motion).

Efficiency

Fraction of input power converted to useful output power: efficiency = Pout/Pin (multiply by 100% for percent).