AP Physics 1 Unit 3 Notes: Understanding Energy Through Work and Potential

Translational kinetic energy

Energy an object has due to moving from place to place; for a particle or center of mass motion (ignoring rotation), depends only on mass and speed.

Kinetic energy formula (translation)

K = (1/2)mv^2, where m is mass (kg) and v is speed (m/s); K is in joules (J).

Speed vs. velocity (for kinetic energy)

Translational kinetic energy depends on speed only, not the direction of velocity; reversing direction at the same speed leaves K unchanged.

Quadratic dependence on speed

Because K ∝ v^2, doubling speed makes kinetic energy four times larger.

Joule (J)

SI unit of energy; 1 J = 1 N·m, highlighting the connection between force through distance (work) and energy.

Work (physics definition)

Energy transferred by a force acting through a displacement; for constant force and straight-line displacement, W = FΔr cosθ.

Dot product (in work)

Work uses the dot product: W = F · Δr, which selects the component of force along the displacement direction.

Angle θ in work

The angle between the force direction and the displacement direction in W = FΔr cosθ.

Scalar (work)

Work is a scalar quantity (not a vector); it can be positive, negative, or zero depending on the angle between force and displacement.

Parallel component of force (F∥)

The part of a force along the displacement direction: F∥ = F cosθ; only this component contributes to work.

Positive work

Occurs when 0° ≤ θ < 90° so the force has a component in the direction of displacement; increases kinetic energy (for net work).

Negative work

Occurs when 90° < θ ≤ 180° so the force component opposes displacement (e.g., kinetic friction); tends to decrease kinetic energy.

Zero work

Occurs when θ = 90° (force perpendicular to displacement) or when displacement is zero; can change direction without changing speed (e.g., centripetal force case).

Net work (Wnet)

The sum of the works done by all forces: Wnet = ΣWi; this (not just one force’s work) determines the change in kinetic energy.

Work–energy theorem

Wnet = ΔK = Kf − Ki; net work on an object equals the change in its translational kinetic energy.

Force vs. position graph (work)

When force varies with position, the work done equals the area under the force–position (F vs x) curve.

Potential energy (U)

Energy stored in a system due to configuration/position of interacting objects; associated with conservative forces.

Conservative force

A force for which work depends only on initial and final positions (not the path); allows definition of a potential energy function U.

Work by a conservative force

Wcons = −ΔU; if a conservative force does positive work, the system’s potential energy decreases.

Gravitational potential energy near Earth (Ug)

Ug = mgh (for approximately constant g); depends on chosen reference height; only changes (ΔUg) are physically meaningful.

Change in gravitational potential energy

ΔUg = mgΔh; if an object moves downward, Δh is negative and Ug decreases.

Reference level for potential energy

The zero of gravitational potential energy is a choice (e.g., floor, tabletop); results are consistent as long as the reference is used consistently.

Spring (elastic) potential energy (Us)

Us = (1/2)kx^2 for an ideal Hooke’s-law spring; depends on displacement x from the spring’s natural length.

Mechanical energy (Emech)

Emech = K + U; if only conservative forces do work, K + U is conserved (Ki + Ui = Kf + Uf).

Nonconservative work (Wnc)

Work done by forces like friction/air resistance that change mechanical energy; energy accounting: Ki + Ui + Wnc = Kf + Uf (often Wnc is negative for friction).