Energy, Work, and Power Cheat Sheet

The core ideas of Energy, Work, and Power distilled into a single, scannable reference — perfect for review or quick lookup.

PiqCue — piqcue.com/energy-work-power/cheatsheet

Quick Reference

Work

The transfer of energy when a force acts on an object through a displacement. Calculated as = Fdcos heta$, where $ is the force magnitude, $ is the displacement, and $ heta$ is the angle between them. Work is measured in joules (J).

Kinetic Energy

The energy an object possesses due to its motion, given by = frac{1}{2}mv^2$. Since velocity is squared, doubling speed quadruples kinetic energy. Kinetic energy is always positive and is a scalar quantity.

Gravitational Potential Energy

Energy stored due to an objects position in a gravitational field, calculated as = mgh$ near Earths surface, where $ is the height above a chosen reference level. The choice of reference level is arbitrary because only changes in PE matter physically.

Conservation of Mechanical Energy

In a system with only conservative forces (gravity, springs), the total mechanical energy = KE + PE$ remains constant. Energy transforms between kinetic and potential forms but the sum never changes.

Work-Energy Theorem

The net work done on an object equals the change in its kinetic energy: {net} = Delta KE = frac{1}{2}mv_f^2 - frac{1}{2}mv_i^2$. This theorem connects the force-displacement perspective with the energy perspective of motion.

Power

The rate at which work is done or energy is transferred: = frac{W}{t}$. For an object moving at constant velocity under a force, = Fv$. Power is measured in watts (W), where 1 W = 1 J/s.

Elastic Potential Energy

Energy stored in a compressed or stretched spring, given by = frac{1}{2}kx^2$, where $ is the spring constant and $ is the displacement from equilibrium. This energy can be fully recovered as kinetic energy when the spring returns to its natural length.

Non-Conservative Forces and Dissipation

Forces like friction and air resistance that convert mechanical energy into thermal energy. When non-conservative forces act, total mechanical energy decreases: $Delta E_{mech} = W_{nc}$, where {nc}$ is negative work done by dissipative forces.

Key Terms at a Glance

Work (W):Energy transferred when force causes displacement: = Fdcos heta$. Measured in joules.

Kinetic Energy (KE):Energy of motion: = frac{1}{2}mv^2$. Scalar, always non-negative.

Gravitational Potential Energy:Energy from height in gravitational field: = mgh$ near Earth surface.

Elastic Potential Energy:Energy in deformed spring: = frac{1}{2}kx^2$.

Mechanical Energy:Sum of KE and PE: {mech} = KE + PE$. Conserved with only conservative forces.

Conservation of Energy:Total energy in isolated system remains constant. Energy transforms but is never created or destroyed.

Work-Energy Theorem:Net work equals change in KE: {net} = Delta KE$.

Power (P):Rate of energy transfer: = W/t$. Measured in watts. Also = Fv$.

Watt (W):SI unit of power: 1 W = 1 J/s.

Joule (J):SI unit of energy and work: 1 J = 1 N m.

Conservative Force:Force with path-independent work. Examples: gravity, spring, electrostatic.

Non-Conservative Force:Force with path-dependent work. Friction and air resistance dissipate mechanical energy.

Horsepower (hp):Power unit: 1 hp = 746 W.

Spring Constant (k):Stiffness measure in Hookes law: = -kx$. Units: N/m.

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