Power Study Pack

Kibin's free study pack on Power includes a 3-section study guide, 8 quiz questions, 10 flashcards, and 1 open-ended Explain review question. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.

Last updated May 21, 2026

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Power Study Guide

Master the physics of power, work, and energy with this study pack covering core equations like P = W/t, P = Fv, and the work-energy theorem. Review unit conversions between watts, kilowatts, and horsepower, plus gravitational and elastic potential energy. Ideal for students tackling problems involving force, velocity, displacement, and conservation of mechanical energy.

Key Takeaways

  • •Power measures how quickly work is done or energy is transferred, defined as P = W/t, where W is work in joules and t is time in seconds.
  • •The SI unit of power is the watt (W), equal to one joule per second; the kilowatt (kW) and horsepower (hp) are common practical units, with 1 hp ≈ 746 W.
  • •Because work equals force times displacement, power can be rewritten as P = Fv, where F is the applied force and v is the velocity of the object — useful when speed rather than time is the known quantity.
  • •Work is the product of force and displacement in the direction of the force: W = Fd cosθ, where θ is the angle between the force vector and the displacement vector.
  • •The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv₀².
  • •Potential energy — gravitational (mgh) and elastic (½kx²) — stores energy that can later be converted into kinetic energy, and the total mechanical energy of a system is conserved when only conservative forces act.
  • •Energy is always conserved across a closed system; apparent energy losses represent conversion into thermal energy or other non-mechanical forms, not true destruction of energy.

Work: The Foundation of Mechanical Energy Transfer

Before power can be understood, work must be defined precisely, because power is simply the rate at which work is accomplished.

Physics Definition of Work vs. Everyday Usage

  • •In physics, work occurs only when a force causes displacement; pushing against an immovable wall does no work in the physics sense, regardless of effort.
  • •Work is a scalar quantity measured in joules (J), where 1 J = 1 N·m.

Mathematical Expression for Work

  • •The formula W = Fd cosθ captures the role of direction: only the component of force parallel to the displacement does work.
  • •When force and displacement are in the same direction (θ = 0°), cosθ = 1 and all the force contributes to work; when they are perpendicular (θ = 90°), cosθ = 0 and no work is done.
  • •Negative work occurs when the force component opposes the direction of motion (θ between 90° and 180°), such as friction slowing a sliding object.

Work Done by Multiple Forces

  • •If several forces act on an object, the net work equals the algebraic sum of the work done by each individual force.
  • •Net work is what determines changes in an object's motion, not the work of any single force in isolation.

Kinetic and Potential Energy

Energy is the capacity to do work, and it exists in mechanical systems in two fundamental forms: kinetic energy associated with motion and potential energy stored by virtue of position or configuration.

Kinetic Energy and the Work-Energy Theorem

  • •Kinetic energy (KE) is defined as KE = ½mv², where m is the object's mass in kilograms and v is its speed in meters per second.
  • •The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv_f² − ½mv_i².
  • •This theorem applies regardless of the path taken; only the initial and final speeds matter for calculating the change in kinetic energy.

Gravitational Potential Energy

  • •Gravitational potential energy (GPE) is stored energy due to an object's height above a reference level, calculated as GPE = mgh, where g ≈ 9.8 m/s² near Earth's surface.
  • •The reference level (h = 0) is chosen for convenience and does not affect calculated changes in gravitational potential energy.

Elastic Potential Energy

  • •Elastic potential energy is stored in deformed elastic materials — most commonly a compressed or stretched spring — and equals PE_elastic = ½kx², where k is the spring constant (N/m) and x is the displacement from equilibrium.
  • •Hooke's Law (F = −kx) describes the restoring force a spring exerts, and this linear relationship is what produces the ½kx² energy storage formula.

Conservation of Mechanical Energy

  • •When only conservative forces (gravity, spring forces) act on a system, total mechanical energy E = KE + PE remains constant.
  • •A roller coaster at the top of a hill trades gravitational PE for KE as it descends; friction and air resistance are non-conservative forces that convert mechanical energy into thermal energy, reducing total mechanical energy in the system.

About this Study Pack

Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.

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