Power Study Pack
Kibin's free study pack on Power includes a 5-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. 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 27, 2026
Power Study Guide
Master the core equations of power — P = W/t and P = Fv — alongside watts, kilowatts, and kilowatt-hours, plus efficiency and the work-energy theorem. Ideal if you need to analyze engines, motors, or real-world energy transfer in college physics.
Key Takeaways
- •Power is the rate at which work is done or energy is transferred, defined mathematically 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; kilowatts (kW) and megawatts (MW) are common multiples used in practical applications.
- •Because work equals force times displacement, power can also be expressed as P = Fv, where F is the applied force and v is the velocity of the object, making this form useful for analyzing engines and motors.
- •Work is done on an object only when a force causes displacement in the direction of that force; the work-energy theorem states that the net work done on an object equals its change in kinetic energy.
- •Potential energy (gravitational and elastic) and kinetic energy are the two primary mechanical energy forms; in a closed system with no non-conservative forces, total mechanical energy is conserved.
- •Efficiency describes what fraction of input power actually performs useful work; real machines always have efficiency less than 100% because some energy is lost to friction and heat.
- •The kilowatt-hour (kWh), a unit of energy rather than power, equals 3.6 × 10⁶ joules and is the standard unit on household electricity bills.
Work: The Foundation of Power
Before power can be understood, work must be defined precisely — in physics, work has a specific meaning tied to force, displacement, and direction that differs from everyday usage.
Physics Definition of Work
- •Work (W) is calculated as W = Fd cosθ, where F is the magnitude of the applied force, d is the displacement of the object, and θ is the angle between the force vector and the displacement vector.
- •When force and displacement are perfectly parallel (θ = 0°), the full force contributes to work; when they are perpendicular (θ = 90°), such as a person carrying a box horizontally while the weight acts downward, no work is done on the box by gravity.
- •The SI unit of work is the joule (J), defined as 1 newton of force acting over 1 meter of displacement.
Work-Energy Theorem
- •The net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv₀².
- •This relationship means that any net force causing displacement will accelerate or decelerate an object in a measurable, calculable way.
- •Only net work — accounting for all forces acting simultaneously — determines the change in kinetic energy, not the work of any single force in isolation.
Mechanical Energy: Kinetic and Potential Forms
Mechanical energy encompasses two interconvertible forms — kinetic energy associated with motion, and potential energy stored by position or deformation — and their interplay governs how objects behave under forces.
Kinetic Energy
- •Kinetic energy (KE) is the energy an object possesses due to its motion, calculated as KE = ½mv², where m is mass in kilograms and v is speed in meters per second.
- •Kinetic energy scales with the square of velocity, meaning doubling an object's speed quadruples its kinetic energy.
Gravitational Potential Energy
- •Gravitational potential energy (GPE) is the energy stored in an object due to its height above a reference point, calculated as GPE = mgh, where g = 9.8 m/s² near Earth's surface and h is height in meters.
- •GPE is a relative quantity — its value depends on the chosen reference level, but changes in GPE are absolute and physically meaningful.
Elastic Potential Energy
- •Elastic potential energy is stored in compressed or stretched springs and elastic materials, calculated as PE_elastic = ½kx², where k is the spring constant in N/m and x is the displacement from equilibrium.
- •A larger spring constant k indicates a stiffer spring that stores more energy for the same displacement.
Conservation of Mechanical Energy
- •In a closed system free from non-conservative forces like friction, total mechanical energy (KE + PE) remains constant: energy converts between kinetic and potential forms but the sum does not change.
- •A roller coaster provides a clear example — at the top of a hill, GPE is maximum and KE is minimum; at the bottom, KE is maximum and GPE is minimum, with the total staying fixed.
Defining and Calculating Power
Power quantifies not just how much work is accomplished, but how quickly it is done — two scenarios can involve identical amounts of work yet differ dramatically in power if they occur over different time intervals.
Average Power Formula
- •Average power is defined as P = W/t, where W is the total work done in joules and t is the elapsed time in seconds.
- •A weightlifter who raises a 500 N barbell by 2 m in 1 second expends 1,000 W; the same lift performed in 2 seconds requires only 500 W — same work, half the power.
- •The SI unit of power is the watt (W), where 1 W = 1 J/s. Larger units include the kilowatt (1 kW = 1,000 W) and megawatt (1 MW = 10⁶ W).
Power as Force Times Velocity
- •Because work equals force times displacement, and displacement divided by time equals velocity, power can be rewritten as P = Fv when force and velocity are in the same direction.
- •This form is especially useful for analyzing vehicles and motors: a car engine producing a constant 4,000 N of traction force at 20 m/s delivers 80,000 W (80 kW) of power.
- •When force and velocity are not parallel, the formula becomes P = Fv cosθ, consistent with the angle-dependent definition of work.
The Horsepower Unit
- •The horsepower (hp) is a non-SI unit of power still used in engineering and automotive contexts; 1 hp ≈ 746 W.
- •James Watt introduced this unit in the 18th century to compare steam engine output to the work rate of draft horses, and it remains embedded in motor specifications today.
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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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A weightlifter raises a 500 N barbell by 2 meters in 1 second. What is the power output?
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Concept 1 of 5
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Work (Physics Definition)
Explain what 'work' means in physics. How is it different from the everyday use of the word, and what conditions must be met for work to actually be done on an object?
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