Momentum, Work, Energy, and Conservation Laws

Comprehensive vocabulary flashcards covering momentum, collisions, impulse, work, power, kinetic and potential energy, the work-energy theorem, conservation laws, symmetries, and simple machines.

Momentum

A vector quantity defined as the product of the mass of an object and its velocity ($p = mv$).

Law of Conservation of Momentum

The principle stating that in the absence of an external force, the total momentum of a system remains unchanged.

Elastic Collision

A collision in which colliding objects rebound without lasting deformation or generation of heat, such that an incoming object of mass $m$ striking an identical stationary mass $m$ stops completely while the stationary object moves off with the incoming object's initial velocity.

Inelastic Collision

A collision in which colliding objects stick together or become deformed upon impact, moving together with a single shared velocity while conserving total system momentum.

Two-Dimensional Collision Momentum

The vector addition of individual initial momentum vectors to determine the combined net momentum of objects colliding when not moving in the same straight line.

Impulse

The product of a constant force acting on an object and the time interval over which it acts ($J = F \times \text{time interval}$), which produces an equal change in the object's momentum ($\Delta mv$).

Energy

A conserved property of a system that enables it to do work, observed when it is being transferred or transformed, functioning as nature's balance sheet.

Matter

The physical substance of the universe that occupies space, has mass, and can be seen, smelled, and felt.

Work

The product of the force exerted on an object and the distance through which the object is moved by that force ($W = F \times d$).

Joule ($\text{J}$)

The SI unit of work and energy, defined as one newton-meter ($1\,\text{J} = 1\,\text{N}\cdot\text{m} = 1\,\text{kg}\cdot\text{m}^2/\text{s}^2$), which is approximately the energy needed to lift a $0.1\,\text{kg}$ apple by $1\,\text{m}$.

Power

The measure of how fast work is done or energy is transferred, defined as work done divided by the time interval ($\text{Power} = \frac{\text{work done}}{\text{time interval}}$).

Watt ($\text{W}$)

The SI unit of power, named after James Watt, defined as one joule of work done per second ($1\,\text{W} = 1\,\text{J/s}$).

Horsepower ($\text{hp}$)

A non-SI unit of power roughly equal to one kilowatt ($1\,\text{horsepower} \approx 1\,\text{kW} = 1000\,\text{W}$).

Kilowatt-Hour ($\text{kW}\cdot\text{h}$)

A unit of energy used by power companies during utility meter readings that represents the total power consumed over a given billing period.

Mechanical Energy

The energy possessed by an object due to its position, motion, or both, consisting of potential energy and kinetic energy.

Potential Energy ($PE$)

Stored energy held in readiness with the potential for doing work, such as in a drawn bow or stretched slingshot rubber band.

Gravitational Potential Energy

The energy stored in an object due to its elevated position against gravity, calculated as mass times acceleration due to gravity times height ($PE = mgh$), equal to the work done lifting it.

Kinetic Energy ($KE$)

The energy of motion possessed by a moving object, equal to half its mass multiplied by the square of its speed ($KE = \frac{1}{2}mv^2$).

Work-Energy Theorem

The theorem stating that the net work done on an object equals its change in kinetic energy ($W = \Delta KE = \frac{1}{2}mv_{\text{after}}^2 - \frac{1}{2}mv_{\text{before}}^2$).

Stopping Distance Relation

The physical principle derived from $F_{\text{net}}d = \Delta KE$ stating that doubling the initial speed of a moving object quadruples ($4\times$) the work and distance required to bring it to a stop.

Law of Conservation of Energy

The fundamental law stating that energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

Pendulum Energy Conversion

The continuous transformation between gravitational potential energy at the highest points of a swing and kinetic energy at the lowest point, keeping the total mechanical energy constant.

Symmetry and Conservation Laws

The fundamental physics correspondence connecting continuous geometric symmetries directly to conservation laws: space translation yields linear momentum, time translation yields energy, and rotation yields angular momentum.

Momentum vs. Kinetic Energy Distinction

The distinction that momentum is a directional vector quantity ($p = mv$) that can cancel to zero, whereas kinetic energy is a non-directional scalar quantity ($KE = \frac{1}{2}mv^2$) dependent on velocity squared that cannot cancel out.

Machine

A device that multiplies force or changes the direction of a force, transforming or transferring energy without being able to create energy or multiply total work.

Principle of a Machine

The energy conservation condition for ideal machines stating that work input equals work output ($\text{Work}_{\text{input}} = \text{Work}_{\text{output}}$ or $(F \times d)_{\text{input}} = (F \times d)_{\text{output}}$).

Simple Machines

The six elementary mechanisms that multiply an applied force over a greater distance: the inclined plane, screw, wedge, wheel and axle, lever, and pulley.