Work, Energy, and Power

Vocabulary practice flashcards covering definitions, formulas, units, principles, and energy transformations from the chapter on Work, Energy, and Power.

Work (in Physics)

Work is said to be done only when a force applied on a body produces displacement of the body in the direction of the force.

Work Done by a Constant Force at an Angle ($\theta$)

The product of the magnitude of the force, the magnitude of displacement, and the cosine of the angle between them: $W = F S \cos(\theta)$.

Positive Work

Work done when the displacement of the body is in the same direction as the applied force ($\theta = 0^\circ$, so $\cos(0^\circ) = 1$ and $W = F \times S$), such as the work done by gravity on a freely falling body.

Zero Work

The condition where the work done by a force is zero, occurring either when there is no displacement ($S = 0$) or when the displacement is perpendicular to the force ($\theta = 90^\circ$, so $\cos(90^\circ) = 0$), such as a body moving along a circular path under a centripetal force.

Negative Work

Work done when the displacement of the body is in a direction opposite to the force ($\theta = 180^\circ$, so $\cos(180^\circ) = -1$ and $W = -F \times S$), such as the work done by frictional force on a rolling ball.

Work Done by Gravity ($W = mgh$)

The work done equal to the product of the weight of a body ($F = mg$) and the vertical height ($h$) through which it is displaced, which is independent of whether the body moves vertically, along a slope, or on stairs.

Joule ($\text{J}$)

The S.I. unit of work, defined as the work done when a force of $1\,\text{N}$ displaces a body through a distance of $1\,\text{m}$ in its own direction ($1\,\text{J} = 10^7\,\text{erg}$).

Erg

The C.G.S. unit of work, defined as the work done when a force of $1\,\text{dyne}$ displaces a body through a distance of $1\,\text{cm}$ in its own direction.

Power

The rate of doing work, or the work done per unit time, given by $P = \frac{W}{t}$ or $P = F \times v$, where $v$ is the average speed.

Watt ($\text{W}$)

The S.I. unit of power, defined as the power spent when $1\,\text{joule}$ of work is done in $1\,\text{second}$ ($1\,\text{W} = 1\,\text{J}\,\text{s}^{-1}$).

Horse Power ($\text{H.P.}$)

A practical unit of power widely used in mechanical engineering, related to the watt by the relation $1\,\text{H.P.} = 746\,\text{W} = 0.746\,\text{kW}$.

Watt Hour ($\text{Wh}$)

The energy spent or work done by a source of power $1\,\text{W}$ in $1\,\text{h}$, equal to $3600\,\text{J}$ or $3.6\,\text{kJ}$.

Kilowatt Hour ($\text{kWh}$)

The energy spent or work done by a source of power $1\,\text{kW}$ in $1\,\text{h}$, equal to $3.6 \times 10^6\,\text{J}$ or $3.6\,\text{MJ}$.

Calorie

The unit of heat energy required to raise the temperature of $1\,\text{g}$ of water from $14.5^\circ\text{C}$ to $15.5^\circ\text{C}$ (or through $1^\circ\text{C}$), equal to $4.18\,\text{J}$.

Electron Volt ($\text{eV}$)

The energy gained by an electron when it is accelerated through a potential difference of $1\,\text{volt}$, equal to $1.6 \times 10^{-19}\,\text{J}$.

Mechanical Energy

The total energy possessed by a body due to its state of rest or of motion, consisting of the sum of its potential energy and kinetic energy.

Potential Energy ($U$)

The energy possessed by a body at rest due to its position or its altered size and shape.

Gravitational Potential Energy

The potential energy possessed by a body due to the Earth's gravitational attraction, defined as zero at infinity and equal to $U = mgh$ at a height $h$ above the Earth's surface.

Elastic Potential Energy

The potential energy possessed by a non-rigid body in its deformed state, equal to the work done by an external force in changing the body's size and shape.

Kinetic Energy ($K$)

The energy possessed by a body due to its state of motion, equal to the work the moving body is capable of performing before coming to rest: $K = \frac{1}{2}mv^2$.

Relation Between Kinetic Energy and Momentum

The mathematical relationship linking linear momentum ($p$) and kinetic energy ($K$): $p = \sqrt{2mK}$ or $K = \frac{p^2}{2m}$.

Work-Energy Theorem

The theorem stating that the increase in kinetic energy of a moving body is equal to the work done by the net force acting in the direction of motion: $W = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$.

Translational Kinetic Energy

The kinetic energy possessed by a body due to its motion along a straight-line path, such as a moving vehicle, a freely falling stone, or a monoatomic gas molecule.

Rotational Kinetic Energy

The kinetic energy possessed by a body due to rotation about a fixed axis, such as a spinning top, a rotating wheel, or the Earth rotating on its axis.

Vibrational Kinetic Energy

The kinetic energy possessed by an object due to its to-and-fro periodic motion about its mean position, such as a clamped wire plucked in the middle or atoms vibrating in a solid.

Solar Cell

A device fabricated from thin slices of semiconductor material that directly converts solar (light) energy into electrical energy.

Nuclear Energy

The energy released due to the loss in mass during nuclear fission or nuclear fusion, converted according to Einstein's mass-energy equation $E = mc^2$.

Geothermal Energy

The energy released by nuclear disintegrations inside the Earth that heats underground water into natural steam, occasionally bursting forth as hot springs.

Electric Generator (Dynamo)

A machine that transforms mechanical energy (specifically rotational kinetic energy of a turbine) into electrical energy.

Electric Motor

A device that converts electrical energy into mechanical energy by using a current-carrying coil placed within a magnetic field to produce rotational torque.

Thermocouple

A device comprising two junctions of dissimilar metals kept at different temperatures that converts heat energy directly into electrical energy.

Degraded Energy (Dissipation of Energy)

The fraction of energy converted during a transformation into non-useful or undesirable forms (such as heat due to friction or radiation to the environment) that cannot be used for productive work.

Principle of Conservation of Energy

The fundamental principle stating that energy can neither be created nor destroyed; it only changes from one form to another, meaning the total energy of an isolated system remains constant.

Mechanical Energy Conservation in Free Fall

The principle verifying that the sum of kinetic energy and potential energy ($K + U = mgh$) remains strictly constant at every point during the descent of an object falling freely under gravity in a vacuum.

Conservation of Energy in a Simple Pendulum

The continuous interchange of energy where total mechanical energy is purely potential energy ($mgh$) at the extreme positions and purely kinetic energy ($\frac{1}{2}mv^2$) at the mean position, giving velocity $v = \sqrt{2gh}$ at the mean position.