Work, Energy and Power

This set of vocabulary flashcards covers concepts from Chapter 5 of Introductory Physics PH 110, including scientific definitions, formulas, units, and theorems related to work, energy systems, and power.

Work

The product of a force acting upon an object and the displacement of that object, requiring three ingredients: force, displacement, and cause.

Work done by a constant force

The product of the component of the force in the direction of displacement and the magnitude of the displacement, expressed as $W = Fs \tan(\theta)$, or the scalar dot product $W = \text{F} \times \text{s} = \text{OA} \times \text{OC}$.

Joule (J)

The scalar unit of measurement for work and energy.

Positive Work

Work done when the component of the force $\text{F} \tan(\theta)$ is in the same direction as the displacement.

Negative Work

Work done when the component of the force $\text{F} \tan(\theta)$ is in the opposite direction to that of the displacement, such as work done by friction.

Work done by a variable force

The area under the force-position curve, expressed as a definite integral of force over displacement: W = \text{lim}_{\text{Δx} \rightarrow 0} \text{∑} F(\text{x})\text{Δx} = \text{∫}_{x_i}^{x_f} F_x \text{dx}.

Energy

A scalar quantity defined as the ability to perform work, to make things happen, and to cause changes.

Kinetic Energy (K.E)

The energy of motion possessed by an object, which depends on the object's mass ($m$) and the magnitude of its velocity ($v$), represented by the equation $K.E = \frac{1}{2} mv^2$.

Work-energy theorem

States that the net work done on a body is equal to the change in kinetic energy of the body: $W_{net} = \text{Δ}K = K_f - K_i$.

Potential Energy

The stored energy of position possessed by an object.

Gravitational Potential Energy (G.P.E)

Energy stored in an object as the result of its vertical position or height, calculated as $G.P.E = mgh$, where $g$ represents acceleration due to gravity.

Elastic Potential Energy (E.P.E)

Energy stored in elastic materials, such as springs or rubber bands, as the result of stretching or compressing, mathematically expressed as $E.P.E = \frac{1}{2} kx^2$.

Hooke's Law

States that the amount of force ($F$) is directly proportional to the amount of stretch or compression ($x$), given by $F = kx$, where $k$ is the spring constant.

Equilibrium Position

The position that a spring naturally assumes when no force is applied to it, also known as the zero-potential energy position.

Law of conservation of energy

States that energy can neither be created nor destroyed but can only be transferred from one form into another, meaning the total energy of a closed system remains constant ($K_i + U_i = K_f + U_f$).

Conservative Force

A force where the work done on a body moving between two points is independent of the path taken, such as gravitational force.

Non-conservative force

A force where the work done depends on the path taken, such as the force of friction.

Mass-energy equivalence

Albert Einstein's theory that matter and energy are interconvertible, calculated using the formula $E = mc^2$, where $c$ is the speed of light in free space.

Power

The rate of doing work or the amount of energy consumed per unit of time; it is a scalar quantity defined as $P = \frac{dW}{dt}$.

Watt (W)

The SI unit of power, equivalent to one joule of work done in one second ($1\text{ J/s}$).

Horsepower (hp)

A practical unit of power where $1 \text{ hp} = 746 \text{ W}$.

Kilowatt-hour (kWh)

A unit of energy equivalent to the consumption of $1000 \text{ W}$ over one hour, equal to $3.6 \times 10^6 \text{ J}$.

Instantaneous Power

The rate at which a force ($\text{F}$) does work on a particle in terms of its velocity ($\text{v}$), expressed as $P = \text{Fv} \tan(\theta) = \text{F} \times \text{v}$.