Physics: Work, Energy and Power

Terminology and fundamental concepts regarding Work, Kinetic Energy, Potential Energy, Power, and Collisions from Chapter 6 of the Physics lecture notes.

Scalar Product (Dot Product)

The product of two vectors $A$ and $B$, denoted as $A.B$, defined as $A B \cos(\theta)$ where $\theta$ is the angle between the two vectors.

Work

The product of the component of the force in the direction of the displacement and the magnitude of this displacement, given by the equation $W = F.d = F d \cos(\theta)$.

Joule ($J$)

The SI unit of work and energy, named after James Prescott Joule ($1811$-$1869$), with dimensions $[ML^2T^{-2}]$.

Kinetic Energy ($K$)

A scalar quantity representing the energy an object of mass $m$ possesses by virtue of its motion at velocity $v$, defined as $K = \frac{1}{2} m v^2$.

Work-Energy (WE) Theorem

A principle stating that the change in kinetic energy of a particle is equal to the work done on it by the net force ($K_f - K_i = W$).

Potential Energy ($V$)

The 'stored energy' of a body by virtue of its position or configuration, such that the force $F(x) = -\frac{dV}{dx}$.

Gravitational Potential Energy

The energy of an object as a function of height $h$, denoted as $V(h) = mgh$, representing work done against gravity.

Conservative Force

A force for which work done depends only on the initial and final positions and is independent of the path taken, such as gravity or spring force.

Non-conservative Force

A force, such as friction, where the work done depends on the particular path taken and results in energy dissipation as heat.

Total Mechanical Energy ($E$)

The sum of the kinetic energy ($K$) and potential energy ($V$) of a system, remaining constant if only conservative forces act upon it.

Hooke’s Law

A law for springs stating that the spring force $F_s$ is proportional to the displacement $x$ from the equilibrium position, expressed as $F_s = -kx$.

Spring Constant ($k$)

A measure of a spring's stiffness, expressed in units of $N\,m^{-1}$, where a large $k$ indicates a stiff spring.

Potential Energy of a Spring

The energy stored in a compressed or extended spring, given by the formula $V(x) = \frac{1}{2} k x^2$.

Mass-Energy Equivalence

The concept proposed by Albert Einstein that mass and energy are equivalent, related by the equation $E = mc^2$ where $c \approx 3 \times 10^8\,m/s$.

Power ($P$)

The time rate at which work is done or energy is transferred, defined as $P = \frac{dW}{dt} = F.v$; its SI unit is the watt ($W$).

Watt ($W$)

The SI unit of power, named after James Watt, defined as one joule per second ($1\,J\,s^{-1}$).

Elastic Collision

A collision in which both total linear momentum and total kinetic energy of the system are conserved.

Inelastic Collision

A collision where total linear momentum is conserved, but part of the initial kinetic energy is transformed into other forms of energy like heat or sound.

Completely Inelastic Collision

A specific type of inelastic collision in which the colliding bodies move together as a single unit after the impact.