Key Points

In science, work is done only when a force applied to an object causes it to be displaced. For work to be done, both a force and a displacement in the direction of the force must exist and be non-zero.

The work done, $W$, by a constant force, $F$, is the product of the force and the displacement, $s$, in the direction of the force. The formula is $W = F \times s$.

The SI unit for both work and energy is the joule (J). One joule is defined as the work done when a force of 1 newton displaces an object by 1 meter along the line of action of the force, so $1 \text{ J} = 1 \text{ N} \times 1 \text{ m}$.

Work done is positive when the force acts in the direction of displacement. It is negative when the force acts opposite to the direction of displacement. Work done is zero if there is no displacement or if the force is perpendicular to the displacement.

Energy is defined as the capacity or ability to do work. An object that possesses energy can exert a force on another object to do work. The unit of energy is the joule (J), the same as work.

Kinetic energy is the energy possessed by an object by virtue of its motion. The formula for kinetic energy is $E_k = \frac{1}{2} m v^2$, where $m$ is the mass of the object and $v$ is its velocity.

The work-energy theorem states that the work done on an object by a net force is equal to the change in its kinetic energy. The formula is $W = \Delta E_k = \frac{1}{2} m v^2 - \frac{1}{2} m u^2$, where $u$ and $v$ are the initial and final velocities.

Potential energy is the energy stored in an object due to its position or configuration. This stored energy has the potential to be converted into other forms of energy, such as kinetic energy.

The gravitational potential energy of an object at a height $h$ above a reference level is given by the formula $E_p = mgh$. Here, $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the vertical height.

This law states that energy can only be transformed from one form to another; it can neither be created nor destroyed. The total energy of an isolated system remains constant.

In the absence of non-conservative forces like friction, the total mechanical energy (the sum of kinetic and potential energy) of a system remains constant. Thus, $E_p + E_k = mgh + \frac{1}{2} m v^2 = \text{constant}$.

Power is defined as the rate of doing work or the rate of energy transfer. It measures how quickly work is done.

Power $P$ is calculated by dividing the work done $W$ by the time taken $t$, so $P = \frac{W}{t}$. The SI unit of power is the watt (W), where $1 \text{ W} = 1 \text{ J/s}$.

The commercial unit of electrical energy is the kilowatt-hour (kWh), often called a 'unit'. It represents the energy consumed by a 1-kilowatt appliance operating for 1 hour.

One kilowatt-hour is equivalent to $3.6 \times 10^6$ joules. This is calculated as $1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s} = 3,600,000 \text{ J}$.