Energy

A. Scientific Definition of Work:

In physics, Work is said to be done by a force on an object if and only if:

1. A non-zero external force $F$ acts on the body.
2. The body is displaced through a distance $s$ in the direction of the force.

• SI Unit: Joule ($\text{J}$): $1\text{ Joule} = 1\text{ Newton} \times 1\text{ meter} = 1\text{ N m}$.
• Definition of 1 Joule: One Joule of work is done when a force of $1\text{ N}$ displaces a body by $1\text{ m}$ in the direction of the force.
• Conditions for Zero Work ($W = 0$):
  • If displacement $s = 0$ (e.g., pushing against a concrete wall without moving it).
  • If the force acts perpendicular ($90^\circ$) to the displacement (e.g., a satellite orbiting Earth in a circular path, or a porter carrying luggage horizontally).

B. Concept of Energy:

Energy is defined as the capacity or ability of a body to do work. Its SI unit is identical to work: Joule ($\text{J}$).

Mechanical energy exists in two primary conjugate states:

1. Potential Energy ($U$ or $PE$):

Energy possessed by a body by virtue of its position (height) or configuration (state of strain):

• Gravitational Potential Energy: Work done in lifting a mass $m$ to a vertical height $h$ against gravity ($W = F \times h = mg \times h$): $$\mathbf{U = mgh}$$
• Elastic Potential Energy: Energy stored in a deformed elastic medium (stretched rubber band, wound clock spring, bent archery bow).

2. Kinetic Energy ($K$ or $KE$):

Energy possessed by a body by virtue of its state of motion:

• $K$ is directly proportional to mass ($m$).
• $K$ is directly proportional to the square of velocity ($v^2$)! (If velocity is doubled, kinetic energy increases fourfold; if velocity is tripled, $K$ increases ninefold!).

A. The Universal Law:

Energy can neither be created nor destroyed; it can only be transformed from one form into another. The total energy of an isolated universe remains strictly constant.

B. Energy of a Freely Falling Body (Mass $m$, Height $h$):

1. At Point A (Top, Height $h$, Velocity $v = 0$): $$U_A = mgh, \quad K_A = 0 \implies E_A = mgh + 0 = \mathbf{mgh}$$
2. At Point B (Midway, dropped distance $x$, Height $h - x$):

   Velocity: $v^2 = 0^2 + 2gx = 2gx$.

   $$U_B = mg(h - x), \quad K_B = \frac{1}{2}m(2gx) = mgx$$ $$E_B = U_B + K_B = mg(h - x) + mgx = \mathbf{mgh}$$
3. At Point C (Just before hitting ground, Height $= 0$):

   Velocity: $v^2 = 2gh$.

   $$U_C = 0, \quad K_C = \frac{1}{2}m(2gh) = mgh \implies E_C = 0 + mgh = \mathbf{mgh}$$

At every point during free fall, $E_{\text{total}} = U + K = mgh = \text{constant}$!

A. Energy Converters in Technology:

• Electric Motor: Electrical Energy $\to$ Mechanical Energy.
• Electric Generator / Dynamo: Mechanical Energy $\to$ Electrical Energy.
• Solar Cell (Photovoltaic): Light Energy $\to$ Electrical Energy.
• Microphone: Sound Energy $\to$ Electrical Energy.
• Loudspeaker: Electrical Energy $\to$ Sound Energy.
• Photosynthesis: Light (Solar) Energy $\to$ Chemical Energy.

B. Sources of Energy:

• Renewable (Inexhaustible & Clean): Solar, Wind, Hydroelectric, Geothermal, Biomass.
• Non-Renewable (Exhaustible & Polluting): Fossil fuels (Coal, Petroleum, Natural Gas), Uranium (Nuclear).