What is Energy?
The energy of a body is defined as its capacity for doing work. Since, the energy of a body is the total quantity of work done,
- it is a scalar quantity (as work is a scalar quantity),
- its dimensional formula is \( [ML^2T^{-2}] \) i.e. same as that of work and
- it is measured in the same units as work i.e. joule in SI and erg in cgs system.
Further, energy and power are different from each other. Whereas, the energy of a body is the total amount of work that a body can do and does not depend on the time in which the work is performed, the power of the body depends on the time in which the work is done.
Energy can exist in various forms such as mechanical energy, heat energy, light energy, sound energy, etc.
We will be studying problems mainly concerned with mechanical energy, which is of two types: namely:
- Kinetic energy
- Potential energy
Different Forms of Energy
While potential and kinetic energy are commonly discussed, energy can appear in various other forms. Some of these include:
1. Thermal Energy: This is the energy a body has because of the random movement of its molecules.
2. Internal Energy: This form of energy comes from the particular arrangement and random motion of a body’s molecules. It combines both the potential energy and the kinetic energy of these molecules. Potential energy is related to the arrangement of molecules against intermolecular forces, while kinetic energy arises from their random motion. Sometimes, internal energy is referred to as the microscopic mechanical energy of the body.
3. Electrical Energy: This energy results from the work needed to move free charge carriers in a specific direction through a conductor.
4. Chemical Energy: In a substance like a chemical compound, this energy is stored due to the chemical bonds between atoms. Chemical reactions release this energy.
Chemical energy is derived from the difference in binding energies of molecules before and after a reaction. A stable chemical compound has less energy compared to its separated parts. Essentially, a chemical reaction rearranges atoms. For example, burning one kilogram of coal, which is made up of carbon, releases \(3 \times 10^7\) J of energy. The energy obtained from burning coal, natural gas, wood, and petroleum is vital for our daily lives.
5. Nuclear Energy: This is the energy stored within an atomic nucleus. It can be released in two main ways:
- Nuclear fission: Splitting a heavy nucleus into lighter nuclei.
- Nuclear fusion: Combining lighter nuclei to form a heavier nucleus.
In both fission and fusion processes, a small amount of mass is converted into nuclear energy, in accordance with Einstein’s mass-energy equivalence.
The following table provides an approximation of the energy associated with various phenomena:
| S. No. | Phenomenon | Energy (J) |
|---|---|---|
| 1 | Energy required to break one bond in DNA | ≈ 10-20 |
| 2 | Energy of an electron in an atom | ≈ 10-18 |
| 3 | Energy of a proton in a nucleus | ≈ 10-13 |
| 4 | Energy associated with discharge of a single neutron | ≈ 10-12 |
| 5 | Energy spent in turning a page | ≈ 10-3 |
| 6 | Work done by a human heartbeat | ≈ 0.5 |
| 7 | Daily food intake of a human adult | ≈ 107 |
| 8 | Energy released in burning 1 litre of gasoline | ≈ 3 × 107 |
| 9 | Kinetic energy of a jet aircraft | ≈ 109 |
| 10 | Energy released in burning 1000 kg of coal | ≈ 1010 |
| 11 | Energy release of a 15 megaton fusion bomb | ≈ 1017 |
| 12 | Annual solar energy incident on Earth | ≈ 5 × 1024 |
| 13 | Rotational energy of Earth | ≈ 1029 |
| 14 | Rotational energy of the Milky Way | ≈ 1052 |
Example:
A toy rocket of mass \( 0.1 \, \text{kg} \) has a small fuel of mass \( 0.02 \, \text{kg} \), which it burns out in \( 3 \, \text{s} \). Starting from rest on a horizontal smooth track it gets a speed of \( 20 \, \text{ms}^{-1} \) after the fuel is burnt out. What is the approximate thrust of the rocket? What is the energy content per unit mass of the fuel? Ignore the small mass variation of the rocket during fuel burning.
Solution:
Here, \( u = 0 \), \( v = 20 \, \text{ms}^{-1} \), \( t = 3 \, \text{s} \)
If \( a \) is the acceleration produced, then
\[
v = u + at
\]
\[
\Rightarrow a = \dfrac{v – u}{t} = \dfrac{20 – 0}{3} = \dfrac{20}{3} \, \text{ms}^{-2}
\]
Therefore, thrust on rocket,
$ \displaystyle F$ $ \displaystyle =$ mass of rocket $ \displaystyle \times $ acceleration produced $ \displaystyle =0.1\times \dfrac{{20}}{3}=\dfrac{2}{3}\text{N}$
The energy content of the fuel is equal to work done in providing a speed of \( 20 \, \text{ms}^{-1} \) to the rocket. If \( S \) is the distance covered by the rocket, then
$ \displaystyle S=ut+\dfrac{1}{2}a{{t}^{2}}$
$ \displaystyle S=0\times 3+\dfrac{1}{2}\times \dfrac{{20}}{3}\times {{3}^{2}}$
$ \displaystyle S=30\text{m}$
Therefore, work done on the rocket, \( W = F \times S = \dfrac{2}{3} \times 30 = 20 \, \text{J} \)
Therefore, energy of the fuel \( (0.02 \, \text{kg}) \) contained in the rocket \( = 20 \, \text{J} \)
Hence, energy content per unit mass of the fuel \( = \dfrac{20}{0.02} = 10^3 \, \text{J} \, \text{kg}^{-1} \)
