Work, Energy, Power and Collision

ENERGY, TYPES OF ENERGY , CONSERVATION OF ENERGY

Energy

The energy of a body is defined as its capacity for doing work.

(1) Since energy of a body is the total quantity of work done, therefore it is a scalar quantity.

(2) Dimension: \([M{{L}^{2}}{{T}^{-2}}]\) it is same as that of work or torque.

(3) Units : Joule [S.I.], erg [C.G.S.]

Practical units : electron volt (eV), Kilowatt hour (KWh), Calories (cal)

Relation between different units:  

1 Joule = \({{10}^{7}}\) erg

1 eV  = \(1.6\times {{10}^{-19}}\) Joule

1 kWh = \(3.6\times {{10}^{6}}\)Joule

1 calorie = \(4.18\,Joule\)

(4) Mass energy equivalence : Einstein’s special theory of relativity shows that material particle itself is a form of energy.

The relation between the mass of a particle m and its equivalent energy is given as

\(E=m{{c}^{2}}\) where c = velocity of light in vacuum.

If \(m=1\,amu=1.67\times {{10}^{-27}}\,kg\)

then \(E=931\,MeV=1.5\times {{10}^{-10}}\,Joule\).

If \(m=1kg\) then \(E=9\times {{10}^{16}}\,Joule\)

Examples : (i) Annihilation of matter when an electron \(({{e}^{-}})\) and a positron \(({{e}^{+}})\) combine with each other, they annihilate or destroy each other. The masses of electron and positron are converted into energy. This energy is released in the form of \(\gamma \)-rays.

\({{e}^{-}}+{{e}^{+}}\to \gamma +\gamma \)

Each  \(\gamma \) photon has energy = 0.51 MeV.

Here two \(\gamma \) photons  are emitted instead of one \(\gamma \) photon to conserve the linear momentum.

(ii) Pair production :  This process is the reverse of annihilation of matter. In this case, a photon \(\gamma \) having energy equal to 1.02 MeV interacts with a nucleus and give rise to electron \(({{e}^{-}})\) and positron \(({{e}^{+}})\). Thus energy is converted into matter.