**Impulse, Momentum, Work and Energy:**

As a part of summary, you can remember various important principles in terms of following equations.

(i) Impulse-Momentum equation along a given direction

(ii) Principle of Conservation of Momentum for a given system of masses M_{1}, M_{2} and M_{3}.

M_{1} V_{1} + M _{2} V_{2} + M _{3} V_{3} = M_{1} V_{1}′ + M _{2} V_{2}′ + M_{ 3} V_{3}′

(iii) Principle of Conservation of Energy

** (a) In case of Conservative-field**

Total Energy content under any position of all the masses in the system is constant.

Considering any two points (1) and (2)

∴ PE (1) + KE (1) = PE (2) + KE (2)

** (b) In case of Non-conservative-field**

∴ PE (1) + KE (1) = PE (2) + KE (2) + Energy lost during movement from position (1) to (2).

(iv) Work Energy Principle on a given mass M

(v) Perfectly Elastic Impact

e = Velocityof Departure/ Velocityof Approach

= (V_{2}′ - V_{1}′) / V_{1} - V_{2} = 1

M _{1} V_{1} + M _{2} V_{2} = M _{1} V_{1}′ + M _{2} V_{2}′ = (m_{1} + m_{2} ) V_{c}

There is no loss of energy throughout perfectly Elastic Impact.

(vi) Perfectly Plastic Impact

e = 0 ∴ V_{2}′ = V_{1}′ = V_{c}

(m_{1 } + m_{2} ) V_{c} = m_{1} V_{1} + m_{2} V_{2}

Energy is lost due to permanent deformation caused by impulsive forces.

E_{lost} = m_{1 }m_{2 } (V_{1} - V_{2} )^{2} /2 (m_{1} + m_{2} )

A large number of examples are solved at the end of most of the important articles so that the application of above referred principles is correctly understood.