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.