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 M1, M2 and M3.
M1 V1 + M 2 V2 + M 3 V3 = M1 V1′ + M 2 V2′ + M 3 V3′
(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
= (V2′ - V1′) / V1 - V2 = 1
M 1 V1 + M 2 V2 = M 1 V1′ + M 2 V2′ = (m1 + m2 ) Vc
There is no loss of energy throughout perfectly Elastic Impact.
(vi) Perfectly Plastic Impact
e = 0 ∴ V2′ = V1′ = Vc
(m1 + m2 ) Vc = m1 V1 + m2 V2
Energy is lost due to permanent deformation caused by impulsive forces.
Elost = m1 m2 (V1 - V2 )2 /2 (m1 + m2 )
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.