Impulse- momentum - work and energy, Mechanical Engineering

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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

1155_Impulse, Momentum, Work and Energy.png

 (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

1462_Impulse, Momentum, Work and Energy1.png

   (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.


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