IIT JEE , AIEEE Forum - Physics , Mechanics

bhupesh

Dear

First do you understand that energy is frame dependent but conservation of energy is frame independent i.e if you will consider the total energy of a system but here is something interesting suppose you are moving to wards an object with certain velocity then it will appear to you as if the object it self is moving towards you certain velocity that means you can assign KE to the object in your frame but on the other hand suppose I am standing by the object it will appear to be at rest to me so I will say KE of the object is zero in my frame . Suppose while moving the object collides with you and you wants to apply conservation of energy you can apply .
                           For me I can again apply the conservation of energy but in my case I will assign KE to the collided object not the colliding object which is in rest in my frame and the result that we will get will be true in our own reference frame they may be separate but true its like suppose a point is two meter left to you and 3 m right to me we are true in our own way.


In your case Cumulative KE means Sum of KINETIC ENERGY with respect to the frame only you not consider the speed of the frame it self .

and you answer is in the Center of mass reference frame you will find minimum cumulative KE. i.e you will not consider speed of the COM it self )

Actually in COM reference frame KE of the system becomes

1/2 M_totalV_CM² + 1/2 m₁V_1²_{( ,rel to COM )} + 1/2 m₂V_{2²(Rel to COM )}Rel to COM : Speed of m₁ and m₂as measured from COM

most importantly the above expression is to total energy not cumulative energy

Imp : You must understand the above expression alond with point that like total KE we can also find out total momentum of the system from COM frame and its zero always

COM is beautiful concept the above two points greatly simplifies many particle problems. Remember in rolling how the total Energy of the rolling body gets divided in to two its because you are calculating from COM frame and with the above expression   you can get for a rolling object total K.E = 1/2 I

² + 1/2 M_totalV²_cm

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