The Main Problem I am Having is with a “Result”
Which is Repeatedly Being Used in Problems
“Work done by Friction(Frictional Losses)on the system is Independent of Reference Frame”
So What they do to solve this Question is this way :
Work by Agency with respect to ground + Work by Friction with respect to ground = Change in Kinetic Energy of The Block
Then With respect to Frame of Reference of Plank They write
Work done by Friction = Change in kinetic energy of Block with respect to Plank = Work by Friction with respect to ground
The Last Part is Tough for me to Swallow .
Consider an instantaneous moment when the block’s speed is v<u. The friction force \vec f_b acting on the block is directed along \vec u and increases the v. So the friction force between the block and the plank is the only force that does a work in order to increase the block’s kinetic energy, or
W_f = \frac{m(u^2-0^2)}{2}.
You could get the same result through working in the plank’s frame of reference – and this is what the authors have done here.
So in total, the work done by the agency is intended to increase the kinetic energy of the system as well as compensate for the energy dissipated due to the friction force acting on the plank, but the friction force acting on the block also equals the kinetic energy of the block. Finally,
W = W_f +\text{K.E.} = \frac{mu^2}{2}+\frac{mu^2}{2},\quad\Rightarrow\quad m=\frac{W}{u^2}=5\text{ kg}.
P.S. The majority of users of this forum are students from Kazakhstan, but we can also respond in English, so don’t bother yourself translating the problems to Russian.
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