A particle of mass m collided with a stationary particle of mass M deviated by an angle π2 whereas the particle M recoiled at an angle θ=30∘ to the direction of the initial motion of the particle m. How much (in per cent) has the kinetic energy of this system changed after the collision, if Mm=5.0?
Since, no external impulsive force is effective on the system "M+m", its total momentum along any direction will remain conserved.
So from px= const.,
mu=Mv1cosθ or, v1=mMucosθ (1)
and from py= const.,
mv2=Mv1sinθ or, v2=Mmv1sinθ=utanθ, [using (1)]
Final kinetic energy of the system
Tf=12mv22+12Mv21
And initial kinetic energy of the system =12mu2
So, % change =Tf−TiTi×100
=12mu2tan2θ+12Mm2M2u2cos2θ−12mu212mu2×100
=12u2tan2θ+12mMu2sec2θ−12u212u2×100
=(tan2θ+mMsec2θ−1)×100
and putting the values of θ and mM, we get % of change in kinetic energy =−40%