Question

doua bile cu masele m1 si m2 se misca una spre cealalta , viteza bilei cu masa m1 fiind de n ori mai mare decat viteza celeilalte bile. care este raportul maselor m1 /m2 stiind ca dupa ciocnirea perfect elastica bla cu masa m1 se opreste

Answer 1

v₁=n*v₂
u₁=(2m₁v₁+m₂v₂)/(m₁+m₂)-v₁
u₁=0=>v₁=(2m₁v₁+m₂v₂)/(m₁+m₂)<=>n*v₂=(2m₁n*v₂+m₂v₂)/(m₁+m₂)=>n*v₂(m₁+m₂)=2m₁n*v₂+m₂v₂<=>n*v₂(m₁+m₂)=v₂(2m₁n+m₂) |:v₂<=>n*m₁+n*m₂=2m₁n+m₂<=>n*m₂=m₁*n+m₂=>n*m₂-m₂=m₁*n<=<m₂(n-1)=m₁*n=>m₂=m₁*n/(n-1)
u₂=(2m₁v₁+m₂v₂)/(m₁+m₂)-v₂<=>u₂=(2m₁n*v₂+m₁*n/(n-1)v₂)/(m₁+m₁*n/(n-1))-v₂<=>u₂={m₁*n*v₂[2+1(n-1)]}/{m₁[1+n/(n+1)]}-v2<=> u₂=v₂(n-1)
v₂(n-1)=(2m₁v₁+m₂v₂)/(m₁+m₂)-v₂<=>v₂(n-1)=(2m₁n*v₂+m₂v₂)/(m₁+m₂)-v₂ |:v₂<=>n-1=2m₁n-m₁<=>m₁=(n-1)/(2n-1)
m₂=m₁*n/(n-1)=[(n-1)/(2n-1)*n]/(n-1)=n/(2n-1)
m1/m2=[(n-1)/(2n-1)]/[n/(2n-1)]=(n-1)/n=1-1/n