K=(mv^2)/2 ; W= ρ*(dp/dt)*dx ; (dp/dt)*dx=(dp/du)n*du. λ=1/sqrt(1-u^2/c^2).
=>
(dp/du)=(d/du)*(mu/sqrt(1-u^2/c^2))=m/(1-(u^2/c^2)^(3/2).
deoarece p(vector)=x*mu(vector) =>
W=ρ*(dp/du)*u*du=ρ*mu/(1-(u^2/c^2)^(3/2)* du. =>
W= (m*c^2/sqrt(1-(u^2-c^2)))-m*c^2=K. (*)
Din ecuatia energiei totale E tot=m*c^2/sqrt(1-(u^2-c^2)) si ecuatia energiei cinetice argumentate mai sus -trimitere la (*)- energia si masa sunt legate (c constanta) => E=mc^2
