Answer to Question #106336 in Mechanics | Relativity for John Edward Interior

Question

A mass breaks suddenly into two parts, masses M and m, with speeds V and v respectively and carrying a total kinetic energy K. If (M/m) = R = 4.2 what fractions of KK does each of the masses carry? (Think about significant figures.)

Answer 1

From the conservation of momentum:

$$mv=MV=RmV→v=RV$$

$$K=0.5mv ^ 2 +0.5Rm\frac{v^2}{R^2}=0.5mv ^2\left(1+\frac{1}{R}\right)$$

$$K_m=\frac{1}{(1+\frac{1}{R})}K=\frac{1}{(1+\frac{1}{4.2})}K=0.81K$$

$$K_M=K-K_m=(1-0.81)K=0.19K$$