Answer to Question #156137 in Quantum Mechanics for Anand

Question

 A particle of mass 3m initially moving with a speed u in the positive x-direction 

collides with a second particle of mass m moving in the opposite direction with an 

unknown speed v. After collision the mass 3m moves along the negative y-direction 

with a speed u/2 and the mass m moves with a speed v in a direction making an angle 

of 45˚ with the positive x-direction. Determine v and v in units of u. Is the collision 

elastic?

Answer 1

(1)

$3m\cdot\frac{u}{2}=mv'\cdot\sin45°\to v'=\frac{3u}{\sqrt{2}}$ . Answer

(2)

$3m\cdot u-mv=mv'\cdot\cos45°$

$3m\cdot u-mv=m\cdot \frac{3u}{\sqrt{2}}\cdot\cos45°\to v=\frac{3u}{2}$ . Answer

(3)

before collide

$KE=\frac{3mu^2}{2}+\frac{mv^2}{2}=\frac{3mu^2}{2}+\frac{m(3u/2)^2}{2}=\frac{21}{8}mu^2$

after collide

$KE=\frac{3m\cdot (u/2)^2}{2}+\frac{m\cdot(3u/\sqrt{2})^2}{2}=\frac{21}{8}mu^2$

So, the collision is elastic. Answer