PHY ===MC (SHOW YOUR WORK)

conservation of momentum
initial momentum = mu
final momentum = mv1+2mv2
u = v1 +2v2
using above forumla, eliminating ans A

conservation of kinetic energy: final energy must be less than initial energy
initial energy = 1/2 m u^2
final energy = 1/2 m v1^2 + m v2^2
u^2 = v1^2 + 2v2^2
ans B & D, final energy > initial energy --> rejected

right answer should be C

According Conservation of momentum, the total momentum of a closed system of objects (which has no interactions with external agents) is constant.
So, before collision
total momentum = mu+2m*0=mu
After collision, the total momentum should also be mu too
A 0.5u*m+0.5u*2m=1.5mu
B 1.5u*m-0.25u*2m=mu
C 0+2m*0.5*u=mu
D -0.5u*m+0.75u*2m=mu
However, B is impossible since the direction is wrong.
D is also impossible, consider the kinetic energy
Before collision
kinetic energy=(1/2)mu^2

After collision
kinetic energy=(1/2)m(-0.5u)^2+1/2(2m)(0.75u)^2=0.6875mu^2>0.5mu^2
The kinetic energy has increased and this should be ipossible

The answer is C

2007-03-04 04:20:44 補充：
in B, I mean the velocity direction of X and Y is wrong