fisica1-youn-e-freedman-exercicios-resolvidos

8.86: (a) For momentum to be conserved, the two fragments must depart in opposite
directions. We can thus write
M V = −M
V
A
A
B
B
Since M = M − , we have
A
M B
( M − MB)
V
V
V
A
A
B
= −M V
B
B
− M
B
=
M − M
B
Then for the ratio of the kinetic energies
KE
KE
A
B
=
1
2
1
2
M
M
A
B
V
V
2
A
2
B
=
M
M
A
B
M
M
2
B
B
=
2
( M − M
B
) M
A
The ratio of the KE’s is simply the inverse ratio of the masses.
From the two equations
M
B
KE
A
= KEB
and KEA
+ KEB
= Q
M
We can solve for
KEB
to find
A
⎛ M ⎞
A
KEA
= Q − KEB
= Q
⎜1−
M
A
M
⎟
⎝ +
B ⎠
Q QM
A
KEB
= =
1+
M + M
M B
M A
(b) If M
B
= 4M
A
, then M
A
will get 4 times as much KE as M
B,
or 80% of Q for
M and 20% for M .
A
B
A
B