- #1
devanlevin
2 balls, with masses of M1, M2, are involved in a plastic collision, one dimentional.. the kinetic energy of the ball m1 is 20 times that of m2. at what ratio between the masses will the new mass(m1+m2) move in the direction the lesser energy mass mas moving.
from Ek1=20Ek2
[tex]\frac{m1v1^2}{2}[/tex]=20[tex]\frac{m2v2^2}{2}[/tex]
from this i get, what i'll call ratio(I)
m1/m2=20(v1/v2)^2
i think there are 2 possible scenarios,
*they are both moving in the same direction
*the momentum of M2 is bigger than M1 ==>P2>P1 but Ek1>Ek2, so M1<M2 but V1>V2,
for the 1st scenario there are 2 cases
a)
(M1)-----> (M2)--->
V1>V2 ===} in which case, using the ratio(I) i got before, if v1>v2 then m1/m2<20
similarily in case 2
(M2)-----> (M1)--->
where v2>v1, here i'll get m1/m2>20
and for the second scenario
(M1)-----> <---(M2)
here i end up with m1/m2<1/20
these answers are similar to the correct answers, according to my textbook, only there ALL the signs are opposites, all the >'s are < etc,
can you see where i have gone wrong or could this be a mistake in the book.
from Ek1=20Ek2
[tex]\frac{m1v1^2}{2}[/tex]=20[tex]\frac{m2v2^2}{2}[/tex]
from this i get, what i'll call ratio(I)
m1/m2=20(v1/v2)^2
i think there are 2 possible scenarios,
*they are both moving in the same direction
*the momentum of M2 is bigger than M1 ==>P2>P1 but Ek1>Ek2, so M1<M2 but V1>V2,
for the 1st scenario there are 2 cases
a)
(M1)-----> (M2)--->
V1>V2 ===} in which case, using the ratio(I) i got before, if v1>v2 then m1/m2<20
similarily in case 2
(M2)-----> (M1)--->
where v2>v1, here i'll get m1/m2>20
and for the second scenario
(M1)-----> <---(M2)
here i end up with m1/m2<1/20
these answers are similar to the correct answers, according to my textbook, only there ALL the signs are opposites, all the >'s are < etc,
can you see where i have gone wrong or could this be a mistake in the book.