Colliding balls with different masses

[devanlevin]

2 balls, with masses of M1, M2, are involved in a plastic collision, one dimensional.. 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
$$\frac{m1v1^2}{2}$$=20$$\frac{m2v2^2}{2}$$
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.

 

[alphysicist]

Hi devanlevin,

2 balls, with masses of M1, M2, are involved in a plastic collision, one dimensional.. 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
$$\frac{m1v1^2}{2}$$=20$$\frac{m2v2^2}{2}$$
from this i get, what i'll call ratio(I)
m1/m2=20(v1/v2)^2

I have not looked closely at the rest of your problem, but here I believe you have made an algebra error. On the right hand side, v1 and v2 should be switched.

 

[devanlevin]

sorry, my mistake, it is meant to be switched,,, its just a typo and in my actual workings its switched,
funnily enough if i left it that way it would work the way the answers are in the book
please take a look at the rest

 

[alphysicist]

2 balls, with masses of M1, M2, are involved in a plastic collision, one dimensional.. 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
$$\frac{m1v1^2}{2}$$=20$$\frac{m2v2^2}{2}$$
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

I don't think the problem is asking about this scenario. If both masses are moving to the right, then after the collision the combined mass will still be moving to the right, no matter what the mass ratio is.

It's true if the leading mass is faster then they will not collide, but the problem states that they do collide, so I don't see where they would be asking this.

*the momentum of M2 is bigger than M1 ==>P2>P1 but Ek1>Ek2, so M1<M2 but V1>V2,

That looks right; we need the momentum of m2 to be larger than that of m1.

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,

What do you mean by similar? Is the only difference the opposite inequality symbol? Your result here looks correct to me.

But you can check it. Your result just says that m2 > 20 m1. So choose m1=1, and choose an m2 that's greater than 20 (40 would be convenient). Then choose v2=1, and calculate the v1 from the KE equation.

Once you have the masses and velocities, if momentum of m2 is larger than m1, then your result should be true.