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# help with m2 collision

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1. A uniform sphere A of mass m is moving with speed u on a smooth horizontal table when it collides directly with another uniform sphere B of mass 2m which is at rest on the table. The spheres are of equal radius and the coefficient of restitution between them is e. The direction of motion of A is unchanged by the collision.

(a) Find the speeds of A and B immediately after the collision.
(b) Find the range of possible values of e.

After being struck by A, the sphere B collides directly with another sphere C of mass 4m and of the same size as B. The sphere C is at rest on the table immediately before being struck by B. The coefficient of restitution between B and C is also e.

(c) Show that, after B has struck C, there will be a further collision between A and B.

i need help with part (c)

for part (a) i got
Va=u/3 (1-2e)
Vb=u/3(e+1)

for part (b) i got e < 0.5
2. (Original post by mohamed-essa)
A uniform sphere A of mass m is moving with speed u on a smooth horizontal table when it collides directly with another uniform sphere B of mass 2m which is at rest on the table. The spheres are of equal radius and the coefficient of restitution between them is e. The direction of motion of A is unchanged by the collision.

(a) Find the speeds of A and B immediately after the collision.
(b) Find the range of possible values of e.

After being struck by A, the sphere B collides directly with another sphere C of mass 4m and of the same size as B. The sphere C is at rest on the table immediately before being struck by B. The coefficient of restitution between B and C is also e.

(c) Show that, after B has struck C, there will be a further collision between A and B.

i need help with part (c)

for part (a) i got
Va=u/3 (1-2e)
Vb=u/3(e+1)

for part (b) i got e < 0.5
What have you tried already for part c?
3. On the other hand, I have just attempted the question myself and have ended up in a horrible sea of u's and e^2's.
This is the monstrosity which is my working
Spoiler:
Show

Sorry, perhaps the maths genius Zacken can help once he's returned
4. (Original post by KaylaB)
What have you tried already for part c?

i worked out the velocity of b after the second collision. Vb2= u/3(e+1).1/3.(1-2e)
5. (Original post by mohamed-essa)
i worked out the velocity of b after the second collision. Vb2= u/3(e+1).1/3.(1-2e)
Basically you just need to show that either A and B are travelling towards each other, or that if they are travelling in the same direction that the one further back has a higher velocity so will eventually catch up
6. (Original post by samb1234)
Basically you just need to show that either A and B are travelling towards each other, or that if they are travelling in the same direction that the one further back has a higher velocity so will eventually catch up
They are equivalent. If they are travelling towards each other then it is necessary that one has a higher velocity than the other as they will be of opposite signs.

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