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# Mechanics Momentum.. help?! watch

1. Sorry it looks really long.. I'm only stuck on the last bit about the minimum speed of A but it's a multiple step question. Please help I'm so confused.

Three uniform spheres 𝐴, 𝐵 and 𝐶 have masses 0.3 kg, 0.4 kg and 𝑚 kg respectively. The spheres lie in a
smooth horizontal groove with 𝐵 between 𝐴 and 𝐶. Sphere 𝐵 is at rest and spheres 𝐴 and 𝐶 are each
moving with speed 3.2 ms-1
towards 𝐵 (see diagram). Air resistance may be ignored.

(a) 𝐴 collides with 𝐵. After this collision 𝐴 continues to move in the same direction as before, but with speed 0.8 ms-1. Find the speed with which 𝐵 starts to move.

(b) 𝐵 and 𝐶 then collide, after which they both move towards 𝐴, with speeds of 3.1 ms-1 and 0.4 ms-1 respectively. Find the value of 𝑚.

(c) The next collision is between 𝐴 and 𝐵. How you can tell that, after this collision, 𝐴 and 𝐵 cannot both be moving towards 𝐶 ?

(d) When the spheres have finished colliding,

(i) Which direction is 𝐴 moving in? ANSWER LEFT (i got this right but only by intuition, if anyone could clear up exactly why please i'd appreciate it.)

(ii) What is the minimum speed of 𝐴?
2. (c), total linear momentum of A and B before collision is 0.3*0.8-0.4*3.1, so the resultant momentum is away from C, therefore they cannot both be going towards C.

d(i) so after the collision discussed in (c), A is moving left and B is moving right. As A is the furthest left, none of the other two can do anything to make it go right again. They would have to collide with it from the left, but that is impossible as they are on the other side.

Have you done anything on the coefficient of restitution?
3. (Original post by stolenuniverse)
x
(im assuming you drew the diagram with A to the left of B and C to the right)

d i) After A and Bs second collision you can deduce the direction A is heading based on the fact A and B cant both be heading towards C.

ii) I think you work out the speed of A after its second collision with B, then see whether that value, 3.2 or 0.8 is smaller, since after the 2nd collision A is heading left then any subsequent collisions involving A will just be B hitting the "back" of A which will only speed it up
4. (Original post by Darth_Narwhale)
(c), total linear momentum of A and B before collision is 0.3*0.8-0.4*3.1, so the resultant momentum is away from C, therefore they cannot both be going towards C.

d(i) so after the collision discussed in (c), A is moving left and B is moving right. As A is the furthest left, none of the other two can do anything to make it go right again. They would have to collide with it from the left, but that is impossible as they are on the other side.

Have you done anything on the coefficient of restitution?
How can you know B is going left? Couldn't A and B both go right?

And no i haven't i've never heard of that.

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Updated: January 29, 2017
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