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1. Can someone help me with this problem and thanks.

A light inextensible string of length 4a has a particle A of mass attached at one end and a particle B of mass m attached at the other end. The string passes through a small smooth ring which is fixed at a point 0 at a distance 3a above a horizontal table. The system is hanging in equilibrium with 0B=2a when a smooth bead of mass 2m which is threaded on the string between 0 and B is released from rest at 0. The bead falls under gravity until it collides and adheres to the particle B to for a composite particle C.

a) Given that the string remains taut, show that the speed of C immediately after the collision is squareroot(ga).
b)find the speed of C immediately before it reaches the table.
2. (Original post by jakegreen)
Can someone help me with this problem and thanks.

A light inextensible string of length 4a has a particle A of mass attached at one end and a particle B of mass m attached at the other end. The string passes through a small smooth ring which is fixed at a point 0 at a distance 3a above a horizontal table. The system is hanging in equilibrium with 0B=2a when a smooth bead of mass 2m which is threaded on the string between 0 and B is released from rest at 0. The bead falls under gravity until it collides and adheres to the particle B to for a composite particle C.

a) Given that the string remains taut, show that the speed of C immediately after the collision is squareroot(ga).
b)find the speed of C immediately before it reaches the table.
Is this from a past paper, coz i sorta remember doin it. I mite have the answer if it is.
3. Does this come with a diagram? Cos it would sure help...
4. there was no diagram and it is M2 Heinemann book,
5. (Original post by jakegreen)
Can someone help me with this problem and thanks.

A light inextensible string of length 4a has a particle A of mass attached at one end and a particle B of mass m attached at the other end. The string passes through a small smooth ring which is fixed at a point 0 at a distance 3a above a horizontal table. The system is hanging in equilibrium with 0B=2a when a smooth bead of mass 2m which is threaded on the string between 0 and B is released from rest at 0. The bead falls under gravity until it collides and adheres to the particle B to for a composite particle C.

a) Given that the string remains taut, show that the speed of C immediately after the collision is squareroot(ga).
b)find the speed of C immediately before it reaches the table.
What is the mass of particle A?

Edit: doh just read it again never mind
6. a) I can't seem to prove that v = sqrt(ga)... I always get v = sqrt(8/3 ga)

7. http://homepages.nildram.co.uk/~walker12/Image2.jpg

Part a worked ok dunno about part b it was a bit rushed. Will translate my scrawl into something readable later but gtg c ya.
8. is the mass of A m?
is the mass of A m?
Yeah! It took me moment to figure it out too. But they are in equilibrium. ergo mass B = mass A = m.
10. After impacting, there's mg acting down on A and 3mg acting down on B/C
So tension in string is now T, say.
They are both subject to the same acceleration = a, say.

Then,

T-mg = ma
3mg - T = 3ma

3mg - mg = 4ma
2mg = 4ma
a = g/2
=====

v² = u² + 2as
v² = ga + 2(g/2)(3a - 2a)
v ² = ga + ga
v² = 2ga
v = sqrt(2ga)
=========
11. (Original post by davedave)
http://homepages.nildram.co.uk/~walker12/Image2.jpg

Part a worked ok dunno about part b it was a bit rushed. Will translate my scrawl into something readable later but gtg c ya.
Ah.. I see where I went wrong. I thought the distance from B to the table was 3a, not from O to the table.

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