M1 Dynamics Question

The question is:

Two particles A and B have masses M and 3M respectively. A and B are connected by a light inextensible string. They are placed on a smooth horizontal table with the string taut. A is projected towards B with speed 2u. After the collision between A and B the speed of A is halved and the direction of travel of A is reversed.

a) Find the speed of B after the impact

I have found this answer using the conservation of motion formula, getting the speed to equal u.

b) Find the common speed of the particles when the string is taut once more.

c) Find the impulse exerted on A at the instant when the string becomes taut.

Any help on parts b) and c) would be really appreciated!

Reply 1

ghostwalker

17

Original post by grace15

The question is:

Two particles A and B have masses M and 3M respectively. A and B are connected by a light inextensible string. They are placed on a smooth horizontal table with the string taut. A is projected towards B with speed 2u. After the collision between A and B the speed of A is halved and the direction of travel of A is reversed.

a) Find the speed of B after the impact

I have found this answer using the conservation of motion formula, getting the speed to equal u.

b) Find the common speed of the particles when the string is taut once more.

c) Find the impulse exerted on A at the instant when the string becomes taut.

Any help on parts b) and c) would be really appreciated!

b) Conservation of momentum. Once the string is taut the particles will both move with the same velocity.

c) Impulse = change in momentum. So, momentum of A after string taut minus momentum of A just prior to string going taut.

Reply 2

old_engineer

11

Original post by ghostwalker

b) Conservation of momentum. Once the string is taut the particles will both move with the same velocity.

c) Impulse = change in momentum. So, momentum of A after string taut minus momentum of A just prior to string going taut.

@ghostwalker no problem with your answers but part (b) of the question has been niggling away at me. The assumption seems to be that the string will go taut and that the two particles will then proceed at the same speed in the same direction. I can see that that could happen, but it's a bit like two particles colliding and coalescing, with loss of kinetic energy. It must be equally possible for the string to snap taut momentarily and for the particles then to recoil towards one another - indeed this would have to happen if both momentum and KE were conserved. I guess I'm just kicking back slightly at the implication in the question that the particles will naturally or necessarily move in tandem after the string has gone taut. Probably not a consideration for M1.