# Inelastic collision involving pulley

1. May 1, 2013

### issacnewton

Here is the problem I am trying

Two blocks A and B of same mass M are connected with
each other with an ideal string of length $2l$ passing over an
ideal pulley. The block A is connected to a light pan C
with an ideal string as shown in figure. A particle of mass
$\frac{M}{2}$ is dropped on pan from height
$\frac{l}{2}$ as shown. If
collision between particle and pan is plastic, acceleration
of B just after the collision is

a) $g$

b) $\frac{g}{9}$

c) $2g$

d) none of above

I have attached the snapshot of the problem. Now, I am thinking on the following lines. Since
the pan is light, when the mass M/2 falls on it, the string attached to the pan will feel the jerk.
And we can think of mass M/2 attached to the pan and accelerating downwards with acceleration g. Do you think this is a good starting point ? I am not sure if my reasoning is correct here...

thanks

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2. May 1, 2013

### haruspex

You don't think the pan and attached masses will reduce the acceleration at all?
Try doing the free body diagrams for the three masses when M/2 has reached the pan.

3. May 2, 2013

### Saitama

I don't know if issacnewton is willing to continue the thread but I would like to understand how to solve this. How did the OP conclude that the acceleration of the pan is g, is this even correct? Basically, how should I approach this problem?

4. May 2, 2013

### issacnewton

Sorry for late reply. I thought that since falling mass is going to hit the pan, its acceleration would be g. Probably this is wrong.

5. May 2, 2013

### haruspex

It's g before it hits the pan of course, but that's not what we want to know.
This is rather a curious problem. I don't know whether it intends to confuse by supplying irrelevant information, but it certainly does that.
It asks for the accelerations just after hitting the pan, not the velocities. So here's a question: do the velocities immediately after impact affect the forces at that time? If not, the history doesn't matter: we can just look at the free body diagram after impact, and not even care that an impact occurred.