Collision around a pendulum

1. Mar 17, 2009

gregcor

1. The problem statement, all variables and given/known data
A pendulum consists of a mass M hanging at the bottom end of a massless rod of length l, which has a frictionless pivot at its top end. A mass m, moving as shown in the figure with velocity v impacts M and becomes embedded.

What is the smallest value of v sufficient to cause the pendulum (with embedded mass m) to swing clear over the top of its arc?

2. Relevant equations

$$p=mv$$

3. The attempt at a solution
I realize that the acceleration must be $$\frac{v^2}{l}=g$$ to swing over the arc. Thus, I found:

$$v_f=mv_i/(m+M)$$, and set Vf equal to $$\sqrt{lg}$$ from the first equation.

I got:
$$v_i=\frac{(m+M)\sqrt{lg}}{m}$$

But the software returned:
Code (Text):
Your answer either contains an incorrect numerical multiplier or is missing one.
Help!
Thanks!

2. Mar 17, 2009

LowlyPion

What is the top of its arc?

Is there a figure you can provide or describe in better detail?

3. Mar 17, 2009

gregcor

Sure. See the attachment.
Thanks!

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