# Collision around a pendulum

#### gregcor

1. Homework Statement
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. Homework 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:
Your answer either contains an incorrect numerical multiplier or is missing one.
Help!
Thanks!

Related Introductory Physics Homework Help News on Phys.org

#### LowlyPion

Homework Helper
What is the top of its arc?

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

#### gregcor

What is the top of its arc?

Is there a figure you can provide or describe in better detail?
Sure. See the attachment.
Thanks!

#### Attachments

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