MHB Max Velocity of a Pendulum Released from Rest

AI Thread Summary
The maximum velocity of a pendulum released from rest at height H is calculated using the formula v = √(2gh), assuming no air resistance. This assumption is equivalent to considering the system in a vacuum, confirming that external factors do not affect the maximum velocity. The discussion then shifts to the scenario of an elastic collision between two masses, where the final velocities are derived using conservation of momentum and kinetic energy. The equations for the final velocities are presented, but there is a query about potential simplification. Overall, the conversation focuses on the dynamics of pendulum motion and collisions in idealized conditions.
Dustinsfl
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A pendulum is released from rest at a distance y = H for the y = 0.

What is the max velocity?
\[
\frac{1}{2}mv^2 = mgh\Rightarrow v = \sqrt{2gh}
\]
where I assumed there was no air resistance.

Would anything change if the system was in a vacuum?
 
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Re: pendulum

Looks right to me.

Assuming that there is no air resistance is equivalent to assuming that the system is in a vacuum.
 
Re: pendulum

Now suppose the first mass has elastic collision with a second mass hanging at equilibrium.
I have solved for the final velocities using CoM and CoKE but can it be simplifies any further is what I am wondering.
\begin{align}
v_1^f &= v_2^f - \sqrt{2gh}\\
v_2^f &= \sqrt{2gh} + v_1^f
\end{align}
 
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