How a Ballistic Pendulum works.

[Nge Zhen Yang]

Hello there. Recently I was tasked to design a lab experiment using a ballistic pendulum.
Now I understand that all the sources of the internet say that by principle of conservation of linear momentum,
(1/2)(m+M)V2 = (m+M)gh , or V2 = 2gh
And then using principle of conservation of energy, we can equate the following:
v = [(m+M)/m]√(2gh) , or better, v = [1+(M/m)]√(2gh)

Here is what I do not get, however. For the ballistic pendulum, the catcher is effectively the mechanism that stops the motion of the pendulum, and the collision is definitely inelastic. However, the equation above seems to suggest that energy is entirely conserved (assuming pivot of pendulum is frictionless)
I just cannot wrap my mind around this concept, and would greatly appreciate some enlightening, thank you very much!

 

[mfb]

Your equation is not for the original capture process, it only describes the pendulum part after the collision happened. Mechanical energy is conserved in this part of the process.
You need another equation for the collision process.