Calculating Bullet Speed Using a Freely Hinged Board

[Nevermore]

I'm doing this without a teacher, so this isn't really a homework question, but this still seemed the most appropriate forum.

I have the following question:
A square board, of side 2a and mass M, is to be used to estimate the speed of bullets. It is freely hinged about one horizontal edge and hangs at rest in a vertical plane. A bullet of mass m, traveling horizontally with speed V hits the borad at its centre and becomes embedded in it. The board then rotates through an angle x before coming to rest.
i) Show that the initial angular speed of the board is 3mv/(4M+3m)a

My attempt:
Using Conservation of Energy:
1/2mV^2 = 1/2Iw^2 (w = angular speed)
=1/2(4/3Ma^2 + ma^2)w^2
w^2 = (3mV^2)/(4M+3m)a^2

This almost gives the solution, but with some 'squarings' that I don't want. Any idea where I've gone wrong?

Thanks!

 

[George Jones]

While energy is conserved, kinetic energy is not, since some of the bullet's initial kinetic energy goes into heating and deforming the wood. Since it is not obvious how must energy goes into these processes, conservation of energy is not useful initially here. Conservation of (angular) momentum is useful.

Once the board starts swinging, conservation of energy can be used.

This thread probably should have been started in the Introductory Physics forum, as this is a math forum. Don't try and move it - maybe a friendly Mentor will come along and move it for us.

Regards,
George

 

[Nevermore]

Thanks for that. I posted it as math because it's part of the math course I'm doing.

 

[George Jones]

Thanks for that. I posted it as math because it's part of the math course I'm doing.

Interesting - I certainly have seen physics applications covered in math courses, but I don't think I've seen this one in a math coures. This type of question is typical for a first-year general physics course.

In any event, did you get it to work out OK? If not, just post some more questions.

Regards,
George

 

[Nevermore]

I've got it now, thanks for the help.