Calculating Bullet Speed Using a Freely Hinged Board

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Discussion Overview

The discussion revolves around a physics problem involving a square board used to estimate the speed of bullets after being struck by one. The scenario includes a freely hinged board that rotates upon impact with a bullet, and participants explore the application of conservation laws to derive the initial angular speed of the board.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes using conservation of energy to derive the angular speed, but expresses confusion over the squaring involved in their calculations.
  • Another participant argues that while energy is conserved, kinetic energy is not fully conserved due to energy loss in heating and deformation, suggesting that conservation of angular momentum is more applicable initially.
  • There is a discussion about the appropriateness of the forum for this question, with differing views on whether it belongs in a math or physics context.
  • A later reply indicates that the initial poster was able to resolve their issue with the problem after receiving feedback.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to solve the problem, with some advocating for conservation of momentum and others for conservation of energy, highlighting a disagreement on the applicability of these principles in this context.

Contextual Notes

There are unresolved assumptions regarding the energy lost to heating and deformation, which complicates the application of conservation of energy. The discussion also reflects a potential misalignment in the categorization of the problem within the forum.

Who May Find This Useful

Students studying introductory physics or those interested in the application of conservation laws in mechanics may find this discussion relevant.

Nevermore
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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!
 
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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
 
Thanks for that. I posted it as math because it's part of the math course I'm doing.
 
Nevermore said:
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
 
I've got it now, thanks for the help.
 

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