# Student question on Forces

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1. May 16, 2017

### Schwarzenberger

Hi everyone!

I have few questions which I think might actually be simple, but I would like some confirmation if possible.
Here's the situation:
I am doing a research project for my MSc. in Forensic Anthropology. The goal of my project is to study the marks left on bones by bladed weapons (in this case, axes) depending on the force applied. I have a device which allows me to fix an axe on it an to "swing" it to hit a bone. The arm on which the axe is fixed measures 51.9 cm, and weight 5143g. The weight of the axes varies between 650g and 1Kg.

My questions were:
- Given that I study the force applied, is it possible to estimate the angle at which I should swing the axe to obtain the same force every time (with every axes)?
- How can I calculate the surface area of the cutting edge of the blade?
- Should I use the formulae to calculate the force of a pendulum?

Thanks a lot!

2. May 16, 2017

### mastrofoffi

I'm definitely not an expert on the subject, but this sound interesting to me so this is how I would do it if I had to; maybe others can point out errors in my approach.

I think a Palmer screw is the right instrument to measure the thickness $h$ of your axes' edge: https://en.wikipedia.org/wiki/Micrometer.
To estimate the length $l$ I would put the tip of the axe's edge on a plywood board, apply some pressure, and then roll it all over; the cut left on the plywood should be, to an acceptable degree of accuracy, the stretching of a circular arc over a plane, and then you can measure it with any simple ruler.
At this point your surface will be $S = hl$

With regard to the "swing angle", I assume your device is somewhat like a torsion pendulum, where you put your axe in an initially stable equilibrium position and then you can pull it back, describing an angle $\alpha$, and in the moment you let the axe go torque swings your axe back toward the equilibrium position. If my interpretation is right then yes, you can estimate the angle at which you should swing your axe to obtain a certain force just by setting up the differential equation for an oscillator.

3. May 16, 2017

### Nidum

Google ' Charpy Impact Test ' and ' Charpy Impact Test Formula '

4. May 16, 2017

### Schwarzenberger

Thanks a lot for your replies!
It actually make a lot of sens to me, which I hope is a good thing.

Concerning the angle, the device is like a rectangular frame (small sides up and down and long sides on the right and left) with a swinging arm fixed on the upper side. I though about tapping an axe on it and then pull the arm back to a certain angle, and let it fall forward to hit the bone. I have a laser I can use to measure the speed of the axe.

I will try to figure out how to determine the angle, because I guess the weight of the axe (added to the weight of the arm) will have a major influence on it.
This may be a silly question, but does a force changes proportionally to the angle? For example, if I use a 600g axe and an angle of 20°, will the force be twice as big if I use an angle of 40°?

Thanks again!

5. May 16, 2017

### Nidum

(1) The actual cutting action will generally involve shearing , elastic deformation , plastic deformation , stress concentration and crack propagation .

(2) Do you understand what potential and kinetic energy are and how to use them to solve dynamics problems ?

6. May 16, 2017

### Schwarzenberger

I have to admit that my knowledge in that area is very limited. I would need to do some reading to understand that.