I'm searching for a theme for my matura project

  • #1
cyberspacy_
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Hello

I'd like to write my matura project on a topic of physics. But I can't really find a topic. I think I'd like to do something in the field of mechanics with reference to everyday life. The project requires an input of myself in this work, that means, i have to do something empirical and not only using secondary sources. Does someone have an idea what would be easy to implement and at the same time interesting to investigate and write about?

Thanks for some ideas
cyberspacy
 
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  • #2
Welcome to PF.

cyberspacy_ said:
I'd like to write my matura project on a topic of physics.
What's a matura project? Are you in university or high school? What year are you? What have you been studying in your Physics classes most recently?
 
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  • #3
The first thing that came to my mind was statics. You could investigate the mechanical load of different materials (glass, wood, concrete with and without armor, etc.)
 
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  • #4
1) Another possible project would be the study of the motion of a frisbee or the mechanics a Roman siege engine ie catapult, trebuchet, or ballista.

2) The ballista is interesting because it used the torsion of twisting ropes to store energy. The Romans built a smaller version called a scorpio on the same principle.

3) Yet another would be longbow vs crossbow vs mongol shortbow. You could calculate arrow speed and distance.

4) Model rocketry has a lot of mechanics.

5) The physics behind famous bouncing bomb of WW2.
 
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  • #5
berkeman said:
Welcome to PF.What's a matura project? Are you in university or high school? What year are you? What have you been studying in your Physics classes most recently?
It's kind of a final work we do in Switzerland after six years of high school and I'm in my fifth year of high school but I had physics in school for only two years. Recently we studied mechanical and aucustic waves, conservation of momentum and energy conservation (really basic stuff). A colleague of mine for example studied the double pendulum (so you can imagine the required difficulty)
 
  • #6
The double pendulum is already not that trivial!

I don't know, how complicated things must be, but already the "simple pendulum" would be a nice research project, which gives plenty of opportunities for both theoretical and experimental work. A rough project would be:

(a) derivation of the equation of motion: ##m L^2 \ddot{\phi}=-m g \sin \phi##, where ##\phi## is the angle with respect to the direction of ##\vec{g}##. The most simple case is where a mass is tight to a much lighter rope ("mathematical pendulum"). Then you can derive the equation of motion by analyzing the forces (gravitational field of the Earth + tension of the rope) on the body and writing down Newton's equation of motion, ##\vec{F}=m\vec{a}##.

More challenging is a rigid body fastened to rotate around a fixed axis, for which you need in addition the moment of inertia, center of mass, etc.

(b) Analyzing the solutions, which is tricky. The equation of motion cannot be solved with the standard elementary functions you are used to (it leads to socalled elliptic functions), but you can demonstrate energy conservation easily as an exact analytical result.

Next you can consider small excitations around the static solution ##\phi=0##, i.e., small amplitudes, where you can set ##\sin \phi \approx \phi##. Then you get "harmonic motion", and you can discuss the solutions of linear differential equations of 2nd order, finding the complete solutions (as superposition of two linearly independent solutions, ##\cos(\omega t)##, ##\sin (\omega t)##. In this approximation the frequency ##f=1/T=\omega/(2 pi)## is independent of the amplitude.

(c) Using the energy-conservation law next you can find the integral determining the exact period of the pendulum, which depends on the amplitude, but this integral is not solvable with elementary functions, but you can derive a series expansion in powers of the amplitude, calculating corrections to the amplitude-independent ##\omega##.

Alternatively you can also try perturbation theory with the amplitude as the expansion parameter. This is, however very amititious on the high-school level.

(d) Experimentally you can use the pendulum to determine the gravitational acceleration, ##g## at your place (using small-amplitude oscillations as a first approximation and discussing the systematical errors using this assumptions etc.). In addition you can also study the dependence of the period on the amplitude and compare it to the theoretical estimates of item (c).
 
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  • #7
Coupled oscillators can show some interesting behavior, see these coupled metronomes. If you want to do something with acoustics, you could think about measuring the intensity of sound from a piano for given key strike velocities, and maybe you could move the decibel meter around in the room to map out how the sound waves are distributing.
 
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