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He found that:
The square of the Velocity is proportional to the initial Height, no matter the mass.
Today, it is proven that:
Velocity=sqrt(2*Height_of_theSlope*g)
The horizontal distance/range of the parabolic motion is proportional to the Velocity:
vx=Velocity*cos(angle)
x=Velocity*cos(angle)*t
The reproduction of Galileo’s experiment
The team tried to reproduce the experiment shown on pictures below using two metallic cylinders of the same volume, one solid the other hollow; thus, the cylinders have different mass: the solid is heavier than the hollow.
1. Calculated: vx=1.25 m/s, t=0.4 s x=0.5 m
Measured: x=0.39 m
2. Calculated: vx=1.25 m/s, t=0.4 s x=0.5 m
Measured: x=0.35 m
3. Calculated: vx=1.25 m/s, t=0.4 s x=0.5 m
Measured: x=0.35 m
4. Calculated: vx=1.72 m/s, t=0.5 s x=0.7 m
Measured: x=0.53 m
Conclusion
As shown above, the horizontal distance is similar for objects that fall from the same height, no matter their mass. Thus:
the final Velocity at the bottom of the ramp is similar for objects that “fall” from the same height h, no matter their mass.
Today, it is possible to measure the velocities (e.g. using position sensors).
Galileo didn’t have the proper measuring devices. He had to think another way.
We followed Galileo’s steps and proved that the velocities are similar just measuring the horizontal distances x!
No fancy stuff!! No expensive user unfriendly meters! Galileo was really brilliant!!! He taught us that in Science the only thing you really need is brains!!!
The students all over the world would really admire him if they had the chance to learn the methods he used in his experiments!!!
Bibliography
- www.sec.org.za/physics/p12mAvsG.html
- http://brunelleschi.imss.fi.it/catalogo/index.html
- www.bbc.co.uk/history/historic_figures/galilei_galileo.shtml
Iconography
- http://users.skynet.be/fb738062
- http://alexis.m2osw.com/images/galileo_person.jpg
- http://academic.shu.edu/honors/aristotle.jpg
- http://galileoandeinstein.physics.virginia.edu/tns_draft/tns_title.jpg
- www.tate.org.uk/shop/images/prints/stives/david_nash.jpg
