Posts Tagged 'Mechanics'

The Spire of Light

 

Towering over O’Connell Street in Dublin, the Spire of Light, at 120 metres, is about three times the height of its predecessor [TM109 or search for “thatsmaths” at irishtimes.com]. The Spire was erected in 2003, filling the void left by the destruction in 1966 of Nelson’s Pillar. The needle-like structure is a slender cone of stainless steel, the diameter tapering from 3 metres at the base to 15 cm at its apex. The illumination from the top section shines like a beacon throughout the city.

spire-nightscape

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The Ping Pong Pendulum

Galileo noticed the regular swinging of a candelabra in the cathedral in Pisa and speculated that the swing period was constant. This led him to use a pendulum to measure intervals of time for his experiments in dynamics. Bu not all pendulums behave like clock pendulums.

PingPongPendulum

The ping pong pendulum.

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Which Way did the Bicycle Go?

“A bicycle, certainly, but not the bicycle,” said Holmes.

In Conan-Doyle’s short story The Adventure of the Priory School  Sherlock Holmes solved a mystery by deducing the direction of travel of a bicycle. His logic has been minutely examined in many studies, and it seems that in this case his reasoning fell below its normal level of brilliance.

As front wheel moves along the positive {x}-axis the back wheel, initially at {(0,a)}, follows a tractrix curve.

As front wheel moves along the positive x-axis the back wheel, initially at (0,a), follows a tractrix curve (see below).

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Emmy Noether’s beautiful theorem

The number of women who have excelled in mathematics is lamentably small. Many reasons may be given, foremost being that the rules of society well into the twentieth century debarred women from any leading role in mathematics and indeed in science. But a handful of women broke through the gender barrier and made major contributions. [TM070: search for “thatsmaths” at irishtimes.com ]

Death of the philosopher Hypatia, by Louis Figuier [Wikimedia Commons].

Death of the philosopher Hypatia, by Louis Figuier
[Wikimedia Commons].

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Falling Bodies [2]: Philae

The ESA Rosetta Mission, launched in March 2004, rendezvoused with comet 67P/C-G in August 2014. The lander Philae touched down on the comet on 12 November and came to rest after bouncing twice (the harpoon tethers and cold gas retro-jet failed to fire).

Comet 67P/Churyumov-Gerasimenko on 11 August 2014. The landing site is on the smaller knob, near the top of the image. Photo copyright ESA.

Comet 67P/Churyumov-Gerasimenko on 11 August 2014. The landing site is on the smaller knob, near the top of the image. Photo copyright ESA.

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Falling Bodies [1]: Sky-diving

Aristotle was clear: heavy bodies fall faster than light ones. He arrived at this conclusion by pure reasoning, without experiment. Today we insist on a physical demonstration before such a conclusion is accepted. Galileo tested Aristotle’s theory: he dropped bodies of different weights simultaneously from the Leaning Tower of Pisa and found that, to a good approximation, they hit the ground at the same time.

Aristotle and Galileo.

Aristotle and Galileo.

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Light Weight (*)

Does light have weight? Newton thought that light was influenced by gravity and, using his laws of motion, we can calculate how gravity bends a light beam. The effect is observable during a total eclipse of the sun: photographs of the sky are compared with the same region when the sun is elsewhere and a radial displacement of the star images is found. But the amount predicted by Newton’s laws is only half the observed value.

Solar-Eclipse Continue reading ‘Light Weight (*)’


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