Monthly Archives: January 2015

Arts, History, Science, Society

Quantum Leaps: Archimedes…

c. 287 – 212 BC

“Give me a place to stand on, and I will move the earth,” Archimedes is reputed to have declared to the people of Syracuse. The practicalities of an earth-bound life may have denied him that particular pedestal but arranging for his patron King Heiron to move a ship by pushing a small lever was considered only a slightly miraculous feat. With such audacious displays, along with his brilliance as an inventor, mechanical scientist and mathematician, it is no wonder Archimedes was so popular and highly regarded among his contemporaries.

The Mathematician

It was not only his peers, however, who benefited from Archimedes’ work. Many of his achievements are still with us today. First and foremost, Archimedes was an outstanding pure mathematician, “usually considered to be one of the greatest mathematicians of all time,’ according to the Oxford Dictionary of Scientists. He was, for example, the first to deduce that the volume of a sphere was 4πr³ x 3, where r is the radius. Other work in the same area, as outlined in his treatise On the Sphere and Cylinder, led him to deduce that a sphere’s surface area can be worked out by multiplying that of its greatest circle by four: or, similarly, a sphere’s volume is two-thirds that of its circumscribing cylinder. He calculated pi to be approximately 22/7, a figure that was widely used for the next 1500 years.

The Archimedes Principle

Archimedes also discovered the principle that an object immersed in a liquid is buoyed or thrust upwards by a force equal to the weight of the fluid it displaces. The volume of the displaced liquid is the same as the volume of the immersed object. Legend has it that he discovered this when set a challenge by King Heiron to find out whether one of his crowns was made of pure gold or was a fake. While contemplating the problem Archimedes took a bath and noticed that the more he immersed his body in the water, the more the water overflowed from the tub. He realised that if he immersed the crown in a container of water and measured the water that overflowed he would know the volume of the crown. By obtaining a volume of pure gold equivalent to the volume of water displaced by the crown and then weighing both the crown and the gold, he could answer the King’s question. On making this realisation, Archimedes is said to have leapt from his tub and run naked along the street shouting ‘Eureka!’, ‘I have found it!’

Levers and Pulleys

Indeed, it was the practical consequences of Archimedes’ work which mattered more to his contemporaries and for which he became famous.

One such practical demonstration allowed King Heiron to move a ship with a single small lever – which in turn was connected to a series of other levers. Mathematically, he understood the relationship between the lever length, fulcrum position, the weight to be lifted and the force required to move the weight. This meant he could successfully predict outcomes for any number of levers and objects to be lifted.

Likewise he came to understand and explain the principles behind the compound pulley, windless, wedge and screw, as well as finding ways to determine the centre of gravity in objects.

Archimedes goes to war

Perhaps the most important inventions to his peers, however, were the devices created during the Roman siege of Syracuse in the second Punic War. The Romans eventually seized Syracuse, due to neglect of the defences, and Archimedes was killed by a Roman soldier while hard at work on mathematical diagrams. His last words are reputed to have been, ‘Fellow, do not disturb my circles!’

Further achievements

Inventions

. Archimedes’ Screw: a device used to pump water out of ships, and also to irrigate fields.

. Archimedes’ Claw: a huge war machine designed to sink ships by grasping the prow and tipping them over, used in the defence of Syracuse.

. Compound pulley systems: enabled the lifting of enormous weights at a minimal expenditure of energy.

. The method of exhaustion: an integral-like limiting process used to compute the area and volume of two dimensional lamina and three-dimensional solids.

Discoveries

. Archimedes was responsible for the science of hydrostatics, the study of the displacement of bodies in water. He also discovered the principles of static mechanics and pycnometry (the measurement of the volume or density of an object).

. Known as the ‘father of integral calculus’, Archimedes’ reckonings were later used by, among others, Kepler, Fermat, Leibniz and Newton.

. Science Book

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Science, Society, Technology

Questions of Science: The Large Hadron Collider…

Why does the Large Hadron Collider (LHC) have to be so physically large, when it is only designed to detect particles that are extremely tiny?

The LHC is a synchrotron, a circular accelerator that uses carefully synchronised electromagnetic fields to accelerate particles to very high speeds. When this involves charged particles on a curved path they release synchrotron radiation, which wastes energy. This is not desirable because most of the particles that physicists are looking for, such as the recently discovered Higgs boson, have large masses and can only be created in high-energy collisions.

The large radius of the LHC’s track is big enough to limit the radial acceleration given to the particles, thus minimising the loss of energy the particles suffer as synchrotron radiation. The superconducting magnets used to control the flow and direction of the particles can accelerate them up to speeds in excess of 99.99 (but less than 100) per cent of the speed of light.

The magnets lie central in answering the question. The size of the LHC is actually a trade-off between three things: the magnets that are available; the energy (or velocity) it is necessary to give the particles; and, the feasible dimensions of the structure.

The faster the particles are moving, the more likely you are to see something interesting happen in a collision. So, it’s important to accelerate the particles, mainly protons, as much as possible.

The protons need to follow a circular path so they can be continuously accelerated by an electric field, and this is done using magnets positioned around the tunnel. The faster the protons travel, the stronger the magnetic fields need to be to keep them on track.

To increase energy there are two possible choices: make the magnets stronger or the accelerator ring larger, so that the particles’ path does not need to be bent so much. At some point there is either a technological or financial limit on the strength of the magnets, leaving the ring size as the only remaining variable.

However, to keep the costs of the project manageable, the LHC was built in an existing tunnel that housed a previous experiment, called the Large Electron-Positron Collider. So the energy to which protons can be accelerated was actually predetermined by limits of technology and funding.

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Arts, Drama, Legal

The Case Of The Flying Toy…

The judge presiding over the case.

The judge presiding over the case.

LADIES AND GENTLEMEN OF THE JURY:

When a person invents something, that invention can be legally protected. The inventor makes an application, and if the invention is found to be original, the Patent Office sends the inventor an official document called a patent. This prevents other people from using the inventor’s idea.

The case you are asked to judge today involves a patented toy called SPIRALWIZ. This unusual flying toy has been sold worldwide by Backwards Industries Incorporated.

Last year, Andrew Dobbs, who is the owner of a small plastics company, began selling an identical toy. He named it FLYFLIP.

Backwards Industries, the plaintiff, has asked the court to stop Andrew Dobbs from selling FLYFLIP because it is a copy of their invention. But Mr Dobbs, the defendant, claims that his grandfather invented FLYFLIP 30 years ago, long before Backwards Industries had the idea.

A scientist for Backwards Industries has given the following testimony:

“My name is Dr Robert Franklin. You might think all scientists are strange people who walk around carrying test tubes and never have any fun, but at Backwards Industries we’re not like that. In fact, my job is to sit around all day and think up ideas for new toys. I invented SPIRALWIZ for Backwards Industries.

“SPIRALWIZ is one of the most unusual flying toys ever invented. When you fling it in the air, it travels straight ahead. Then it rises skywards, flips upside down, and floats gently back into your hand.”

EXHIBIT A below is a photograph of this amazing toy.

As proof that SPIRALWIZ is an original invention, Backwards Industries also submitted EXHIBIT B, see below. This is the patent issued to the scientist from Backwards Industries who claims to have invented SPIRALWIZ.

Andrew Dobbs challenges Backwards Industries. In claiming that the toy was an old idea of his grandfather’s, he offers the following testimony:

“As a boy, I remember Grandpa telling me about his idea for a toy that would fly back into the hands of the person who threw it. He was working on it for a long time. Then he surprised me one day when he brought home this fantastic gadget.

“We went out in the garden and he showed me how it worked. We took turns throwing the toy in the air. We played with it all afternoon. But Grandpa had no idea of ever selling it as a product. He just worked on his idea for the fun of it. In fact, the next day he was busy working on another invention, musical gum that plays a tune as you chew it.”

While no one else saw Grandpa Dobbs’ toy, Andrew Dobbs claims that his grandfather kept careful records. He had notebooks for all his inventions and they were stored in the attic when the old man died.

Mr Dobbs located his grandfather’s notes. EXHIBIT C, below, is the last page of the notebook that shows a drawing of the toy. You will observe that the sketch is identical to SPIRALWIZ that Backwards Industries claims to have invented.

No one saw a working model of Grandpa Dobbs’ toy besides Andrew Dobbs. But Mr Dobbs offers the testimony of a friend who knew of his grandfather’s experiments.

“My name is Charlie Watson. Grandpa Dobbs was a good friend of mine. I know, I know… you think it’s funny that I called him Grandpa when we weren’t even related. But that’s what everybody called him. I spent a lot of time with him when he was working on that crazy toy idea.

“Every day, for three weeks, I drove him to a remote field on the outskirts of town. Grandpa didn’t want anyone to see him working on his invention. To reach the field, we had to drive down a long, bumpy road that few people in the town knew.

“I never bothered Grandpa while he was trying to get the toy to work. I just went digging in the road, looking for unusual rocks for my geology collection. The road was covered with stones and rocks of all kinds. I used to find a lot of garnet and tourmaline.

“I clearly remember the last day we went to the field together. I was busy examining a large boulder when Grandpa ran over to me very excited. He said he had finally got his flying invention to work.

“But Grandpa wouldn’t show me the toy. He was very secret about all his inventions.

“As we drove home, Grandpa began writing in his notebook. He wouldn’t even show me what he was writing. Then he slammed the notebook shut. He said, ‘I’m glad that’s finished. It took a long time to get that toy to work. Now on to my next invention.’”

A lawyer for Backwards Industries claims the drawing in EXHIBIT C is a fake. He has stated:

“Except for the sketch on the last page, the notebook contains no written description of the invention – or statement that it even worked. There are no other drawings in the notebook.

“In fact, in his notebook, Grandpa Dobbs wrote about his experiments that failed. He never wrote that he could get the toy to work properly. And it seems strange that he would not show the invention to his friend, Charlie Watson. Could he have been ashamed that he had failed to get his toy to work?

“No, old Mr Dobbs never got his flying toy to work. In fact, we believe his grandson, Andrew Dobbs, really drew the sketch himself. He knew he would have to stop selling FLYFLIP if Backwards Industries could prove to the court that the invention was theirs.”

 

LADIES AND GENTLEMEN OF THE JURY:

You have just heard the Case of the Flying Toy. You must decide the merit of Backwards Industries’ claims. Be sure to carefully examine EXHIBITS A, B and C.

Was Grandpa Dobbs the original inventor of the flying toy? Or was the drawing in his notebook a fake?

EXHIBITS:

EXHIBIT A

EXHIBIT A

EXHIBIT B

EXHIBIT B

EXHIBIT C

EXHIBIT C

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