How the Hammer Throw Is Like a Particle Accelerator

Interesting comparison of hammer throw to the particle accelerator. Aivars Lode

The hammer throw, one of the most unusual events in the 2012 Summer Games, is a lot like a particle accelerator. For those who may not be familiar with the hammer throw, here’s a quick rundown:

• The goal is to throw a steel ball, attached to the end of a long cable, as far as you can.
• Men throw a 16-pound ball affixed to a cable that’s 3 feet, 11.75 inches long.
• Women throw an 8.82-pound ball affixed to a cable that’s 3 feet, 11 inches long.
• Competitors stand in a circle 2.12 meters in diameter and swing the hammer, spinning one to four times before releasing it.
• The world record for men is 86.74 meters, set by Yuriy Sedykh in 1986. For women, the record is 79.42 meters, set last year by Betty Heidler.

Simple, right? Not really. The hammer throw combines strength, balance and timing in an event that requires nearly perfect technique. So how does this make the hammer throw like a particle accelerator?

Here is a picture of the synchrotron at Fermi Lab:

Photo: U.S. Dept. of Energy

I would show you something from CERN, but it’s underground and you can’t see anything.

The goal of high-energy particle physics is to get these particles (like a proton) up to really high speeds and then smash them into something. One way of getting these protons moving really fast would be to just put them in a constant electric field. Constant field means constant force and constant acceleration. Simple, right? Well, simple except that you must have something to make this external electric field, something the proton would get out of pretty quick.

Still, they have linear particle accelerators. They are useful for some things, but they can’t get a particle moving as fast as a synchrotron. The two do essentially the same thing, but the big difference is that after the particle leaves the acceleration part of the synchrotron, it enters a magnetic field that curves it around in a circle so the particle can go through the acceleration part again.

Accelerating the particle in a circle increases the effective distance over which the force acts on the particle. Yes, I have simplified this process, but you get the idea. The same thing happens with the hammer throw. If an athlete tried to simply throw the hammer, do you know what would happen? They’d call it the shot put. And so here is a GRE question: The shot put is to a linear accelerator as the hammer throw is to….

The correct answer would be “synchrotron.”

How Fast Are These Hammers?

This is a little tricky. Let me start with the record for the men’s throw at 86.74 meters. I can calculate the initial speed when thrown if I make two assumptions. First, that the hammer was released at certain angle. Let me pick 45° above the horizontal (although I am sure this wasn’t exactly true). Second, that the air drag on the hammer during its motion is small enough to be ignored. I will check this after I have an estimate for the speed.

So, if the ball is thrown with an initial speed v0 at an angle of 45° above the horizontal, this looks like your plain old projectile motion problem. In these types of problems, the only force on the ball is the gravitational force acting downward. This would give a vertical (I will call it the y-direction) of -9.8 m/s²and a horizontal acceleration of 0 m/s². Since I know the two accelerations, I can write the following two kinematic equations.

Two important notes here. First, I have made the assumption that the hammer starts at the location x = 0 meters and y = 0 meters. Second, I put the vertical acceleration as -g where g = 9.8 m/s2. If I know the angle θ, how do I find the velocity? If I take the x-equation and solve for the time, I can substitute that expression into the y-equation and then solve for the velocity. If the ball starts and ends at the same height (essentially true) then:

Now, I can put in values for x = 86.7 meters and θ = 45°. This gives an initial hammer speed of about 29 m/s (or about 65 mph).

What About Air Resistance?

Is it ok to assume there is negligible air resistance? One way to answer this question is to calculate the acceleration of the hammer due to just the air resistance force and compare this to the acceleration due to the gravitational force. The typical model for the magnitude of the air resistance force looks like this:

In case you aren’t familiar with this model, here are some details:

• v is the magnitude of the hammer’s speed with respect to the air.
• ρ is the density of the air (with a value of about 1.2 kg/m3).
• A is the cross sectional area of the object. I will assume the hammer looks just like a sphere. This means the cross sectional area will be that of a circle.
• C is the drag coefficient. This depends on the shape of the object. A good estimate for a sphere would be about 0.47 (no units).

I can use a velocity of 29 m/s, but what about the radius? The official rules state the length of the hammer, but not the radius of the ball at the end. I wonder if the mass at the end even has to be round? So, let me just say that it is made of steel with a density of about 7800 kg/m³. If the mass of the ball is about 7.2 kg (I took off a small bit for mass of the cable), then this would give a ball volume of 9.2 x 10-4 m³. Assuming it is a sphere, this would give a radius of 6 cm. Now, I can put these values into the air resistance model and get a maximum force of 2.7 Newtons. This would cause an acceleration (due just to the air resistance) of 0.37 m/s². That’s pretty small compared to the vertical acceleration. I don’t think it is such a terrible idea to ignore the air resistance.

How Does This Even Work?

Now we are getting somewhere. How do you make a ball go faster by swinging it around in a circle? Honestly, I am not quite sure. This means it is experiment time. Step 1: Get daughter to swing ball around outside. Step 2: Record motion by standing on top of swing set (for overhead view). Step 3: video analysis.

Here is the video if you are interested.

Essentially, the string exerts a force on the ball. There are two things this force can do: It can change the speed of the ball or it can change the direction of the motion of the ball. Let me show two shots of this motion. In this first shot, the force is pulling partly in the same direction as the velocity of the ball.

When there is a force in the same direction as the velocity, it will cause the ball to accelerate. When the force is only perpendicular to the direction of the velocity, the force will only cause the ball to change directions. Here is an example of that part of the motion.

You can’t always be pulling the ball in the same direction that it moves or it would “get away from you.” Also, you can’t just pull on the ball perpendicular to the way it is moving or it would never increase in speed.

Moving back to the hammer throw, I suspect essentially the same thing happens. Yes, the person also moves forward during the throw, but I suspect this motion isn’t exactly essential.

Bonus Calculation: Distance Dependence on Launch Angle

Just how critical is this launch angle? If the assumptions of no air resistance and ending at the same height as the start are valid enough, then I can make a plot. This is a plot of the hammer distance as a function of launch angle with an initial speed of 29 m/s.

So you can see that by getting the launch angle off by 5° would shorten your throw. Instead of 86 meters, you would just get around 84 meters. Of course if you launch at 30°, you will take around 10 meters off your range.

Mars is Melting

Nasa studies show that Mars polar caps are melting I guess that is due to man made global warming as well and nothing to do with the influence of the sun? Aivars Lode

It's not every day you get to watch a planetary ice cap vanish, but this month you can. All you need are clear skies, a backyard telescope, and a sky map leading to Mars.

Actually, you won't need the sky map because Mars is so bright and easy to find.

Just look south between midnight and dawn on any clear night this month. Mars is that eye-catching red star, outshining everything around it. It's getting brighter every night as Earth and Mars converge for a close encounter on August 27th.

Above: Amateur astronomer Thomas Williamson of New Mexico took this picture of Mars on August 1st. He used an 8-inch telescope and a digital web camera. [more]

Mars has gotten so big in recent weeks that even a backyard telescope will show details on the planet's surface: dust clouds, volcanic terrains, impact basins. Best of all is the south polar cap. Made of frozen CO₂ or "dry ice," it reflects more sunlight than any other part of the planet. The southern hemisphere of Mars is tipped toward Earth and the bright cap is remarkably easy to see.

Don't wait too long to look, though, because the ice will soon be gone.

Like Earth, Mars has seasons that cause its polar caps to wax and wane. "It's late spring at the south pole of Mars," says planetary scientist Dave Smith of the Goddard Space Flight Center. "The polar cap is receding because the springtime sun is shining on it."

As the cap shrinks it develops rifts, dark spots, and a ragged border. Lately, for instance, amateur astronomers using 8-inch and larger telescopes have been watching a frosty mountain range emerge from the ice. Says Smith, "these are the Mountains of Mitchel"--named after the Ohio astronomer who first spotted them 150 years ago. A bold dark rift called Rimas Australis cuts through the polar ice just south of those mountains. (These features are visible in Thomas Williamson's photograph of Mars at the beginning of this story.)

Something else to look for is the "Cryptic region"--a dark zone hundreds of km wide. Even after the ice above it recedes, the Cryptic region remains remarkably cold according to infra-red cameras onboard NASA's Mars Global Surveyor spacecraft. No one is sure what the Cryptic region is, "but it's probably big enough to see from Earth," notes Smith.

Left: A brightness map of the martian south pole one Mars-year ago. The Cryptic region is the blue-green area around the 4 o'clock position. Reds and yellows denote frozen CO2. This map was created by Dave Smith using data from the 1 micron detector of the laser altimeteronboard Mars Global Surveyor. [enlarge]

Here's an amazing fact: The seasonal polar caps are made of martian air that freezes during winter. Depending on the time of year, more than a quarter of the martian atmosphere can be found lying on the ground around the poles. (The atmosphere is 95% CO₂; that's why the seasonal polar caps are made of dry ice.)

As seasons come and go, carbon dioxide shifts back and forth--lying on the ground during cold months, floating through the air during warmer months. The world-wide air pressure rises and falls by 25%.

For comparison, the air pressure inside a hurricane on Earth is often only a few percent lower than ambient. You can experience a full 25% difference in pressure by traveling from sea level to the top of a 9000 ft (3000 m) mountain. Just try running a 100 yard dash up there.

Right: The ups and downs of air pressure on Mars recorded by NASA's Viking Landers. [more]

The south polar cap is vaporizing now, which means CO₂is rushing back into the atmosphere. "Remember, though," adds Smith, "there are two polar caps on Mars--north and south. While the south polar cap is vaporizing the north polar cap is growing. It's a balancing act. Overall air pressure will be greatest when there's the least amount of CO₂ on the ground." The next such peak is due in early October--that is, early southern summer on Mars.

The boost in pressure has some interesting consequences. It won't make the martian atmosphere thick by Earth-standards. At best the air pressure on Mars is 100 times less than Earth. But it might become thick enough in some places for liquid water to flow.

NASA spacecraft have detected frozen water beneath the surface of Mars. Liquid water, on the other hand, is scarce. Why? On a warm summer day, ice doesn't melt, it vaporizes--skipping directly from solid to gas. This happens because the air pressure is so low. But a small boost in pressure could be enough to allow ice to melt and water to flow under a warm summer sun. Southern summer, therefore, might be a good time for future human explorers to visit. (For more information read Science@NASA's Making a Splash on Mars.)

On the other hand, thicker air also encourages dust storms, which are a big problem on Mars. Small dust clouds stirred by sun-warmed winds sometimes grow to encircle the entire planet. In 2001 such a storm lasted for months and frustrated astronomers who couldn't see through the haze.

Will that happen again this year? No one knows.

Dividends prove even more valuable in anxious times Read more: http://www.smh.com.au/business/dividends-prove-even-more-valuable-in-anxious-times-20120731-23czk.html#ixzz22dOkiFcE

As I have commented a number of times that dividends should provide at least some stability of income vs the pursuit of growth. Aivars Lode

BLOOMBERG group founder and current New York mayor Michael Bloomberg said last February that ''if somebody offers you a guaranteed 7 per cent on your money for the rest of your life, you take it and just make sure the guy's name isn't Madoff''.

The comment sounded more radical in the US than it did here. Until the global crisis, double-digit capital gains were the Holy Grail for US sharemarket investors. American groups that cycled a fair proportion of earnings back to shareholders in dividends were more often than not considered to be bereft of ideas and growth options.

Here in Australia, dividend yield has always been more important. Its central role was cemented in 1987 when the Hawke-Keating government introduced dividend imputation - a tax credit that recognises that dividends are paid by companies out of income that is already taxed, and one that is more valuable in the hands of investors when dividends are high, and company tax is paid at the top rate.

My colleague Ian Verrender pointed out yesterday that the global hunt for yield is creating a mismatch between the value of the Australian dollar, which is holding up, and commodity prices, which have been falling: the Reserve Bank's index of commodity prices fell by 13.3 per cent between August and June, but at more than $US1.05 yesterday the $A was not far from its July 27, 2011, high of $US1.10, and up more than 8 per cent in two months.

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Foreign buying of triple A-rated Australian government bonds that has almost halved yields in 18 months helps explain that unusual state of affairs, and the same search for yield is on in our sharemarket, where the big banks and Telstra are the defensive investor's Fabulous Five.

A ''risk-off'' rally like that one that began at the end of last week on reports that the European Central Bank was about to take action to shore up Spain and boost Europe's economic growth in theory makes defensive yield plays such as Telstra less attractive.

There was enough interest in the telco yesterday, however, to carry its shares above $4 for the first time since December 2008, and they have risen by 20 per cent so far this year in a market that has risen by 5.4 per cent overall. Westpac is up almost 17 per cent, CBA is up by just under 18 per cent, ANZ is 15 per cent higher and NAB is up 7 per cent.

Morgan Stanley's estimate is that since 1970 the shares in the MSCI global market index have risen an average of 5.1 per cent a year. The same shares have risen by 8.3 per cent on a total return measure that rakes in dividends, so share price gains have been the biggest contributor to the total gain.

Morgan Stanley US strategist Adam Parker and the MS global strategy team say, however, that the result is skewed by unusually large price gains in the 1980s and 1990s ''that are unlikely to be repeated going forward''.

Over the very long term dividends have accounted for about half the global sharemarket's growth, and they have been a crucial driver of shareholder returns since the crisis everywhere, including here. The S&P/ASX 200 benchmark index of top listed companies hit bottom on March 6, 2009, and is now 35 per cent higher. The ASX 200 accumulation index has risen 55 per cent over the same time, with the 20-percentage-point difference accounted for by dividends.

Dividends always boost returns, of course, but they are much more valuable to investors in markets that are under pressure, as they have been now for five years. The ASX 200 index's 146 per cent gain between March 2003 and November 2007 when the local market peaked became a 199 per cent gain after dividends, for example, a 36 per cent improvement. The same index's 31 per cent price loss since the the end of July 2007 when the markets were tipping into the crisis is more than halved to 14 per cent when dividends are included, and that dividend-enhanced total shareholder gain of 55 per cent since the market bottomed in March 2009 is 57 per cent better than the share price-only return.

The share gains already made by Telstra and the big banks have trimmed their dividend yields, but they are still magnets. Telstra is still on gross dividend of 10 per cent. NAB is yielding 10.15 per cent, Westpac 9.9 per cent, CBA 8 per cent and ANZ 8.6 per cent.

There are other high-yield niches including investment trusts and infrastructure funds, and in a recent report on high-yield shares that looks at yield but also earnings outlooks and balance sheet strength, Goldman Sachs nominates UGL group, Woolworths, Coca-Cola Amatil and CFS Retail Property Trust alongside ANZ as its top recommendations.

The Fabulous Five should remain popular, however. All shares carry price risk, but you could do worse than borrow Bloomberg's post-crisis playbook and lock in some of the quality yields this market is offering.

The unspoken truth about Apple

Apples products: are they high end, the best of the best or clever marketing? Regardless as I have said all along reality is all about perception. Aivars Lode

July 30, 2012: 7:43 AM ET

  

Despite its unparalleled cool factor -- and profits -- the Cupertino company's products aren't always the highest of the high-end.

By Don Reisinger, contributor

FORTUNE -- Apple has created a brand identity that, seemingly, no other company in the technology industry can match. And although the company's reputation is partly derived from its former charismatic leader, Steve Jobs, and a loyal fan base has always propped the iPhone maker up, Apple's products have become synonymous with high-quality, high-end devices that ooze high-tech "cool."

It's easy to see why. In the computing space, the company's aluminum-based Macs are the industry's beauty queens to Dell (DELL) and HP's (HPQ) black-box uglies. And in the smartphone and tablet markets, all other companies have tried desperately to mimic Apple's design philosophy with products that look awfully similar to their Cupertino-crafted counterparts. Apple's (AAPL) designs have proven so impressive that the company's design chief, Jonathan Ive, has won numerous design awards. He has even been knighted in the U.K. for his contributions to the industry.

Such sleek designs often convey a sense that Apple's products are of higher quality than their competitors. In fact, BrandIndex, an organization that measures consumer attitudes towards companies, found late last year that Apple's perception is exceedingly high, earning a score of 76 out of a possible 100. The company's iPod scored a 73, its iPad nabbed a 69, and the iPhone came in with a 65. The Mac followed with a 61.

MORE: Google's playbook won't work at Yahoo

But is that really warranted? Is Apple really the company that delivers the highest of the high-end? Not a chance.

Of course, such a claim is nothing new to tech experts that have been following the industry for years. Corporate IT decision-makers have consistently said that they can get more bang for the buck out of a Windows-based PC. But an increasing number of so-called "mainstream" consumers are now moving to Macs, iPhones, and iPads. Their perception, apparently, is that Apple is delivering the very best in terms of quality and value.

Although quality and value are subjective measures, seeing what consumers are actually getting for their hard-earned cash isn't so difficult to quantify. Let's take the iMac, a popular, all-in-one computer Apple sells at a price starting at $1,199. For that sum, consumers are getting Mac OS X, which is a plus, as well as a 21.5-inch screen. A 2.5GHz quad-core processor and 500GB hard drive help round out the offering.

There's just one issue: Dell has it beat -- by a mile. For just $850, consumers can buy an all-in-one PC with a 23-inch screen and the same 2.5GHz quad-core processor. Add that to the 1TB hard drive and 1080p display, and it's clear customers are getting a better value from Dell.

It's a similar story on the notebook side, where Apple is selling a 15-inch MacBook Pro for as little as $1,799. At that price, customers are getting a 2.3GHz quad-core Intel Core i7 processor, 4GB of memory, and a 500GB hard drive. Not bad, right?

MORE: Dark days ahead for Netflix?

Well, HP is offering customers a way to save $500 with a notebook boasting a 15.6-inch full HD screen that comes with a 2.2.GHz Intel Core i7 processor, 8GB of memory, and a 750GB hard drive. And its design isn't so dissimilar to the MacBook Pro's.

Even Apple's mobile products shouldn't be considered high-end.The iPhone 4S is nice, but it doesn't have the quad-core processor found in the HTC One X nor the 4G LTE service available in Samsung's new Galaxy S III. Apple's new iPad has a smaller screen (9.7 inches) than many of its chief competitors, like the Samsung Galaxy Tab 2, and its quad-core graphics are held back a bit by its dual-core processor. (Of course, the number of available apps is another matter...)

In terms of specs, therefore, it's hard to call Apple the highest of the high-end. The company has higher-end features, including the Retina display in its new MacBook Pro and mobile products. The truth is, however, that there are several companies delivering products with better components.

But quality components and value are two very different things.

Informed consumers know that they can buy cheaper products from Apple's competitors and get more powerful components, but the intangibles keep them coming back for iPhones and Macs. Apple's products look nicer, the company's store experience is more streamlined, and it's just "cooler" to be an Apple customer. One of the reasons many in the tech and design industries revere Jobs, of course, was his ability to know what to leave out of a product -- as much as what to put in, be it the most high-end or not.

So, maybe Apple doesn't need to be "high-end." Clearly, just being Apple is working out.

Used Lamborghinis Linger on H.K. Lots Amid China Lull

Chinas slowdown is imminent.  Aivars Lode

By Bloomberg News - Jul 29, 2012 12:47 PM ET

Waiting lists for ultra-luxury cars in Hong Kong are getting shorter and used-car lots are cutting prices on Lamborghinis, Ferraris and Bentleys in the latest sign of China’s slowdown.

At first glance, the numbers are deceiving: Sales of very expensive new autos surged 47 percent in the first six months, according to industry analyst IHS Automotive. Look more deeply, however, and another picture emerges, especially in the city’s used-car lots.

Enlarge image Used Lamborghinis Linger on Hong Kong Lots Amid China Lull

A model poses with a luxury Lamborghini SpA sports cars during the Shanghai International Circuit Club Challenge, in Shanghai, China. Photographer: Qilai Shen/Bloomberg

Dealers of such second-hand cars say job cuts and the worsening global economic outlook are creating uncertainty among the finance-industry and expatriate professionals who make up the bulk of their buyers. Morgan Stanley (MS), Citigroup Inc. (C) and Deutsche Bank AG are among firms with Asian headquarters in Hong Kong that are cutting jobs worldwide.

“The more expensive the car, the more dry the business,” said Tommy Siu at the Causeway Bay showroom of Vin’s Motors Co., the used-car dealership he founded two decades ago. Sales of ultra-luxury cars have halved in the past two or three months, he said. “A lot of bankers don’t want to spend too much money for a car now. At this moment, they don’t know if they’ll have a big bonus.”

Unlike Rolex watches, Gucci handbags and other luxury goods, Hong Kong’s car market hasn’t been distorted by the more than 28 million mainland Chinese who flocked to the city last year. Mainland shoppers spend 44 billion euros ($54 billion) on luxury goods while traveling overseas to locations such as Hong Kong and Europe, according to CLSA Asia-Pacific Markets.

‘True Look’

“In the car market, it’s not buying like watches,” said Booz & Co.’s Russo. “Here you are getting a true look at a category of product bought by Hong Kong buyers. It’s a pulse check on how Hong Kong residents view the stability of the financial system.”

The new-car figures look better because of some short-term developments. The release of the latest models from Ferrari and Lamborghini and the opening of the first Hong Kong showroom by McLaren -- maker of the 592-horsepower MP4-12C carbon-fiber coupe -- have given sales a bump. Meantime, depressed demand in Europe means a bigger allocation of new cars for Hong Kong dealers.

With the highest proportion of billionaires in the world, according to a Boston Consulting Group report released in May, Hong Kong has enough buyers unaffected by market conditions to keep new sales going, said Bill Russo, a Beijing-based senior adviser at Booz & Co.

‘Saying Something’

There were 273 new Bentleys, Lamborghinis, Rolls Royces, Ferraris, Aston Martins and McLarens sold in the six months to June 30, up from 186 in the first half of last year, according to Englewood, Colorado-based IHS. This outpaced the 23 percent gain in the U.S., the world’s richest nation, and the 40 percent jump in mainland China, the world’s biggest car market, IHS data show.

For these buyers, price isn’t an issue and settling for second-hand is not an option, Russo said.

“It’s the brand image and it says something about you,” said Russo, who was formerly Chrysler Group LLC’s China head. “Used-car buyers are more price sensitive and economic cycles will affect these shoppers more. They are paying for the cars with their income as opposed to their savings.”

The European debt crisis is slowing expansion in emerging markets including China, the International Monetary Fund said this month, when cutting its global economic growth forecast for next year to 3.9 percent from 4.1 percent.

Aspirational Buyers

Hong Kong’s economy eked out 0.4 percent growth in the first quarter, the slowest since escaping the recession caused by the 2008 global credit crisis. Average daily turnover on the city’s stock exchange, the world’s fourth biggest, was 22 percent lower in the first half than the corresponding period of 2011. Asia-Pacific takeovers have dropped 22 percent to $306 billion, according to data compiled by Bloomberg.

People shopping in the second-hand market are typically aspirational buyers who are more likely to sit it out rather than trade down when they can’t afford the brand they want.

“An uncertain economic outlook encourages consumers, particularly those without a buffer provided by sizeable financial assets, to pause on big-ticket purchases,” said Tom Rafferty, a London-based Economist Intelligence Unit analyst.

Vin’s Siu said the drop in high-end customers who typically account for 30 percent of turnover at his 300-lot business was the most important factor behind a 20 percent drop in total sales. Expatriates made up about 70 percent of customers, he said. “A lot of expats are leaving Hong Kong,” he said. “For every 10 who are leaving, two are coming.”

Mercedes Discount

To spur demand, dealers in pre-owned cars are slashing their prices -- together with how much they’re willing to pay sellers.

A yellow, 2011 Lamborghini Gallardo 550 recently listed for HK$2.88 million ($371,000) on second-hand car website 28car.com is about $830,000 cheaper than a new model -- chump change that would buy a new Mercedes E-Class Coupe to run the kids to school. A silver-gray 2011 Ferrari California with 980 kilometers (613 miles) on the clock is available for HK$2.68 million. That’s a 19 percent discount to a brand new 2012 vehicle, and HK$400,000 cheaper than a 2011 version sold by Ferrari’s official in-house used-car dealer.

“We started cutting prices at the beginning of the year to stimulate sales because the market was slow,” said Tony Chan, a director at GP Motors a short walk up the hill from Vin’s, adding that second-hand Ferraris and Bentleys are leaving the 30-lot dealership at half the speed of last year.

Someone looking to sell a 2009 Bentley Continental will have to accept HK$1.7 million, a third less than they would have received at the start of the year, Chan said.

In the basement automall beside Hong Kong’s Grand Hyatt hotel, trader Samuel Chui said he has stopped buying more cars.

“People want cash now, they don’t want the commodity,” said Chui, who reduced the number of car lots he rents from 15 to nine at the end of last year as business began to slow. “We’ve got plenty of stock and it’s not moving.”