Newtonian Mechanics


posted Tuesday, 17 August 2010

Excerpt from the section on Work.

The SI unit of work is the joule.

[ J = Nm = kg m2/s2 ]

Work and energy can be expressed in the same units. Unfortunately, there are a lot of units for energy beside the joule. (This is discussed in another section of this book.) The ones most commonly seen in the US in the early Twenty-first Century are probably calorie (diet and nutrition), Btu (heating and cooling), kilowatt hour (electric bills), therm (natural gas bills), quad (macroeconomics), ton of TNT (nuclear weapons), erg (older scientists), and foot pound (older engineers). The first two in this list, the calorie and the Btu, were first introduced by Nineteenth Century scientists studying calorimetry. (The French gave us the calorie and the English gave us the British thermal unit or Btu.) The last one in the list, the foot pound, was introduced by Nineteenth Century scientists studying mechanics. In the Nineteenth Century, calorimetry and mechanics were separate disciplines. Calorimetry is the study of heat. Mechanics is the study of motion and forces. A learned gentleman (and they usually were men at this time) might study both, but he probably didn’t link them in any significant way. That is, unless his name was Joule.

James Prescott Joule (1818–1889) was a wealthy English brewer who dabbled in various aspects of science and economics. Sometimes these endeavors overlapped. He invented the foot pound as a unit of work. (Foot being the unit of displacement and pound being the unit of force.) This enabled him to quantitatively compare the "economical duty" of different mechanical systems. Coal-fired steam engines were the primary source of industrial might at the time, but electricity was emerging on the high tech horizon. Joule realized that mechanical work, heat, and electric energy were all somehow interconvertible. Heat can do work. Work can make heat. Work can make electricity, Electricity can do work, Electricity can make heat. Heat can make electricity. Energy was something that could take on multiple forms.

Joule’s most famous experiment is probably the determination of the mechanical equivalent of heat (to be discussed in more detail elsewhere in this book, I hope). Heat was measured in British thermal units (by the British at least) and work was measured in foot pounds (which Joule invented). Joule established that one British thermal unit of heat was equivalent to approximately 770 foot pounds of mechanical work. (Very close to today’s value of 778 ft lb/Btu.) This result was essential in the realization that, despite appearing in multiple forms, energy was one thing.

The International System of Units which began to dominate the scientific world in the mid-Twentieth Century was French in origin. Foot pounds and British thermal units had no place in this much more logical and consistent system. 12 inches in a foot. 16 ounces in a pound. 128 ounces in a gallon in the US and who knows how many in the UK. The math was much too difficult. Parlez-vous les unités métriques? The SI was French in origin, but international in nature. When the call went out to name the unit of energy, the answer was Joule! Absolument!

What’s weighs a newton?

posted Sunday, 25 April 2010

The newton is a unit of force. Weight is a force that we are all familiar with. Which of the following fruits has a weight that is closest to one newton?

macintosh apple red delicious apple cavensish banana
McIntosh Apple (151.3 g) Red Delicious Apple (216.4 g) Cavendish Banana (160.0 g)
valencia orange tangerine tomato
Valencia Orange (178.0 g) Tangerine (96.7 g) Tomato (152.8 g)
chicken egg    
Chicken Egg (65.9 g)    

Use the weight formula.

W = m g

Solve for mass. Substitute one newton for weight and one standard earth gravity for gravity.

m =  W  =  1 N  = 0.102 kg = 102 g
g 9.8 m/s2

The 96.7 gram tangerine comes closest to this value. Not all tangerines weigh 98.7 grams, however, so this is only a rule of thumb. There are certainly apples, bananas, oranges, tomatoes, and other fruits out there with a mass of approximately 102 grams and a weight of approximately one newton.

Those of you familiar with multiple choice tests should have eliminated the chicken egg as a possible answer. A chicken egg is only metaphorically the "fruit of the chicken".

A related problem for Americans only. Verify the rule of thumb that one newton is approximately equal to a quarter pound.

Here’s the way I usually do it — using values I’ve memorized from years of use.

 W =  mg 
 2.2 lb =  (1 kg)(9.8 m/s2) 
  1 lb =  4.45… N 
 1 N =  0.224… lb 

Here’s a more accurate way to do it — using values that are exact by definition.

 W =  mg 
 1 lb =  (0.45359237 kg)(9.80665 m/s2) 
 1 lb =  4.44822162… N 
 1 N =  0.224808943… lb 

Not quite a quarter pound, but you get the idea.

0.20 lb  <  0.224808943… lb  <  0.25 lb
 ⅕ lb   <  1 N  <  ¼ lb

The fraction 9/40 gives a decimal expansion of 0.225, which is accurate to three significant figures. Not my favorite fraction, but it gets the job done. With sixteen avoirdupois ounces in a pound, one newton is also about 3½ ounces.

1 N ≈  9 lb  ×  16 oz  =  18 oz  = 3½ oz
40 1 lb 5

Science caught in the Web 2010-04-17

posted Saturday, 17 April 2010

  • space stations (centrifugal force)

Science caught in the Web 2010-04-03

posted Saturday, 3 April 2010

Frisbee patent family tree

posted Sunday, 14 February 2010

Walter Frederick Morrison, inventor of the Frisbee, died Tuesday, 9 February 2010 at the age of 90. US design patent 183,626 for a “flying toy” was issued to Morrison on 30 September 1958. The Wham-O toy company (which also sold the hugely popular hula hoop) bought the rights to the Frisbee from Morrison in 1957 in return for lifetime royalties.

Patent writers are required to cite "prior art". Morrison cited three US and one French patent in his application. He was in turn cited by at least 16 later patents — including a redesign of the Frisbee by Wham-O employee Ed Headrick, who claims to have been the toy’s true inventor. Headrick’s patent has been cited at least 81 times.

US Patent D137521 US Patent 1404132 US Patent 2690339
US Patent D183626
US Patent 4212131 US Patent 5290184 US Patent US Patent D266528
US Patent D295429 US Patent D310692 US Patent <empty>D346413 US Patent D346626
US Patent D347452 US Patent D349930 US Patent D390282 US Patent D405847
US Patent D464380 US Patent D552690 US Patent 5721315 US Patent 3359678

Science caught in the Web 2010-02-06

posted Saturday, 6 February 2010

Science caught in the Web 2010-01-30

posted Saturday, 30 January 2010

Science caught in the Web 2010-01-23

posted Saturday, 23 January 2010

Compressed Air Magazine

posted Friday, 1 January 2010

Compressed Air Magazine (CAM) was established in 1896 "to promote the capabilities of compressed air" — a new technology at the time. Compressed air is still important at the dawn of the Twenty-first Century, but the first few decades of this periodical are more fun to read than the current editions. (Check out the selections at the end of this post.) All 114 years are available for free — if you register — through the CAM website. Google Books has managed to scan a few volumes as of 2010. The Google scans look nicer, but the CAM website is absolutely complete and up to date.

I came across this particular article in after watching a documentary on Russia Today about the Moscow subway system. Twenty minutes into the video, a subway motorman comments on unusual barometer readings in certain tunnels. As he says this, he waves his hands in front of his instrument panel.

Is this a common event? Is barometric pressure routinely measured by subway motormen? I still don’t know, but a quick search turned up this article in CAM.

The author measured the barometric pressure in the first and last cars of a 1914 New York City subway train. At the time, the subway system was less than a decade old an consisted of only a single line — one that started in Brooklyn, ran up the east side of Manhattan, went crosstown on 42nd Street, continued uptown on Broadway, and ended in the Bronx. (This route is now a part of three different subway lines.) He was able to measure pressure variations caused by elevation changes and by position within the train. The latter of these effects would have been much more subtle in 1914 when subway trains were only three cars long. (Trains are now eight cars long on these lines.) I see a potential problem for The Physics Hypertextbook in here somewhere.

Flipping through the pages of this book brought me to this next data gem about a pneumatic grain elevator.

Mass flow rate appears to be directly proportional to the horsepower of the motor. Once again, how do I make this into a problem for The Physics Hypertextbook? Please enjoy the following selections from Compressed Air Magazine as you prepare your answer to these questions.

gas mask patent

The Hand of Google

posted Monday, 28 December 2009

I was trolling the Internet the other day looking for historical quotes about energy. I came across this mysterious image on the third page of a book at Google Books.

Behold, the hand of Google. Note that the hand of Google only needs to protect its fingertips. Competitors take note. The palm of the hand of Google is unprotected.

I also found the quote I was looking for. It’s one of the first written examples of the word energy being used in its modern sense.

The term energy may be applied, with great propriety, to the product of the mass or weight of a body, into the square of the number expressing its velocity.

This quote is from Thomas Young — of Young’s modulus and Young’s double slit experiment. I found it in Volume I of his 1807 magnum opus A Course of Lectures on Natural Philosophy and the Mechanical Arts. The image with the pink tipped hand came from Google’s copy of Volume II. They do not have a fully searchable copy of Volume I available yet. I had to go to U Penn’s Online Books Page to find both volumes. Volume I has all the text, so if you’re looking for a good Young quote start here. Volume II is mostly diagrams, so if you’re looking for old-timey scientific images for your website or ID3 art start there.