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Newtonian Mechanics

Joule

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!

physics.info/news/?p=2538

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

physics.info/news/?p=1567

Science caught in the Web 2010-04-17

posted Saturday, 17 April 2010

  • space stations (centrifugal force)

physics.info/news/?p=1477

Science caught in the Web 2010-04-03

posted Saturday, 3 April 2010

physics.info/news/?p=1353

Frisbee patent family tree

posted Sunday, 14 February 2010

US Patent D137521 US Patent 1404132 US Patent 2690339
       
   
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. US Patent D183626 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 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
       
                 
3930650 3948523 3959916 4031655 4080753 4086723 4132029 4151674 4151997 4153252 4152863 D251927 4157632 4174834 4196540 4204357 4205484 4216611 4253269 4265454 4288942 4431196 4456265 D275976 4516947 D286657 4669995 4681553 4737128 D295429 4802875 4889347 D310691 5009623 D337623 5232226 5254077 D341390 5263819 5269716 5290184 D346413 5326110 D349930 D350783 D356717 5423705 5484159 D369191 5531624 5540610 5553570 D386221 D386222 D386223 D387817 D388134 D390282 5799616 D398939 5816880 5829714 D401288 D401289 D402318 5964636 6073588 6179737 D445461 6585551 6755711 6764371 6918809 6971940 6991508 7081032 7217169 7270332 D562918 D564877 D568091
                               

physics.info/news/?p=1136

Science caught in the Web 2010-02-06

posted Saturday, 6 February 2010

physics.info/news/?p=973

Science caught in the Web 2010-01-30

posted Saturday, 30 January 2010

physics.info/news/?p=971

Science caught in the Web 2010-01-23

posted Saturday, 23 January 2010

physics.info/news/?p=965

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

physics.info/news/?p=3818

The World’s Smallest Snowman

posted Thursday, 31 December 2009

physics.info/news/?p=861