posted Tuesday, 7 December 2010
posted Tuesday, 7 December 2010
posted Saturday, 4 September 2010
posted Saturday, 28 August 2010
posted Saturday, 21 August 2010
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!
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?
|McIntosh Apple (151.3 g)||Red Delicious Apple (216.4 g)||Cavendish Banana (160.0 g)|
|Valencia Orange (178.0 g)||Tangerine (96.7 g)||Tomato (152.8 g)|
|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|
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.
|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.
|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|
posted Saturday, 17 April 2010
posted Saturday, 3 April 2010
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.|
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posted Saturday, 6 February 2010