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Old Sep 17th 2014, 02:37 PM   #1
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About Units and F = mA

Newton used the dimensions, f,m,l and t, in his 2nd Law. English Engineering Units and later System Internationale Units were defined with the 2nd law as basis.

It is interesting how this happened. An excellent book, "The Science of Measurement" (H.A. Klein) is a great read. Here's a short piece I wrote.

http://www.thermospokenhere.com/wp/0.../potatoes.html

Jim at TSH
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Old Sep 17th 2014, 02:59 PM   #2
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I don't follow your equation 5, defining g_c. It's clearly not the familiar gravitational constant g, but rather is a dimensionless entity with value 1. Why introduce it all?

Also, your equation 7 is precisely the way that Newton wrote his law (though his calculus notation was a bit different). In most physics text books the law is introduced as F times t = change in momentum, or F = Delta momentum/delta t, which in the limit as t goes to zero becomes the derivative as you wrote it. If one assumes that mass is constant it makes the mathematics of solving high school physics problems much easier (similar to assuming acceleration is constant in using equations of motion), and so 99% of the time F=ma is correct for typical homework problems. Of course students should be reminded that the true 2nd law is as you wrote it.

Finally, one suggestion for clarity - you may want to change this sentence: "English Engineering defines the magnitude of force to equal that of mass" to "English Engineering defines the magnitude of force acting on an object by Earth's gravity at sea level to equal the magnitude of that mass."

Last edited by ChipB; Sep 17th 2014 at 03:08 PM.
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Old Sep 18th 2014, 02:08 PM   #3
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Thanks ChipB - No response needed!

ChipB, Thank you for your comments and help.

My opinion is the quest of simpler math (avoidance of bottom rung calculus at least in the 90's, 10's) by HS physics has harmed science education. It has me upset. Nothing can be done, of course. I don't know you, You work hard at PHF. You can't do anything. Maybe I should just take a laxative (sp).

Originally Posted by ChipB View Post
I don't follow your equation 5, defining g_c. It's ... Why introduce it all?
It was introduced in engineering texts until 98 I know. If you have not seen "g_c" you are lucky. I don't know if this is around anymore - I hope not.

Originally Posted by ChipB View Post
Also, your equation 7 is precisely the way that Newton wrote his law (though his calculus notation was a bit different). In most physics text books the law is introduced as F times t = change in momentum, or F = Delta momentum/delta t, which in the limit as t goes to zero becomes the derivative as you wrote it. If one assumes that mass is constant it makes the mathematics of solving high school physics problems much easier (similar to assuming acceleration is constant in using equations of motion), and so 99% of the time F=ma is correct for typical homework problems. Of course students should be reminded that the true 2nd law is as you wrote it.
Thank you for this summary. I have only a few, older texts here. I think you have said: d(mV)/dt =sum(F) was Newton's form. One assumes he had a reason for placing "d(mV)/dt" left of equality. (My conjecture is momentum is a property and sum of forces is a construct). These days our physics publicists have adopted the form: "F = Delta momentum/delta t."

However, now as before, our equations read left-to-right. Newton's 2nd Law got "flopped" left-term-right" and "right-term-left" (so the equation tells what force is?). For the idea "sum(F)," a simpler term, "F" (called "net" ) was inserted. Force is a construct. A way to think; like double-entry bookkeeping.

"Easier math for HS students? Easier math to do easier physics? Easier than "what is a derivative?" Easier than Newton's definition of velocity. Easier than what Newton knew in 1680?

I fixed the "point of clarity," thank you. Ignore my typos, please!

Thank you, Jim Pohl
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Old Sep 18th 2014, 03:07 PM   #4
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Originally Posted by THERMO Spoken Here View Post
Thank you for this summary. I have only a few, older texts here. I think you have said: d(mV)/dt =sum(F) was Newton's form. One assumes he had a reason for placing "d(mV)/dt" left of equality. (My conjecture is momentum is a property and sum of forces is a construct). These days our physics publicists have adopted the form: "F = Delta momentum/delta t."

However, now as before, our equations read left-to-right. Newton's 2nd Law got "flopped" left-term-right" and "right-term-left" (so the equation tells what force is?). For the idea "sum(F)," a simpler term, "F" (called "net" ) was inserted. Force is a construct. A way to think; like double-entry bookkeeping.
I have two comments to make.

First, Physics is "case sensitive," which means that a is not the same as A and v is not the same as V.

Second, the "net force" in Newton's 2nd is not quite what you are talking about...the net force is the "net external force" acting on an object. Your constructs are all due to external conditions.

-Dan
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