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- From: Lawrence London <lfljvenaura@gmail.com>
- To: machinist@lists.ibiblio.org
- Subject: [machinist] Equation Question
- Date: Fri, 31 Jan 2014 21:22:09 -0500
http://www.practicalmachinist.com/vb/general/equation-question-279285/
This is a confusing area where somewhat different definition of pound are commonly used. From Wikipedia:
"The pound or pound force (symbol: lb, lbf, lbf) is a unit of force in some systems of measurement including English engineering units and British gravitational units.[1]
Definitions[edit]
The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.[2]
The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed. Today, in accordance with theGeneral Conference on Weights and Measures, standard gravity is usually taken to be 9.80665 m/s2 (32.174 049 ft/s2).[3][4]
The acceleration of the standard gravitational field (gn) and the international avoirdupois pound (lbm) define the pound-force as:[5]
<>
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf·s2/ft. In other contexts, the unit "pound" refers to a unit of mass. In circumstances where there may otherwise be ambiguity, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish.
<>
In the gravitational systems, the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit[8]—the use of Newton's Second Law, F = m·a, requires another factor, gc, usually taken to be 32.174049 lbm·ft/lbf·s2 = 32.174049 lbm/slug. "Absolute" systems are coherent systems of units: by using the slug as the unit of mass, the "engineering" FPS system avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units..."
So, we really have to define which system we are using. Otherwise there can be disagreement over such seemingly simple questions. In one system the pound is defined as a specific fraction of a kilo.
Denis
-
Equation Question
Q:- Three blocks are used to tilt a sine plate. The total height of the three blocks is 4.5 inches. The first block is 3 times as thick as the second block. The second block is twice as thick as the third block. How thick is each block ?
My solution is like this 3(x) + 2(x) + x = 4.5''
3x + 2x + x = 6x
6x=4.5
x=4.5/6
x=0.75
formula is 3(x) + 2(x) + x = 4.5''
3(0.75) + 2(0.75) + 0.75 = 4.5''
2.25'' + 1.5'' + 0.75'' = 4.5''
4.5'' = 4.5''
Now , according to answer mention in book it is , 0.5'', 1'' , 3''
Can any one tell me where am i wrong or are Smith & Peterson, Mathematics for Machine Technology mentioned wrong , hope they will be right but HOW ?
Thanks
Asad -
01-29-2014, 04:44 PM #2
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01-29-2014, 04:55 PM #3
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You mis-wrote your equation a bit.
Do it a slightly different way.
First block = x
Second = y
Third = z
So by the conditions:
x = 3y
y = 2z
and x + y + z = 4.5
So sub in:
3y + y + 0.5y = 4.5
so y (second block) = 1
and so on.
When you wrote the equation the second term is in error. -
-
I like x for the third block, 2x for the second block and 6x for the third block
6x + 2x + x = 4.5 9x = 4.5 x = 4.5/9 = 1/2 or 0.5
blocks are 0.5, 1.0 and 3.0asadkazmi and Polaraligned like this. -
Hi Asad,
The secret to exams is to be extra careful when you read the question, Read as many times as it takes to be clear.
Trick questions are always good.. A rooster lays an egg on the table of a crappy chinese mill, the table traverses rapidly from X=-100 to X=+100, which way does the egg roll off?
(a) -ve X direction
(b) +ve X direction
(c) neither
Ray -
01-30-2014, 01:45 AM #10
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Originally Posted by RayG
Hi Asad,
The secret to exams is to be extra careful when you read the question, Read as many times as it takes to be clear.
Trick questions are always good.. A rooster lays an egg on the table of a crappy chinese mill, the table traverses rapidly from X=-100 to X=+100, which way does the egg roll off?
(a) -ve X direction
(b) +ve X direction
(c) neither
Ray
Trick questions should also be precise.
Important tot know is whether the egg is boiled or not. -
01-30-2014, 02:08 AM #11
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And is that egg-laying rooster pre-op or post-op?
Chip -
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01-30-2014, 03:18 AM #13
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Never heard this one, but after doing some math and just about ready to post an answer in the thousands..... I rethought and got the trick... Originally Posted by Sea Farmer
How many grooves are in the record?
Is the answer "2"? -
-
01-30-2014, 08:54 AM #16
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depends upon whether it is boiled or not Originally Posted by asadkazmi
@RayG : how on this earth a rooster can lay an egg ?
so answer is 'neither' but even if he lay an egg then it will also not move due to inertia , isn't it ?
a boiled egg will move a litttle
an unboiled egg just a little more -
Yes, I thought about this as well, the correct answer is neither, because there is no egg. Unless it's a post-op sex change rooster with a madonna complex. Originally Posted by asadkazmi
@RayG : how on this earth a rooster can lay an egg ? so answer is 'neither' but even if he lay an egg then it will also not move due to inertia , isn't it ?
But the question remains, IF there was an egg which way would it roll, the answer is probably both ways, first to the -ve side as the table accelerates in a +ve direction, then to the +ve side as the table decellerates on it's trapezoidal velocity profile, whether it rolls off the table will depend on exact values for accel, decell and length of table etc.. etc.. so the answer is, none of the above.
Ray
PS.. and of course whether it was hard-boiled. -
Dan,
Are you an algebra teacher or did you just finish an algebra class?
Big B
Originally Posted by Dan Cassaro
Call the three blocks a, b, and c
a=3b
b=2c
We also know that a+b+c=4.5
So, we can rewrite that as: (substituting 3b for a)
3b+b+c=4.5
and then...
3b+b+b/2=4.5
grouping like terms...
4.5b= 4.5
OK, so b = 1.
a=3(1) or 3
b=1
b=2c, which = c=b/2
c=.5
So,
3+1+.5=4.5 -
01-31-2014, 03:21 AM #20
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Yup. You got it Originally Posted by Royldean
Never heard this one, but after doing some math and just about ready to post an answer in the thousands..... I rethought and got the trick...
Is the answer "2"?
Reply
sorry, a pound is a pound.
Really that is right but points out the problem with weight
measurements like "pound" vs mass measurements like kilogram. The
conditions under which the same piece of brick are measured will have a
significant impact on the reading obtained. Take the same brick under
water and its measured weight will be different. But a kilogram of
brick is the same in space, under water, at the equator, or on top of Mt
Everest. The pound of material under one condition witll measure
differently under all these conditions. This is a confusing area where somewhat different definition of pound are commonly used. From Wikipedia:
"The pound or pound force (symbol: lb, lbf, lbf) is a unit of force in some systems of measurement including English engineering units and British gravitational units.[1]
- 1 Definitions
- 2 Conversion to other units
- 3 Foot-pound-second (FPS) systems of units
- 4 See also
- 5 Notes and references
Definitions[edit]
The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.[2]
The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed. Today, in accordance with theGeneral Conference on Weights and Measures, standard gravity is usually taken to be 9.80665 m/s2 (32.174 049 ft/s2).[3][4]
The acceleration of the standard gravitational field (gn) and the international avoirdupois pound (lbm) define the pound-force as:[5]
<>
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf·s2/ft. In other contexts, the unit "pound" refers to a unit of mass. In circumstances where there may otherwise be ambiguity, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish.
<>
In the gravitational systems, the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit[8]—the use of Newton's Second Law, F = m·a, requires another factor, gc, usually taken to be 32.174049 lbm·ft/lbf·s2 = 32.174049 lbm/slug. "Absolute" systems are coherent systems of units: by using the slug as the unit of mass, the "engineering" FPS system avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units..."
So, we really have to define which system we are using. Otherwise there can be disagreement over such seemingly simple questions. In one system the pound is defined as a specific fraction of a kilo.
Denis
- [machinist] Equation Question, Lawrence London, 01/31/2014
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