What Is the Universal Gravitation Constant in English to 7 Significant Figures?

[Machinehead73]

Homework Statement

Does anyone know what the universal graviation constant is in english to 7 significant figures. metric is around 6.67x10^-11 and 1kg = .0685 slug. In the english system the constant is 3.43x10^-8 but I need to get it to the right sig figs. Can anyone help out on this. I not for sure how to the conversion. Thanks

Homework Equations

The Attempt at a Solution

 

[JazzFusion]

You CANNOT get the conversion to 7 significant figures if you only know the metric quantity to 3.

You must either know the metric value to at least 7 significant ficures and convert (making sure all your conversion factors also have at least 7 significant figures), OR you must look is up in English units.

(Wikipedia gives the constant in SI units to 6 significant figures.)

 

[Machinehead73]

The gravitational constant I think that is being referred to is the one in my textbook and this 6.6742(10) x 10^-11 N*m^2/kg^2 . THe number in parentheses indicate one-standard-deciation experimental uncertainties in final digits, so the book says. And my problem says that to be aware the range of acceptable answers is only +/- .000011.

Thanks for your help!

 

[Redbelly98]

The latest value (as of 2006) is

6.67428 (67) x 10^-11 m³ kg^-1 s^-2​

It is essentially known only to 4 significant figures; no system of units will have it to 7 figures.

See: http://physics.nist.gov/cgi-bin/cuu/Value?bg
or http://physics.nist.gov/cuu/Constants/index.html

 

[Machinehead73]

I see your point. I am sure the instructor is going by what is givin in the textbook.
It gives an approximate value and a current best value. The approximate value is 6.67x10^-11 N*m^2/kg^2 the current best is 6.6742(10) x10^-11 N*m^2/kg^2. I think with this info he wants use to get our answer to 7 sig fig. What I believe the current value is saying is
6.674210 is 7 sig figs the last 2 number in par. is one standard deviation. I need to know how to get from the metric value given and turn it into english values to 7 sig figs
Any help would be great. Thanks!

 

[Redbelly98]

The approximate value is 6.67x10^-11 N*m^2/kg^2 the current best is 6.6742(10) x10^-11 N*m^2/kg^2.

6.6742 only has 5 significant figures.
The (10) is giving the uncertainty in terms of the last two digits, it is not actually part of the 6.6742. It means to think of the number as

6.6742±0.0010​

Since there is uncertainty in the 4th significant figure, I would say it is accurate to 4 significant figures. Whether you say 4 or 5, there is no way to get to 7 significant figures from this! In any system of units, metric, English, or other. Nobody can help you with that task because it is impossible.

If you just want to convert to English units then follow standard procedures for converting units. But the result will still have just 4 or 5 significant figures (not 7). If you need help with doing the conversion, including converting the uncertainty, feel free to ask.

 

[Machinehead73]

OK I need help with doing that an finding the uncertainty.

 

[Redbelly98]

Okay. To start with, which English units do you want to convert to?

Next question, what would 1 meter be in English units?

 

[Machinehead73]

1 meter = 2.54 ft. right and 1kg = .0685 slugs right.

 

[Redbelly98]

Correct on the mass conversion, but try again with meters-to-feet.

 

[Machinehead73]

That would be 1 meter = 3.2808399 feet.

 

[Redbelly98]

Okay, that's right.

Wherever you see meters in the quantity you are converting, replace it with the equivalent value of 3.2808399 feet. Since we have m² (meters squared), that would become

m² = (3.2808399 ft)² = 3.2808399² ft² = 10.76391 ft²​

So putting that into G, we get (as an intermediate, not final, result):

G = 6.6742x10^-11 N*m^2/kg^2
= 6.6742x10^-11 N*(3.2808399 ft)²/kg²
= 6.6742x10^-11 x 10.76391 N*ft²/kg²
= 7.184049 × 10^-10 N*ft²/kg²
​

Follow the same procedure to convert the N and kg into English units, and the result will be G in English units. Oh, and follow the usual rules for significant figures when you present the final answer.

 

[Machinehead73]

Would I take the what a kg = in lbs and divide it by that?

 

[Redbelly98]

First you'll need to decide what mass unit you're converting to. (You mentioned slugs earlier, but now you are talking about pounds.) Did your class professor give you the units that are to be used?

Replace the "kg" in the expression with it's equivalent English-unit mass (either slugs or pounds, you need to find that out). Remember that this quantity is to be squared, since the units are kg². And yes, you will be dividing since the kg² is being divided.