Gravitational force between two 1g masses of electrons

[Astraithious]

Homework Statement

Imagine you could place 1g of electrons 1.0 m away from another 1g of electrons. calculate the electrical force and gravitational force between them.

Homework Equations

fe= kQ1Q2/r^2
fg=Gm1m2/r^2

The Attempt at a Solution

So the number of electron is

N= 0.001 / 9.1*10^-31 = 1.074*10^27 electrons

The the total charge is

q= N*e
= 1.074*10^27 * (1.6*10^-19)
= 1.718*10^8 coulomb so plugging that into fe= kQ1Q2/r^2 i get 2.7 x 10^10 n roughly for the force between them, however this seems to be incorrect as the answer given is 2.9 x 10^26

second part was easy and comes to 6.67^10^-17

my understanding of the ratio is

F_e/F_g=(k*e^2/r^2)/(G*m_e^2/r^2)
=k*e^2/G*m_e^2 [/B]

which comes out to roughly 4.2 x 10^42 depending on the rounding you did on the constants.

so using that ratio on 6.67 x 10^-17 the answer isn't either mine nor the one given on the work sheet.

Any help would be great, I'm sure its theory I'm misunderstanding but perhaps the math is off too. thanks!

 

[DEvens]

Check your units? You have to get the right units for mass, charge, Newton's constant, and Coulomb's constant.

 

[gneill]

You might want to find and use values for the various constants that have more decimal places, preferably more places than you want to keep as significant figures in any results. For example, a more accurate value for the mass of the electron is 9.1094 x 10^-31 kg.

The digits of your value for N look to be off a bit. Check your calculation.

What value did you use for the electrical force constant, k?

 

[Astraithious]

for k i used 9.0 x 10^9, I used constants from our information given but mass of an electron was from elsewhere. I am not sure what step was incorrect or if i need to even find the total charge in 1g of electrons then plug those into my equation. I tend to make things too complicated

 

[gneill]

for k i used 9.0 x 10^9, I used constants from our information given but mass of an electron was from elsewhere. I am not sure what step was incorrect or if i need to even find the total charge in 1g of electrons then plug those into my equation. I tend to make things too complicated

As a habit I keep on hand values of the constants with more decimal places and use them. I keep lots of extra digits in intermediate values, and don't round anything until the end for presentation purposes. This keeps roundoff and truncation errors from creeping into significant figures.

Your value for k is fine. A version with more decimal places won't make much difference here: k = 8.89755 x 10⁹ Nm²/C². I was interested in the power of ten you used, since your force value's order of magnitude ended up way off. So maybe a finger problem on your calculator? Also, redo your calculation of N, as it and your value for q are a bit low.

 

[Astraithious]

I just redid my values and it was a calculator error, my q is now 1.759 x 10^8 which is a great deal more. i end up with a final electrical force of 2.8 x 10^26 n but the ratio seems off shouldn't it be 4.1 to 4.3 x 10^42 : 1 with my electrical force i just can't get that ratio , thoughts?

 

[gneill]

I just redid my values and it was a calculator error, my q is now 1.759 x 10^8 which is a great deal more. i end up with a final electrical force of 2.8 x 10^26 n but the ratio seems off shouldn't it be 4.1 to 4.3 x 10^42 : 1 with my electrical force i just can't get that ratio , thoughts?

Could be more calculator issues. Your values for F_e and F_g now look fine, so their ratio should be good. What value are you getting? You need to show what you've done and how you've done it in order to for others to spot a problem.

FYI, the "N" for Newtons is always upper case.