# Gravitational force between two 1g masses of electrons

• Astraithious
In summary, the conversation discusses the calculation of electrical and gravitational forces between 1g of electrons placed 1.0 m apart. The conversation includes a discussion of the number of electrons, total charge, and values for relevant constants. After some initial miscalculations, the correct values for electrical and gravitational forces are determined, as well as the ratio of the two forces. The conversation ends with a clarification on the use of units for Newtons.
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.

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!

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

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?

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

Astraithious said:
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.

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?

Astraithious said:
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 Fe and Fg 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.

## 1. What is the formula for calculating the gravitational force between two 1g masses of electrons?

The formula for calculating the gravitational force between two 1g masses of electrons is F = (G*m1*m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the two electrons, and r is the distance between them.

## 2. How does the distance between two 1g masses of electrons affect the gravitational force between them?

The gravitational force between two 1g masses of electrons is inversely proportional to the square of the distance between them. This means that as the distance between the electrons increases, the force decreases, and vice versa.

## 3. What is the value of the gravitational constant (G)?

The value of the gravitational constant (G) is approximately 6.674 x 10^-11 N*m^2/kg^2. It is a fundamental constant that is used to calculate the gravitational force between two objects.

## 4. Can the gravitational force between two 1g masses of electrons be repulsive?

No, the gravitational force between two 1g masses of electrons is always attractive. This is because electrons have a negative charge and according to the law of gravity, objects with opposite charges attract each other.

## 5. How does the mass of the electrons affect the gravitational force between them?

The gravitational force between two 1g masses of electrons is directly proportional to the product of their masses. This means that as the mass of the electrons increases, the force between them also increases, and vice versa.

Replies
3
Views
715
Replies
8
Views
2K
Replies
6
Views
2K
Replies
23
Views
2K
Replies
12
Views
1K
Replies
2
Views
2K
Replies
5
Views
922
Replies
7
Views
2K
Replies
5
Views
2K
Replies
2
Views
1K