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Gravitational force between two 1g masses of electrons

  1. Jun 2, 2015 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    fe= kQ1Q2/r^2
    fg=Gm1m2/r^2

    3. 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


    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!

     
  2. jcsd
  3. Jun 2, 2015 #2

    DEvens

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    Education Advisor
    Gold Member

    Check your units? You have to get the right units for mass, charge, Newton's constant, and Coulomb's constant.
     
  4. Jun 2, 2015 #3

    gneill

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    Staff: Mentor

    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?
     
  5. Jun 2, 2015 #4
    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
     
  6. Jun 2, 2015 #5

    gneill

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    Staff: Mentor

    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.
     
  7. Jun 3, 2015 #6
    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?
     
  8. Jun 3, 2015 #7

    gneill

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    Staff: Mentor

    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.
     
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