compare the electrostatic and gravity force between a proton of charge +e and of mass M at a distance r fr

Question

Please i was asked to solve this but it seems quite difficult for me, compare the electrostatic and gravity force between a proton of charge +e and of mass M at a distance r from an electron of charge -e of mass m, take the proton to be 1840 times heavier than the electron. Evaluate their relative magnitude i.e the ratio of the electrostatic force of attraction to the gravitational force of attraction? Please i need answers really fast.

Answer 1

The gravitational force between two things is:

F_G = G×(m₁ × m₂)/(r²)

.....where G≈6.7×10^-11

 

The electrostatic force between two things is:

F_E = k×(q₁ × q₂)/(r²)

.....where q is the charges and k≈9.0×10⁹

 

Plug in the values they give you (in this case the letters they give you).

Let the mass of the electron be m₁ and let the mass of the proton be m₂, which is equal to 1840×m₁.

After you've plugged in everything to the right side of both formulas, we make the ratio by:

Creating a fraction of F_E/F_G using what you plugged in for the formulas.

Most of the stuff in the fraction will not cancel out, but something will (Hint: r²).

 

Hope this helps.

∼F

Answer 2

I will set this up for you, but YOU do the calculations.

 

Electrostatic force:

 

F_e = ke²/r²

 

Gravitational force:

 

F_g = G(1840m)m/r² = 1840Gm²/r²

 

Ratio:

 

F_e/F_g = (ke²/r²) / (1840Gm²/r²) = ke² / (1840Gm²)

 

Now just plug in the numbers in appropriate units and get your answer.

 

k = 9 x 10⁹ Nm²/C²

 

G = 6.67 x 10^-11 Nm²/kg²

 

e = 1.6 x 10^-19 C

 

m = 9.11 x 10^-31 kg

 

You should be able to finish from here.