Answer to Question #162226 in Physics for Pixis

Question

Solve the problem and show the complete solution.

Given: mp = 1.673 x 10-27 kg Qp = 1.602 x 10-19 C

me = 9.109 x 10-31 kg Qe = - 1.602 x 10-19 C

1. Determine the ratio of the Felect to the Fgrav between an electron and proton when separated by d = r.

a) What is the magnitude of Felect?

b) What is the magnitude of Fgrav?

c) What is the ratio of Felect / Fgrav?

Answer 1

a)

$$F_e=\dfrac{kQ_pQ_e}{r^2},$$ $$F_e=\dfrac{9\cdot10^9\ \dfrac{Nm^2}{C^2}\cdot(1.602\cdot10^{-19}\ C)^2}{(0.5\cdot10^{-10}\ m)^2}=9.24\cdot10^{-8}\ N.$$

b)

$$F_g=\dfrac{Gm_pm_e}{r^2}$$ $$F_g=\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot1.673\cdot10^{-27}\ kg\cdot9.109\cdot10^{-31}\ kg}{(0.5\cdot10^{-10}\ m)^2},$$ $$F_g=4.06\cdot10^{-47}\ N.$$

c)

$$\dfrac{F_e}{F_g}=\dfrac{9.24\cdot10^{-8}\ N}{4.06\cdot10^{-47}\ N}=2.27\cdot10^{39}.$$