Question

5 Extras credit Below is for your extra credit. This is based on the Friday's lecture. 1) If you give away 1% of electrons in your body to your boyfriend/girlfriend, what would be the force between two of you? Assume 30 cm (one foot) separation between two. 2) Next if two Earths are facing each other, what would be the gravitational force between the two Earths? 3) Compare the electric force and gravitational force above, and comment on your finding. 4) From the above, comment on how human body is constructed. Why can your body keep the same shape every day (well, more or less...)?

Answer 1

1)

n = number of electron in the body = 1.5 x 10²⁸

n₁ = number of electrons in boyfriend's body = 0.99 n = 0.99 x 1.5 x 10²⁸ = 1.485 x 10²⁸

n₂ = number of electrons in girlfriend's body = 1.01 n = 1.01 x 1.5 x 10²⁸ = 1.515 x 10²⁸

e = magnitude of charge on electron = 1.6 x 10^-19 C

q₁ = magnitude of charge on the body of boyfriend = n₁ e = (1.485 x 10²⁸ ) (1.6 x 10^-19) = 2.376 x 10⁹

q₂ = magnitude of charge on the body of girlfriend = n₂ e = (1.515 x 10²⁸ ) (1.6 x 10^-19) = 2.424 x 10⁹

r = distance between the girlfriend and boyfriend = 30 cm = 0.30 m

Using coulomb's law , force between the two is given as

F = k q₁ q₂/r²

F = (9 x 10⁹) (2.376 x 10⁹ ) (2.424 x 10⁹)/(0.30)²

F = 5.76 x 10²⁹ N

2)

m = mass of earth = 5.98 x 10²⁴ kg

r = distance between the centers of two earths = 2 R = 2 x 6.4 x 10⁶ m = 12.8 x 10⁶ m

F' = gravitational force between the two earths

Gravitational force is given as

F' = G m²/r²

F' = (6.67 x 10^-11) (5.98 x 10²⁴)²/(12.8 x 10⁶)²

F' = 1.45 x 10²⁵ N

3)

Ratio of electric and gravitational force is given as

R = F/F'

R = (5.76 x 10²⁹)/(1.45 x 10²⁵)

R = 39724.14