Just how strong is the electric force? suppose you had two small boxes, each containing 1.0 g of protons. (a) if one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long! ) string, what would be the tension in the string? express your answer in newtons and in pounds. do you need to take into account the gravitational forces of the earth and moon on the protons? why? (b) what gravitational force would each box of protons exert on the other box?

Let's use Newton's Law of Second Motion: F=ma. When no other direct force is acting on the system, the acceleration is due to the gravity. The modified equation becomes: F = mg. So, yes, you need to take into account the gravitational accelerations in the moon and on Earth. 

g,moon = 1.622 m/s²
g,Earth = 9.81 m/s²

The net force is the tension of the string:

F,Earth - F,moon = Tension
Tension = (1/1000 kg)(9.81 m/s²) - (1/1000 kg)(1.622 m/s²)
Tension = 8.188×10⁻³ N

To convert, 1 pound force is equal to 4.45 Newtons:

Tension = 8.188×10⁻³ N * 1 lbf/4.45 N
Tension = 1.84×10⁻³ lbf

Less force and energy was applied