Chapter 2.4, Problem 169E

[T] The following problems consider the scalar form of Coulomb’s law, which describes the electrostatic force between two point charges, such as elections. It is given by the equation $F\left(r\right)=k_e\frac{\left|q_1{q}_2\right|}{r^2}$ where k_eis Coulomb's constant, $q_i$ are the magnitudes of the charges of the two particles, and r is the distance between the two particles.

169. Instead of making the force 0 at R, instead we let the force be ${10}^{-20}$ for $r\ge R$. Assume two protons, which have a magnitude of charge $1.6022\times {10}^{-19}C$ , and the Coulomb constant $k_e=8.988\times {10}^{9}N{m}^2/C^2$ . Is there a value R that can make this system continuous? If so, find it.

Recall the discussion on spacecraft from die chapter opener. The following problems consider a rocket launch from Earth's surface. The force of gravity on the rocket is given by $F\left(d\right)=-mk/d^2$, where m is the mass of the rocket, d is the distance of the rocket from the center of Earth, and k is a constant.