An asteroid of mass 58,000 kg carrying a negative charge of $15 \mu \mathrm { C }$ is $180 \mathrm {~m}$ from a second asteroid of mass $52,000 \mathrm {~kg}$ carrying a negative charge of $11 \mu \mathrm { C } \text {. }$ What is the magnitude of the net force the asteroids exert upon each other, assuming we can treat them as point particles? (G = 6.67 × 10^-11 N ∙ m²/kg², k = 1/4 πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

The net force is the sum of the gravitational force and the electrostatic force. The gravitational force is attractive and the electrostatic force is repulsive. The gravitational force is given by:$$F_g = G \frac{m_1 m_2}{r^2}$$where G is the gravitational constant, m1 and m2 are the masses of the asteroids, and r is the distance between them.The electrostatic force is given by:$$F_e = k \frac{q_1 q_2}{r^2}$$where k is the Coulomb constant, q1 and q2 are the charges of the asteroids, and r is the distance between them.The net force is:$$F_{net} = F_g + F_e$$$$F_{net} = G \frac{m_1 m_2}{r^2} + k \frac{q_1 q_2}{r^2}$$$$F_{net} = (6.67 	imes 10^{-11} 	ext{ N} \cdot 	ext{m}^2/	ext{kg}^2) \frac{(58,000 	ext{ kg})(52,000 	ext{ kg})}{(180 	ext{ m})^2} + (8.99 	imes 10^9 	ext{ N} \cdot 	ext{m}^2/	ext{C}^2) \frac{(-15 \mu 	ext{C})(-11 \mu 	ext{C})}{(180 	ext{ m})^2}$$$$F_{net} = 0.000040 	ext{ N}$$

An Asteroid of Mass 58,000 Kg Carrying a Negative Charge 15μC15 \mu \mathrm { C }15μC

An Asteroid of Mass 58,000 Kg Carrying a Negative Charge $15 \mu \mathrm { C }$