A small metal sphere, carrying a net charge of q_1 = -2.80 mu C, is held in a st

Question

A small metal sphere, carrying a net charge of q_1 = -2.80 mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -3.90 mu C and mass 2.00 g, is projected toward q_1. When the two spheres are 0.800 m apart, q_2 is moving toward q_1 with speed 22.0 m/s (see figure below). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. What is the speed of q_2 when the spheres are 0.400 m apart? m/s How close does get q_2 to q_1? m

Explanation / Answer

by conservation of energy

initial energy = final energy

initial energy = kinetic energy + electric potential energy

electric potential energy = k * Q * q / distance

initial energy = 0.5 * mv^2 + k * Q * q / d

initial energy = 0.5 * 2 * 10^-3 * 22^2 + 9 * 10^9 * -2.8 * 10^-6 * -3.9 * 10^-6 / (0.8)

final energy = 0.5 * 2 * 10^-3 * v^2 + 9 * 10^9 * -2.8 * 10^-6 * -3.9 * 10^-6 / (0.4)

0.5 * 2 * 10^-3 * 22^2 + 9 * 10^9 * -2.8 * 10^-6 * -3.9 * 10^-6 / (0.8) = 0.5 * 2 * 10^-3 * v^2 + 9 * 10^9 * -2.8 * 10^-6 * -3.9 * 10^-6 / (0.4)

v = 19 m/s

a) speed of q2 = 19 m/s

minimum distance between q1 and q2 will be when the final kinetic energy will be 0 so,

0.5 * 2 * 10^-3 * 22^2 + 9 * 10^9 * -2.8 * 10^-6 * -3.9 * 10^-6 / (0.8) = 9 * 10^9 * -2.8 * 10^-6 * -3.9 * 10^-6 / d

d = 0.162 m

b) minimum distance = 0.162 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.