A small metal sphere, carrying a net charge of q 1 = -3.10 ? C , is held in a st

Question

A small metal sphere, carrying a net charge of q1 = -3.10?C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.90?C and mass 1.40g , is projected toward q1. When the two spheres are 0.800 m apart, q2is moving toward q1 with speed 22.0 m/s (Figure 1) . Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

Part A

What is the speed of q2 when the spheres are 0.390m apart?

Part B

How close does q2 get to q1?

Explanation / Answer

We can solve this problem by energy conservation point of view

When two spheres are 0.800 m apart

The kinetic energy is

Ka = 0.5 * M2 * V2^2

Ka = 0.3388 m

Potential energyof q2 in electric field of q1 is

Pa = Kq1 q2 / D = 8.98 * 10^9 * -3.1 * - 7.90 * 10^-12 / 0.800 = 0.2748 m

When 2 spheres are 0.390m apart

Kb = 0.5 * M2 * V2^2

Kb = 0.7 * V2 ^2 ( here v2 is unknown)

Potential energy Pb = Kq1 q2 / d = 8.98 * 10^9 * -3.10 *-7.90* 10^-12 / 0.390 = 0.5638 m

PART A

1) To find V2,

Ka + Pa = Kb + Pb

0.3388 + 0.2748 = 0.7* V2^2 + 0.5638

V2^2 = 0.0498

V2 = 0.223 m/s

PART B

2) Ka + Pa = Kc + Pc

here Kc = 0

0.3388 + 0.2748 = 0.2199 / S

S = 0.3583 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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