A small metal sphere, carrying a net charge of q 1 = -2.40 C , is held in a stat

Question

A small metal sphere, carrying a net charge of q1 = -2.40 C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.20 C and mass 1.50 g , is projected toward q1 . When the two spheres are 0.800 m apart, q2 is 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.

What is the speed of q2 when the spheres are 0.410 m apart?

How close does q2 get to q1 ?

Explanation / Answer

Here ,

let the speed of sphere q2 0.410 m from the charge q1 is v m/s

Using conservation of energy

initial mechanical energy = final mechanical energy

0.5 * 0.0015 * 22^2 + 9*10^9 * 2.4 *10^-6 * 7.20 *10^-6/0.8

= 0.5 * 0.0015 * v^2 + 9*10^9 * 2.4 *10^-6 * 7.20 *10^-6/0.410

solving for v

v = 15.41 m/s

the speed of sphere 2 at 0.410 m from sphere 1 is 15.41 m/s

let the closest the sphere gets is q2 to q1 is d

using conservation of energy

0.5 * 0.0015 * 22^2 + 9*10^9 * 2.4 *10^-6 * 7.20 *10^-6/0.8

= 9*10^9 * 2.4 *10^-6 * 7.20 *10^-6/d

d = 0.278 m

the closest distaance between the spheres q2 and q1 is 0.278 m

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