Question

A small metal sphere has a mass of 0.11 g and a charge of -25.0 nC. It is 10.0 cm directly above an identical sphere that has the same charge. This lower sphere is fixed and cannot move. If the upper sphere is released, it will begin to fall. 

Part A 

What is the magnitude of its initial acceleration? 

Answer 1

Answer 2

SOLUTION :

q1 = q2 = - 25.0  * 10^(-9) C 

d = 10 cm = 10 *10^(-2) m 

Electrical force exerted on q1 by fixed charge q2, Fe :

= k q1 q2 / d^2

= 9*10^9 * (- 25.0 * 10^(-9))^2  / (10*10^(-2))^2 

= 5.625 * 10^(4) N 

This force Fe, causes q1 to moove up (away from q2 being of same polarity).

So, the acceleration (say a m/s^2)  due to this will be upward.

m a = Fe 

=> a = Fe / m = 5.625 * 10^(-4) / (0.11 *10^(-3)) = 5.1136 m/s^2

Acceleration due to gravity = g = 9.806 m/s^2 downward.

So, net initial  acceleration downward = 9.806 - 5.1136 = 4.6924 = 4.69 m/s^2 (ANSWER).