Asmall metal sphere has a mass of 0.16 g and a charge of -26.0 nc . it is 10 cm directly above an identical sphere with the same charge. this lower sphere is fixed and cannot move.

force: 6.08*10^(-4) N; acceleration: 6.0 m/s^2

Explanation:

This problem has two questions, which are interconnected. As two charged spheres are located next to each other,  there is an electrostatic force exists in between them. As the charges of the spheres have the same sign, the force has repel nature. To be more precise, upper sphere is acted upon two forces- gravitational force, which acts downwards, and electric force, which acts upwards. We need directions of these forces to calculate and analyse acceleration of the sphere.

To calculate electrostatic force, which exists between the spheres, we can use Columb's law:

, where Q1 and Q2- charges, R- distance, between charges; e- electrostatic constant. Note, that in some cases, (1/(4πε)) is known as a constant k=9*10^9 Nm^2/C^2.

For the given values, force of electrostatic relations is equal to: F=6.08*10^(-6) N

To calculate acceleration, we can use second Newton's law. As we discussed above, there are two forces acting on the top sphere, and these forces have opposite directions, so the components on the vertical axis will have different signs. As a result, analysis of the acceleration can follow the next process:

Note, that we choose positive direction of the y-axis downwards. Note, that acceleration also acts downwards- it follows gravitational force.

Finally, we can see that the electric relations slow down the particle. However, during the motion, once the distance between charges reduces, the electrostatic force will increase and the given acceleration should be recalculated. Given answer is for the initial period, once the distance is 10cm. In its motion, the spheres might not collide, as the electrostatic force will go to infinity, once the distance goes to 0.

-4 on