Question

An outside force, Fo, brings two small metal spheres, A and B, at rest from a long distance away to a point where they are 1 meters apart. They are then connected by a non-conducting string of negligible mass. The spheres have mass mA = 5.8 g and mB = 9.5 g and both have equal positive charges of 5 μC. (You may assume the length of the string is much greater than the radii of the spheres.)

1)What was the total work done by the outside force to bring the spheres to the point described?
2)What was the total work done by the electric field when the two sphere were brought together as described?
3)What is the potential energy of the two sphere system after they have been brought together as described? (You may assume the spheres had zero potential energy when they were a long distance apart.)
4)Suppose you cut the string. At that instant, what is the magnitude of the acceleration of sphere A?
5)At that instant, what is the magnitude of the acceleration of sphere B?
6)After a very long time, what is the magnitude of the velocity of sphere A?
7)After a very long time, what is the magnitude of the velocity of sphere B?

Answer 1

1)

The total work done by outside force is
`W_(o)=0.294J`

2)

The total work done by the electric field is
`-W_(o) =-0.294J`

3)

The potential energy of the two sphere system is
`PE = W_(o) = 0.294J`

4)

The magnitude of the acceleration of sphere A is
`a_(A) = 66.868m/s^2`

5)

The magnitude of the acceleration of sphere B is
`a_(B) = 26.747 \ m/s^2`

6)

The magnitude of velocity sphere A after a very long time is
`v_(A) = 10.251 \ m/s`\

7) The magnitude of velocity sphere B after a very long time is
`v_(B) = 4.1 m/s`

Step-by-step explanation:

The explanation is shown on the first and second uploaded image