Question

Two small metal cubes with masses 2.0 g and4.0 g are tied together by a 4.9-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.2 μC .

The string is cut. What is the speed of each sphere when they are far apart?
Hint: There are two conserved quantities. Make use of both.

The mechanical energy of the system is 0.89 J and the tension in the string is 18.1 N

Answer 1

To solve this problem you have to know about Kinetic energy and coulomb's law

Step 1.

Definition:

Kinetic Energy: The kinetic energy of a body is the energy that has due to its motion . It is defined as the work needed to accelerate a body of a given mass from rest to the speed displayed

Coulomb's law: The magnitude of each of the electrical forces with two point charges that interact at rest is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance between them and has the direction of the line joining

Step 2.

We analyze the system before the cut string, first we calculate the force of the cube B on A and late the force of the cube A on B.

How you can see this force it's same at the tension in the string, and must be so to keep the system in balance

We analyze the system after the cut string, the forces exerted on both cubes make these experience an acceleration

both cubes traveling at different speeds but the same instant of time, you need calculate the time for this equation

We equate the equation and have the following

Now energy conservation system represent it as follows

substitute values ​​and resolve

If you have any question please let me know in the comments