# Tension in a rope connecting charged spheres.

• -Dragoon-
In summary, the system described involves two positively charged spheres with equal masses and charges connected by a rope at a distance of 5 cm. The system is in static equilibrium and the net force is equal to 0. To find the tension, one can isolate one of the spheres and draw a Free Body Diagram, summing the forces for static equilibrium.
-Dragoon-

## Homework Statement

Two positive charged spheres, with masses m = 2.0 g and with the same charge 2 µC are connected by a rope that is a distance of 5 cm. The charged spheres are at rest and the system is in static equilibrium.

N/A.

## The Attempt at a Solution

The system is in static equilibrium, which implies the net force is 0:
$\displaystyle\sum_i (f_x)_i = F_1on2 - F_2on1 + T = 0 => T = F_2on1 - F_1on2 = \frac{kq^2}{r^2} - \frac{kq^2}{r^2} = 0.$

Thus, I end up with tension being equal to zero since the force the charged sphere on the left exerts on the charged sphere on the right is equal and opposite to the forced the charged sphere on the right exerts on the left.

But, I have the wrong answer. Where did I go wrong?

Tension acts on both spheres, and in opposite directions. If you sum all the forces you'll end up with the unsurprising result that |F2on1| = |F1on2|, that is, they are both pushing each other with the same magnitude of force.

To find the tension, isolate one of the spheres and draw the Free Body Diagram. Sum the forces there. What should they sum to for static equilibrium?

## 1. What is the concept of tension in a rope connecting charged spheres?

Tension is the force exerted by a rope or string when it is pulled in opposite directions by two objects. In the case of charged spheres, the tension in the rope is caused by the repulsive force between the like charges on the spheres.

## 2. How does the amount of charge on the spheres affect the tension in the rope?

The amount of charge on the spheres directly affects the tension in the rope. As the amount of charge increases, the repulsive force between the like charges also increases, resulting in a greater tension in the rope.

## 3. Can the distance between the spheres affect the tension in the rope?

Yes, the distance between the spheres can affect the tension in the rope. As the distance between the charged spheres decreases, the repulsive force between them increases, resulting in a greater tension in the rope.

## 4. How does the length of the rope connecting the spheres impact the tension?

The length of the rope does not directly impact the tension in the rope. However, if the length of the rope is too short, it may not be able to withstand the tension and break. If the length is too long, it may sag and decrease the tension in the rope.

## 5. Can the tension in the rope change over time?

Yes, the tension in the rope can change over time. As the amount of charge or distance between the spheres changes, the repulsive force and resulting tension in the rope may also change. Additionally, external factors such as temperature and humidity can also affect the tension in the rope.

Replies
2
Views
504
Replies
1
Views
639
Replies
23
Views
1K
Replies
8
Views
2K
Replies
6
Views
2K
Replies
14
Views
2K
Replies
6
Views
982
Replies
1
Views
865
Replies
5
Views
2K
Replies
8
Views
974