Q. 59

Expert-verified
Found in: Page 626

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# You have a lightweight spring whose unstretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5.0 cm. You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 4.5 cm. What is the magnitude of the charge (in nC) on each bead?

The magnitude of charge in each bead is 33 nC.

See the step by step solution

## Step 1: Given Information

Mass attached to the spring

Unstretched length of the spring

Stretched length due to mass

Stretched length due to charges on the beads

Separation between the charged beads

## Step 2: Calculation

Force due to stretching of spring is given as:

Where,

change in length of the spring

spring constant

The change in the length of the spring after the addition of mass is:

This stretching is due to the weight of the additional mass attached to the spring, hence,

By rearranging the terms, we get the spring constant as:

Now, the electrostatic force between the beads with the same charge can be given as:

Where,

For this case, the force due to the stretching of spring is given as:

The change in the length of the spring due to electrostatic force between the charged beads is:

Since this stretching is due to the electrostatic force between the charged beads, hence,

By rearranging the terms, we get the spring constant as:

By comparing the equations (1) and (2), we get,

By substituting the values in the above equation, we get,

## Step 3: Final answer

Hence, the magnitude of the charge on each bead is 33 nC.