# Spring and electrostatic forces

• Krique
In summary, a lightweight spring with an unstretched length of 4.0 cm was used to measure charge by attaching one end to the ceiling and hanging a 1.0 g mass from it, resulting in a stretched length of 5.0 cm. By also attaching two small plastic beads with equal charges to the opposite ends of the spring and placing it on a frictionless table, the spring stretched to a length of 4.5 cm. Using the equation -kx=mg, a spring constant of 981 N/m was calculated. Then, using Coulomb's law, the charges were solved for, with a correction needed for the mass (0.001 kg) and the sign of the variables in the equations.
Krique

## Homework Statement

You have a lightweight spring whose unstretched length is 4.0 cm. You're curious to see if you can use this spring to measure charge. 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.

## The Attempt at a Solution

When the spring is hanging from the ceiling, it has no acceleration. And since it is lightweight, I assume that the mass of the spring does not matter. The only forces acting on the spring while hanging are the weight of the block and the force of the spring, which should cancel out. So (mass)(gravity) = -kx. We are given that the unstretched length is 4 cm, so we know that x = .01 m. The mass is 1g, and gravity is always -9.81 m/s^2. We can then solve for k. I got 981 N/m.

Now that I have the spring constant, I solved for the charges. When it is on the table, the only forces acting on the spring in the horizontal direction are the charges and the spring, which cancel each other out. So K (Q1*Q2)/r^2 = -kx. In this case, x is .005 m and r is .045 m. k is the same as before, 981. Q1 is equal to Q2 because they have the same charge. I assume K to be 8.99*10^9 because that is what all of our homework assignments have been using.

Solving for Q1^2, I got -1.105*10^-12. This makes Q1 and Q2 non real answers. If I drop the negative, they are 1.05*10^-6 C, which is also incorrect. Any ideas where I am going wrong?

#### Attachments

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Last edited by a moderator:
Krique: The mass is 0.001 kg, not 1. Try it again and see if this makes your answer correct. In both of your equations, change -k*x to k*x. And change g = -9.81 m/s^2 to 9.81 m/s^2. Your ke value in Coulomb's law is correct; ke = 8.9876e9 (N*m^2)/C^2.

Last edited:
Oh man, I feel dumb for missing that. Thanks :)

## What is spring force?

Spring force is a conservative force that is exerted by a spring when it is stretched or compressed. It follows Hooke's Law, which states that the force is directly proportional to the displacement from equilibrium.

## What is electrostatic force?

Electrostatic force is the force of attraction or repulsion between electrically charged particles. It is caused by the interaction of positive and negative charges, and follows Coulomb's Law.

## How are spring force and electrostatic force similar?

Both spring force and electrostatic force are conservative forces that follow a mathematical relationship (Hooke's Law for spring force and Coulomb's Law for electrostatic force). They both involve the interaction of two objects and can cause either attraction or repulsion.

## How are spring force and electrostatic force different?

The main difference between spring force and electrostatic force is the type of interaction that causes the force. Spring force is caused by the displacement of a spring, while electrostatic force is caused by the interaction of electrically charged particles. Additionally, spring force is only present when the spring is being stretched or compressed, while electrostatic force can exist even when the charged particles are not moving.

## How do spring and electrostatic forces affect everyday objects?

Spring and electrostatic forces play a significant role in our daily lives. Springs are used in objects such as mattresses and car suspensions, while electrostatic forces are responsible for the attraction between clothes in a dryer and the functioning of electronic devices. They also play a crucial role in the structure of atoms and molecules, making them essential for life as we know it.

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