# Calculating Displacement of a Spring with Two Forces

• andreea92
In summary, the conversation is about determining the displacement of a spring when it is stretched by two forces acting on each end. The person asking the question is confused about how to calculate the displacement and whether the forces should be added together or treated as a vectorial sum. The expert explains that a spring in tension will always have two forces acting on it and they could either be equal and opposite or different, resulting in acceleration. The person is grateful for the clarification and now understands the concept.
andreea92

## Homework Statement

My question is what is the displacement of a spring if the spring is stretched by two forces, each acting on an end of it? I've looked on the internet but I've only found examples where the spring is attached to a ceiling.
Are there two restoring forces acting from opposite directions? Is the resultant force their vectorial sum or do I simply add the values?

## The Attempt at a Solution

I would really appreciate your help on this matter because this is very confusing to me, although I do understand how it works when one end of the spring is fixed.
I hope I explained this clearly because English isn't my first language and hopefully I didn't mess up any of the physics terminology, and I'm really sorry if I did. Thanks in advance!

A spring in tension (or compression) will always have two forces acting on it. You are familiar with the forces being equal and opposite, but they could be different, in which case, the spring would accelerate.

Last edited:
Thank you so much! I get it now.

## 1. How do you calculate the displacement of a spring with two forces?

The displacement of a spring with two forces can be calculated using the formula: Δx = (F1 + F2) / k, where Δx is the displacement, F1 and F2 are the two forces acting on the spring, and k is the spring constant.

## 2. What is the spring constant and how is it related to displacement?

The spring constant, denoted by k, is a measure of the stiffness of a spring. It is directly proportional to the force required to displace a spring by a certain distance. This means that a higher spring constant results in a smaller displacement for a given force, and vice versa.

## 3. Can the displacement of a spring be negative?

Yes, the displacement of a spring can be negative. This means that the spring has been compressed instead of stretched. The negative sign indicates the direction of the displacement, not its magnitude.

## 4. What happens to the displacement if the two forces are in the same direction?

If the two forces are in the same direction, the displacement of the spring will be larger than if the forces were acting in opposite directions. This is because the forces are working together to stretch the spring further.

## 5. Can the displacement of a spring be zero?

Yes, the displacement of a spring can be zero if the net force acting on the spring is zero. This means that the spring is in equilibrium, with the forces balancing each other out and no displacement occurring.

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