# Concept Question: Work done by a Spring

• Flamefury
In summary, the conversation is discussing the work and potential energy involved in holding onto and stretching a spring. It is confirmed that the work done is positive, the change in potential energy is positive, and the spring does positive work. The spring does negative work when it is returning to equilibrium after being stretched. The individual's understanding of the direction of displacement and force is correct.
Flamefury
I just need confirmation that I'm thinking of this in the right way. It's looks so simple that I feel I'm overthinking things and messing up.

You are holding onto a spring that is already stretched. You then proceed to take that spring to equilibrium slowly.

(a) The work you do is positive.
(b) The change in potential energy of the spring is positive.
(c) Your work is double that of the work of the spring.
(d) The spring does negative work.
(e) The spring does positive work.

Es = 1/2 * K * x^2, where x is the amount compressed. Since it's outstretched, that'd mean x is negative, right?
In that case, you'd start with negative energy and moving to zero. The spring is resisting the stretch and trying to pull back, which is the same direction as the spring's distance is going. So that would mean the spring's doing positive work.

Would e) be the correct answer or is my understanding wrong?

If the displacement is in the same direction as the force, the work is positive.

Your understanding is correct. In this scenario, the spring is doing positive work because it is exerting a force in the same direction as its displacement. This results in an increase in potential energy, as indicated by the equation you provided. Therefore, the correct answer is (e) The spring does positive work.

## 1. What is work done by a spring?

The work done by a spring refers to the amount of energy transferred to or from the spring due to a change in its length or position. This can be calculated by multiplying the force applied to the spring by the distance it moves.

## 2. How is the work done by a spring calculated?

The work done by a spring can be calculated using the formula W = 1/2kx^2, where W is the work done, k is the spring constant, and x is the displacement of the spring.

## 3. What is the unit of measurement for work done by a spring?

The unit of measurement for work done by a spring is joules (J), which is the same as the unit for energy.

## 4. How does the work done by a spring change with respect to the displacement?

The work done by a spring increases as the displacement of the spring increases. This is because the spring is able to store more potential energy as it is stretched or compressed further.

## 5. Can the work done by a spring be negative?

Yes, the work done by a spring can be negative if the force applied to the spring is opposite to the direction of its displacement. This means that the spring is releasing energy instead of absorbing it.

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