Question

Is compressing a spring positive or negative work?

Answer 1

According to Hooke's law, a spring's force is proportional to its displacement (or linear amount of stretching or compressing): $F=-kx$

Where $k$ is referred to as the spring constant of the force. Each spring's force constant is unique.

1. All of the crucial measurements and phrases for a coil spring are defined in the diagram. A spring has a natural length for each mass hung on it (the mass could be zero), at which it is neither compressed (shortened) nor expanded (lengthened). At that time, the spring's upward force perfectly balances the gravitational force acting on the mass and spring (remember that the spring itself has mass).
2. When the spring is compressed, the coordinate $x$ is negative; at its natural length, it is zero; and when the spring is extended, it is positive. Since we consider $F$ to be the restoring force, the minus sign in $F=-kx$ is there by convention. A positive force is needed to prolong the spring after it has been compressed, and a negative force is needed to shorten it after it has been extended in order to return it to its original length.

In general, Hooke's law is accurate for any spring within a limited range of motion. We know from experience that a spring can be stretched to the point where it suffers damage and stops working properly.

Hence, work done on a spring when it is compressed is negative.