# When is the work on a spring negative and when is it positive?

PhyIsOhSoHard
I have a problem understanding whether a sign should be positive or negative when it comes to a spring.

In my book, there is an example with a glider attached to a spring, and the glider is moving away from the spring so it expands.
It says that in order to use the work-energy theorem, it has to be the work done by the spring on the glider, which is the negative of the following equation:

$W=\frac{1}{2}mv_2^2-\frac{1}{2}mv_1^2$

Can somebody explain the "work done by the spring" and "work done on the spring"? How do I know which situation I have?
Why is the work negative in this situation?
And if the glider went the opposite direction, towards the spring, would that mean the work-energy theorem is positive?

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rtshah
Direction of spring force is always against its extension . Since F = - kx if the this is opposite to instantaneous displacement of body then negative work is done or if it is along the displacement positive work is done

Homework Helper
Gold Member
I have a problem understanding whether a sign should be positive or negative when it comes to a spring.
you are not alone.
In my book, there is an example with a glider attached to a spring, and the glider is moving away from the spring so it expands.
It says that in order to use the work-energy theorem, it has to be the work done by the spring on the glider, which is the negative of the following equation:

$W=\frac{1}{2}mv_2^2-\frac{1}{2}mv_1^2$
Yes, but that is confusing, isn't it?
Can somebody explain the "work done by the spring" and "work done on the spring"? How do I know which situation I have?
By newton's 3rd law, you always have both situations, but usually you are looking at work done on the object by the spring.
Why is the work negative in this situation?
Work done on an object by a spring is negative when the displacement and force on the object are in opposite directions. When the glider is moving away from the spring, it is pulling on the spring, so by Newton 3, the the spring is pulling back on the glider. Since the force on the glider is back, but the displacement of the glider is forward, work done by the spring on the glider is negative.
And if the glider went the opposite direction, towards the spring, would that mean the work-energy theorem is positive?
Yes, the direction of the spring force on the object is back (it is pulling it back), and the glider is moving back, same direction, work is plus. It is often better to use conservation of energy equation rather than work-energy, since the plus/minus signs can be handled easier. But nonetheless, it is a good exercise using work-energy.

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