7.5  Work Done by a Spring Force

Let us know examine the action of a variable force, the spring force, on an object. This force is given by:

where is the displacement of the free end from its relaxed state and is the spring constant. We see that this force is proportional to the displacement of the free end of the spring. We also notice that the force is always opposite the displacement.

If  is positive, the spring is stretched toward the right on the x-axis, then the force is negative (it pulls toward the left). If is negative, the spring is stretched toward the left on the x-axis, then the force is positive (it pulls toward the right).

The work done by a spring force

If the spring is initially unstretched and then

The work done by an applied force

If an object is attached to a spring and at rest before and after displacement, the work done by an externally applied force is the negative of the work done by the spring force.

 
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