The spring is now compressed so that the unconstrained end moves from x=0 to x=L. Using the work integral W=∫xfxiF⃗ (x⃗ )⋅dx⃗ , find the work done by the spring as it is compressed. Express the work done by the spring in terms of k and L?

solution:

the spring force exerted by spring with spring constant k is given by

where k is spring constant

and x is deformation of spring

in order to calculate word done by the spring

the work done by the spring as it is compressed from x=0 to x=L

inserting the limits x=0 and x=L

we get work done in terms of k and L

answer would be letter choice (a),   a ball resting on a shelf. would be another example of potential energy   >   stored energy > not moving.

a ball spinning on a finger   >   kinetic energy > moving energy

a ball rolling on the ground   >   kinetic energy   > moving energy

a   ball flying through the air   > kinetic energy   >   moving energy

hope that                                         : )