- #1

gkangelexa

- 81

- 1

My question involves elastic potential energy and work…

So we know that a change in potential energy = Work done, as long as the forces are conservative...

**delta U = Work done**

Let’s say we have a spring…

**Work done/by on a spring is, W= ½ kx^2**

**Also, the potential energy at a position on the spring is: U =½ kx^2**

So if we have a spring with K = 360, the potential energy if you push it in 5 cm is: U = (1/2)(360)(.05)^2 = .45

If we then push it to 12 cm, U is now (1/2)(360)(.12)^2 = 2.59

So the difference in potential energy from 5 cm to 12 cm is 2.59-.45 which is 2.14.

But the U = Work done

The work done to move from 5 cm to 12 cm should be equal to the difference in potential energy from position 5 cm to position 12 cm.

But when I calculate the work done to push the spring from 5 cm to 12 cm (a difference of 7 cm) it’s (1/2)(360)(.07)^2 = .882…

.882 does not equal 2.14…

When I try this method with gravitational potential energy (U = mgh; W = mgh) it works.

The work done to lift an object from a height of 5 m to a height of 12 cm is equal to the difference in potential energy from 5 to 12.

Why doesn’t it work with elastic potential energy just like it works with gravitational potential energy?