- #1
gkangelexa
- 81
- 1
Hi! This is probably something silly but here goes.
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?
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?