Calculate the extension displacement for a linear spring with a certain spring constant and a spring potential energy.

Example question:

A linear spring has a potential energy of 25 J and a constant of 510 N/m. How far has it been stretched?


spring potential energy: Us = 25 J

spring constant: k = 510 N/m

Starting formula

Algebra: multiply each side by 2

Algebra: 2's cancel on right

Algebra: divide each side by k

Algebra: k's cancel on right

Algebra: take square root of each side

Algebra: square root of x^2 is x

Algebra: switch left and right

Plug in numbers with units

Math: sqrt(2(25)/510) = 0.313....

Final result with significant figures and unit