Question

Rearrange the elastic potential formula to find an extension.

a) E= k⋅x^2/4
b) E= k⋅x/2
c) E=2⋅k/x
d) E=k⋅x

Answer 1

To find the extension, rearrange the elastic potential energy formula by equating it to the work done by the spring and using Hooke's law to substitute the force in terms of the extension. The expression for the extension is x = W/(kd).

Step-by-step explanation:

The elastic potential energy stored in any deformed system that obeys Hooke's law and has a displacement x from equilibrium and a force constant k is given by the equation PEel = kx². To rearrange this formula to find the extension, we can use the fact that elastic potential energy is equal to the work done on the spring, which is given by W = Fd, where W is the work done, F is the force exerted by the spring, and d is the displacement or extension.

First, we can equate the elastic potential energy to the work done: PEel = W. Then, we can substitute the force exerted by the spring in terms of the extension using Hooke's law: F = kx. Finally, we substitute the work done with the force and displacement: W = Fd = kxd. Rearranging this equation gives us the expression for the extension: x = W/(kd).