# Work done by a spring & its potential energy

by Archit Patke
Tags: mechanical energy, spring force, work energy
 P: 1 According to work - mechanical energy theorem , W = K(final) - K(initial) + U(final) - U(initial) . . . . (1) as we define Potential energy as negative of work done by conservative force and assuming that the only force in this situation is Spring force then , W(spring) = K(final) - K(initial) As work done is calculated by finding component of spring force in direction of displacement. How can we say that U(final) - U(initial) applies for all possible conditions of extension of spring as displacement may not be in direction of force ? Spring force = 0.5kx2
HW Helper
P: 6,345
 Quote by Archit Patke According to work - mechanical energy theorem , W = K(final) - K(initial) + U(final) - U(initial) . . . . (1) as we define Potential energy as negative of work done by conservative force and assuming that the only force in this situation is Spring force then , W(spring) = K(final) - K(initial) As work done is calculated by finding component of spring force in direction of displacement. How can we say that U(final) - U(initial) applies for all possible conditions of extension of spring as displacement may not be in direction of force ? Spring force = 0.5kx2
Welcome to PF!

First of all, your equation (1) defines the external work done by/on a system. If no energy is added or lost (Wext = 0), Kf + Uf = Ki + Ui.

Second, your question is not clear. What do you mean when you say U(final) - U(initial) applies? U(final) - U(initial) is not a mathematical statement.

Finally, your statement: Spring force = 0.5kx2 is not correct. F = -kx.

AM
P: 5,462
 Finally, your statement: Spring force = 0.5kx2 is not correct. F = -kx.
In case this was a simple slip, the formula

$$W = \frac{1}{2}k{e^2}$$

W = work, e = extension, k = spring constant

Refers to the work done in extending a spring = potential energy stored in that spring on extension.

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