Please check my maths and my units as I am. The work done by you to stretch the spring is the same but with opposite sign. In this activity, you can see the forces involved, the work done and you. We look at springs in more detail later in this section. The work done to compress (or elongate) a spring, for example, varies depending on how far the spring has already been compressed (or stretched).

This is the work done by the elastic force. This spring constant is also called the stiffness of the spring. Calculus Calculus (OpenStax) 6: Applications of Integration 6.5: Physical Applications. So #k=20/6=10/3# lbs/inches that substiituted in the expression for work (I) gives: #-k*(24-18)=-20=F_(el)# It is #-20# because you immagine the stretching (from a force) in the positive #x# direction so that your #F_(el)# is in the negative #x# direction. The work done on the spring is actually the work by you and is kx², and the work done by the spring is 1/2 kx² ( this is the actual energy you transfer to spring ) so this is the work energy produced in the spring. You can find #k# from the second part of your problem where you have: MTH 256 Applied Differential Equations (4) Fall, Winter, and Spring term Prerequisites: MTH. x i is the initial position of the spring. Ive done repair work before but never on a Tinplate engine. W xf x F x dx xf x kxdx 1 2kx2 2 1 2kx2 1 W x i x f F x d x x i x f k x d x 1 2 k x 2 2 - 1 2 k x 1 2. When a force is applied on a spring, and the length of the spring changes by a differential amount dx, the work done is Fdx. in actuality the equation should be -F2x but it is still algebraically correct.

the negative sign indicates that the restorative force is in the opposite direction of the applied force. It involves the elastic force which is given by Hooke's Law as #F_(el)=-kx# where #x# is the elongation and #k# is the spring constant (and the negative sign indicates that is a force always opposite to the displacement from equilibrium!).īut this is a VARIABLE force (depends on #x#) so for the work you have to integrate and get: If you integrate the force (F) on spring over a distance, you get the following equation. k, being the spring constant, is always a positive number.

Workdone by a spring calculus