CK-12-Physics - Intermediate

http://www.ck12.org Chapter 6. Work and Energy

FIGURE 6.14

This shows how the applied force is

related to the distance the spring is

stretched.

FIGURE 6.15

Writing the equation for the potential energy stored in the spring requires finding the value of the force. Since the
relationship is linear, we can use the average force. UsingFigure6.15 as an example, we notice that the initial force
is 0.0 N and the final force is 3.0 N. The average force is therefore^0 + 23.^0 = 1 .5N and so the total work in stretching
the spring 0.25 m (and hence the amount of energy stored in the spring) is:

W=Favgx= ( 1. 5 )( 0. 25 ) = 0. 375 J

An equation for the potential energy stored in a spring can be derived as follows:

Taking the initial force as zero and the final force asFf, we have,W=Favgx=(^0 + 2 Ff)x=(^0 + 2 kx)x=^12 kx^2. This is the
equation for the potential energy(PE)stored in a spring:Wa p plied=PE=^12 kx^2.

Check Your Understanding

1. Why is a spring with a 200 N/m spring constant more difficult to stretch than a spring with a 100 N/m spring
   constant?