How much work must you do to change its length from 9 cm to 14 cm?

A spring has a relaxed length of 6 cm and a stiffness of 200 N/m. How much work must you do to change its length from 9 cm to 14 cm?How much work must you do to change its length from 9 cm to 14 cm?
Find the spring potential energy at both lengths.



SPE1 = 1/2*k*(L1-L0)^2

SPE2 = 1/2*k*(L2-L0)^2



W = SPE2 - SPE1

W = 1/2*k*(L2-L0)^2 - 1/2*k*(L1-L0)^2



Simplify:

W = 1/2*k*((L2 - L0)^2 - (L1-L0)^2)



Plug in data:

k:=200 N/m; L0 := 0.06 m; L1:=0.09 m; L2:=0.14m;



Result:

W = 0.55 JoulesHow much work must you do to change its length from 9 cm to 14 cm?
Solution

K = 200N/m

Change in length = 14 ?9 = 5cm = 0.05m

F = Kx

F = (200) (0.05)

F = 10N

Now using

W = F.X

W = (10) (0.05)

W = 0.5Joules

So you have to perform 0.5 Joules of work on the spring in order to change its length from 9 cm to 14 cm.