The energy stored in a spring is
E = 1/2 (k x²)
' k ' is the spring constant . . . the number of newtons of force it takes to stretch or compress the spring by one meter from its relaxed length
' x ' is the distance the spring is stretched or compressed
For this problem, we know ' E ' and ' x ', and we need to find ' k '.
E = 1/2 (k x²)
1,000 = 1/2 (k) (0.025²)
1,000 = 1/2 (k) (0.000625)
Multiply each side by 2 :
2,000 = (k) (0.000625)
Divide each side by 0.000625:
(2,000) / (0.000625) = k
k = 3,200,000
The spring constant is 3.2 x 10⁶ Newtons per meter .
This is a very stiff spring ! My calculator says that if you want to stretch it just 1 inch, you have to pull it with a force of 18,285 pounds ! ! If such a spring exists, it might be used as part of the suspension for a tank or a concrete truck.
