It took 1700 J of work to stretch a spring from its natural length of 2m to a length of 5m. Find the spring's force constant.

The work to stretch a spring from its rest position is

(1/2) (spring constant) (distance of the stretch) ²

E = 1/2 k x².

You said it takes 1700 joules to stretch the spring 3 meters from its rest position, so we can write

1700 joules = 1/2 k (3m) ²

1 joule = 1 newton-meter

1700 N-m = 1/2 k (3m) ²

Multiply each side by 2: 3400 N-m = k · 9m²

Divide each side by 9m² k = 3400 N-m / 9m²

= (377 and 7/9) newton per meter

W = (1/2) kx^2, where W=work required to stretch the spring from its equilibrium position

k = spring constant

x = displacement = 5 - 2 = 3m

1800 J = (1/2) (k) (3) ^2

by solving it we get

k = 400 answer.