Help Me please!! Can't figure this out!

Question

According to Hooke's Law, the force required to hold the spring stretched x m beyond its natural length is given by f(x) = kx, where k is the spring constant.

Suppose that 4 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 49 cm.

Find the exact value of k, in N/m.

k =  ? N/m

(a)

How much work (in J) is needed to stretch the spring from 36 cm to 44 cm? (Round your answer to two decimal places.)

= ? J

(b)

How far beyond its natural length (in cm) will a force of 15 N keep the spring stretched? (Round your answer one decimal place.)

= ? cm

Answer 1

a) k=force/distance stretched

W=∫kxdx or kx²/2

W(49) - W(32)=(1/2)k(49² - 32²)

4=0.5k(1377)

0.00581=k

b) W(44) - W(36)=(1/2)*0.00581*(44² - 36²)

W=1.86 or 1.9 J

c)

15=0.00581x

2581.7=x