7. In physics, Hooke's law states that the force F (measured in newtons, N)
needed to extend a spring by x units beyond its natural length is
directly proportional to the extension x. Assume that the constant of
proportionality is k (known as the spring constant for a particular spring).
(a) Write F as a function of x.
(b) A spring that has a natural length of 12 cm is stretched by a force of
25 N to a length of 16 cm. Work out the value of the spring constant k.
(c) What force is needed to stretch the spring to a length of 18 cm?