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 6 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 40 cm.
Find the exact value of $k$, in N/m.
$k = \boxed{\phantom{00000}}$ N/m
(a) How much work (in J) is needed to stretch the spring from 36 cm to 38 cm? (Round your answer to two decimal places.)
$\boxed{\phantom{00000}}$ J
(b) How far beyond its natural length (in cm) will a force of 40 N keep the spring stretched? (Round your answer one decimal place.)
$\boxed{\phantom{00000}}$ cm
