Question

An unstretched spring has a length of 10cm when the spring is stretched by a force of 16 Newtons it's length is increased to 18 cm what is the spring constant of the spring

Answer 1

Hook's law states that the relationship between the force F applied to a spring and the elongation/compression $\delta x$ of the spring (with respect to its equilibrium position) is
$F=-k \Delta x$
where k is the spring constant, and the negative sign simply means that the direction of the force is opposite to the displacement.

In our problem, the spring is stretched by
$\Delta x= 18 cm - 10 cm=8 cm=0.08 m$
And so we can use Hook's law to find the spring constant (we can ignore the sign and consider only the magnitude of the force, 16 N):
$k= \frac{F}{\Delta x}= \frac{16 N}{0.08 m} =200 N/m$