Question

A spring of length 9.7 meters stretches to 9.8 meters when a 0.4 kg mass is hung vertically from one end. What is the spring constant?

Answer 1

Given,

The initial length of the spring, l=9.7 m

The length of the spring after stretching, L=9.8 m

The mass, m=0.4 kg

The magnitude of the restoring force of the spring due to the stretching from the mass will be equal to the force applied by the mass, which is nothing but the weight of the mass.

Thus,

`\begin{gathered} mg=k\Delta x \\ =k(L-l) \end{gathered}`

Where g is the acceleration due to gravity, k is the spring constant, and Δx is the stretch in the length of the spring.

On substituting the known values,

`\begin{gathered} k=\frac{mg}{(L-l)_{}} \\ =(0.4*9.8)/(9.8-9.7) \\ =(3.92)/(0.1) \\ =39.2\text{ N/m} \end{gathered}`

Thus the spring constant is 39.2 m