Question

A 0.050 kg object is attached to a spring with a spring constant of 150.0 N/m. The other end of the spring is attached to a wall in such a way that it rests on a frictionless horizontal surface. A force is exerted on the spring so that it experiences simple harmonic motion. How much work would be done on this spring to compress it by 15.0 cm?

Answer 1

Given:

The mass of the object is,

$m=0.050\text{ kg}$

The spring constant is,

$k=150.0\text{ N/m}$

The compression of the spring is,

$\begin{gathered} x=15.0\text{ cm} \\ =0.15\text{ m} \end{gathered}$

To find:

The work would be done on this spring to compress it

Explanation:

The force on the spring is,

$\begin{gathered} F=\lvert{kx}\rvert \\ =150.0\times0.15 \\ =22.5\text{ N} \\ \end{gathered}$

The work done in the spring,

$\begin{gathered} W=Fx \\ =22.5\times0.15 \\ =3.375\text{ J} \end{gathered}$

Hence, the work is 3.375 J.