Question

You hang a mass of 1.541 kg on a spring and let it slowly stretch the spring. It itstretches the spring a total of 0.428 m, how much energy is stored in the spring? Take gto be 9.81 m/s2

Answer 1

ANSWER

3.24 J

EXPLANATION

Let's draw a diagram of this situation first:

As we can see, after the spring stretches, we have two forces acting upon the mass: the spring force and the gravity force (also known as the weight of the mass). Since the mass is not moving at this moment, by Newton's Second Law of Motion:

$\begin{gathered} F_s-F_g=0 \\ \text{ therefore} \\ F_s=F_g \end{gathered}$

So the spring force is:

$F_s=mg$

Now, the potential energy of the spring - which is the energy stored in the spring, is:

$U_s=\frac{1}{2}\cdot\Delta y\cdot(-k\cdot\Delta y)=\frac{1}{2}\cdot\Delta y\cdot F_s$

So for this problem, the potential energy is:

$U_s=\frac{1}{2}\cdot\Delta y\cdot m\cdot g$

Replacing with the values:

$U_s=\frac{1}{2}\cdot0.428m\cdot1.541\operatorname{kg}\cdot9.81m/s^2=3.24J$

We have that the energy stored in the spring is 3.24 J, rounded to the nearest hundredth.