I was supposed to help a 9yo with her science homework. Being an engineer (albeit the electronics kind) I felt pretty confident that I would be able to handle this task.

The homework was all exercises from this book:

More particular, it was about springs

Springs essentially work according to Hooke’s Law, that, according to Wikipedia, states:

As long as they are not stretched or compressed beyond their elastic limit, most springs obey Hooke’s law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length:

where

- x is the displacement vector – the distance and direction the spring is deformed from its equilibrium length.
- F is the resulting force vector – the magnitude and direction of the restoring force the spring exerts
- k is the rate, spring constant or force constant of the spring, a constant that depends on the spring’s material and construction.

Coil springs and other common springs typically obey Hooke’s law. There are useful springs that don’t: springs based on beam bending can for example produce forces that vary nonlinearly with displacement.

Now, it’s been 25 years since I studied these things, and I am ready to admit I forgot the name of Mr. Hooke and the exact wording of his law. However, I did actually remember that springs essentially work in a linear fashion.

So let us look at the actual questions. The overall question is:

Question one:

Excuse me, it is as far as I can see absolutely impossible to answer that question based on the information given. One would have to make some serious assumptions in order to answer. If we assume that those two springs have the same spring constant, that they are shown in equilibrium and that none of the “weights applied” will stretch the spring beyond it’s elastic limit, then the correct answer would be that they will stretch exactly the same.

Even forgetting everything I know about forces I would find this one hard to answer.

The same goes for the rest of the questions. Since there is absolutely no information about the spring constant, one would have to assume it’s the same.

In other words it is as far as I can see impossible to answer any of these questions, or it would require some serious assumptions to do so.