Question

An object of mass `0.60` `kg` stretches a particular spring by `0.06` `m`, and a particular wooden block extends the same spring by `0.10` `m`. What is the mass of the wooden block? What is its weight?

Answer 1

The object's weight is `9.8` `N` and its mass is `1.0` `kg`.

Explanation:

Remember that weight is a force, measured in newton (N). I suspect the question is actually asking for the mass of the block, measured in kilogram (kg), but we will find both anyway.

We should work in SI units, so that means changed cm to m. The original object extends the spring by `0.06` `m` while the block of wood extends it by `0.10` `m`.

Our first step is to find the spring constant, `k`, using the equation:

`F=kx`

Rearranging,

`k=F/x`

Now the force will be the weight of the object (not its mass):

`F = mg = 0.60xx9.8=5.9` `N`

So `k=F/x=5.9/0.06=98.33` `Nm^-1` (spring constants are also sometimes expressed in the equivalent units `kgs^-2`)

Now we can use the spring constant to determine the weight of the block of wood:

`F=kx=98.33xx0.10=9.8` `N` (rounding off)

This is the answer to the question about the weight of the block of wood, but let's find out its mass, just in case:

`F=mg`

`m=F/g=9.8/9.8=1.0` `kg`

This makes sense: `0.6` `kg` extended the spring by `6` `cm`, so a mass that extends it by `10` `cm` is going to be heavier.