# What steps would you take to determine the density of a rubber eraser?

Mar 31, 2016

Find mass, then volume, then divide mass by volume:

$d = \frac{m}{V}$

#### Explanation:

1st) Find the volume $V$ of the rubber. To make the calculation easier, one can cut it into a cubic form or a rectangular cuboid. Therefore, you can estimate the volume by multiplying all sides $a \cdot b \cdot c$. Use $c m$ for distance.
2nd) Weight the rubber $m$ in grams.
3rd) Density is equal to the division of the weight in step 2 by the volume in step 1. Doing so with the units given gives the result in $\frac{g}{c {m}^{3}} = \frac{g}{m l}$

$d = \frac{m}{V} = \frac{m}{a \cdot b \cdot c}$

Another way to do this:

1st) Weight the rubber $m$ in grams.
2nd) Find a liquid that doesn't dissolve the rubber. I believe water suits fine. Fill a cylindrical glass with water until a certain height. Mark that height with a marker. Then immerse the rubber in the liquid and mark the new height. Find the difference between the two heights Δh.
3rd) As before, density is equal to mass divided by volume. The volume difference, which is the volume of a cylinder, is equal to the rubbers volume. Therefore, find the diameter of the glass $d$

d=m/V=m/(πr^2*Δh)=m/(π(d/2)^2*Δh)=(4m)/(πd^2*Δh)

The second method however holds an error in case the rubber has pores and absorbs some of the water, effectively displacing the air inside the rubber and increasing its real density. So if you do both, expect the 2nd method to have a slightly bigger density. However, the 1st method requires very good measurements and/or cuts.