Answer
3 rubber bands
Work Step by Step
Acceleration is defined by $a = \frac{F}{m}$
Setting up the initial problem with a relativistic model of acceleration results in $a = \frac{2F}{m}$. Substituting $a$ with $\frac{a}{3}$ allows us to find to total relative acceleration for 3 times the initial acceleration. $\frac{a}{3} = \frac{2F}{m} \rightarrow a = \frac{6F}{m} $. Now to find the force relative to the mass, rewrite the equation in terms of mass $m = \frac{6F}{a}$ and substitute $m$ for $2m$ since the mass in the equation is 2 times the mass we are looking to find, and then solve the new equation for acceleration. $2m = \frac{6F}{a} \rightarrow m = \frac{3F}{a} \rightarrow a = \frac{3F}{m}$. Here, we can see that $3F$ or 3 rubber bands are needed.
