Answer
The tube has a length of $~~78.4~cm~~$ in the electrons' reference frame.
Work Step by Step
We can find $\gamma$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{1-\frac{(0.99999997~c)^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{0.0000000599999991}}$
$\gamma = 4082.5$
Let $L_0 = 3.2~km$
We can find the length $L$ of the tube in the electrons' reference frame:
$L = \frac{L_0}{\gamma}$
$L = \frac{3.2~km}{4082.5}$
$L =0.000784~km$
$L = 78.4~cm$
The tube has a length of $~~78.4~cm~~$ in the electrons' reference frame.
