Answer:
The observed volume of the box is 3.796 cubic meters.
Explanation:
The observed length is determined by the formula for the Length Contraction:
[tex]L = \frac{L_{o}}{\gamma}[/tex]
Where:
[tex]L[/tex] - Proper length, measured in meter.
[tex]\gamma[/tex] - Lorentz factor, dimensionless.
The Lorentz factor is represented by the following equation:
[tex]\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}} }}[/tex]
If [tex]v = 0.8\cdot c[/tex], then:
[tex]\gamma = \frac{1}{\sqrt{1-\frac{0.64\cdot c^{2}}{c^{2}} }}[/tex]
[tex]\gamma = \frac{1}{\sqrt{1-0.64}}[/tex]
[tex]\gamma = \frac{5}{3}[/tex]
Therefore, the observed length is:
[tex]L = \frac{3}{5}\cdot L_{o}[/tex]
Given that [tex]L_{o} = 2.6\,m[/tex], the observed length is:
[tex]L = \frac{3}{5}\cdot (2.6\,m)[/tex]
[tex]L = 1.56\,m[/tex]
The observed volume of the box is:
[tex]V = L^{3}[/tex]
[tex]V = (1.56\,m)^{3}[/tex]
[tex]V= 3.796\,m^{3}[/tex]
The observed volume of the box is 3.796 cubic meters.
