A box at rest has the shape of a cube 2.6 m on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies pa

Question

A box at rest has the shape of a cube 2.6 m on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.80c. What is the volume of the box as we observe it

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bonexptip 5 months 2021-08-23T20:33:40+00:00 1 Answers 21 views 0

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    2021-08-23T20:35:14+00:00

    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:

    L = \frac{L_{o}}{\gamma}

    Where:

    L – Proper length, measured in meter.

    \gamma – Lorentz factor, dimensionless.

    The Lorentz factor is represented by the following equation:

    \gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}} }}

    If v = 0.8\cdot c, then:

    \gamma = \frac{1}{\sqrt{1-\frac{0.64\cdot c^{2}}{c^{2}} }}

    \gamma = \frac{1}{\sqrt{1-0.64}}

    \gamma = \frac{5}{3}

    Therefore, the observed length is:

    L = \frac{3}{5}\cdot L_{o}

    Given that L_{o} = 2.6\,m, the observed length is:

    L = \frac{3}{5}\cdot (2.6\,m)

    L = 1.56\,m

    The observed volume of the box is:

    V = L^{3}

    V = (1.56\,m)^{3}

    V= 3.796\,m^{3}

    The observed volume of the box is 3.796 cubic meters.

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