Principles of Special Relativity - AP Physics 2

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Question

Determine the observed length of a $3\textup{ m}$ rod traveling along it's long axis at $0.75\textup{ c}$ in relation to an observer.

$\textup{c}=3.00*10^8\ \frac{\textup{m}}{\textup{s}}$

Answer

Using the formula for length contraction:

$L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Where is the rest length,

is the velocity of the object

is the speed of light

is the observed length

Plugging in values

$L=3\sqrt{1-\frac{(.75c)^2}{c^2}}$

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Question

Determine the observed length of a $7\textup{ m}$ rod traveling along it's long axis at $0.86\textup{ c}$ in relation to an observer.

Answer

Use the following equation:

$L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Where is the rest length,

is the velocity of the object

is the speed of light

is the observed length

Plugging in values

$L=7\sqrt{1-\frac{(.86c)^2}{c^2}}$

$L=3.57\textup{ m}$

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Question

A long rod is traveling at in relationship to an observer along it's long axis. Determine the observed length.

Answer

Using

$L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Plugging in values

$L=3*\sqrt{1-\frac{(.75c)^2}{c^2}}$

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Question

A tall rocket is traveling at in relationship to an observer along it's long axis. Determine the observed length.

Answer

Using

$L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Plugging in values

$L=363*\sqrt{1-\frac{(.57c)^2}{c^2}}$

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