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AP Physics 2 : Principles of Special Relativity

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Example Questions

Example Question #1 : Principles Of Special Relativity

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

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

Possible Answers:

$1.98\textup{ m}$ $\displaystyle 1.98\textup{ m}$

$3.98\textup{ m}$ $\displaystyle 3.98\textup{ m}$

$2.5\textup{ m}$ $\displaystyle 2.5\textup{ m}$

$2.36\textup{ m}$ $\displaystyle 2.36\textup{ m}$

$3\textup{ m}$ $\displaystyle 3\textup{ m}$

Correct answer:

$1.98\textup{ m}$ $\displaystyle 1.98\textup{ m}$

Explanation:

Using the formula for length contraction:

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

Where L_0 $\displaystyle L_0$ is the rest length,

$\displaystyle v$ is the velocity of the object

$\displaystyle c$ is the speed of light

$\displaystyle L$ is the observed length

Plugging in values

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

L=1.98m $\displaystyle L=1.98m$

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Example Question #1 : Principles Of Special Relativity

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

Possible Answers:

$3.57\textup{ m}$ $\displaystyle 3.57\textup{ m}$

$6.68\textup{ m}$ $\displaystyle 6.68\textup{ m}$

$2.54\textup{ m}$ $\displaystyle 2.54\textup{ m}$

None of these

$8.44\textup{ m}$ $\displaystyle 8.44\textup{ m}$

Correct answer:

$3.57\textup{ m}$ $\displaystyle 3.57\textup{ m}$

Explanation:

Use the following equation:

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

Where L_0 $\displaystyle L_0$ is the rest length,

$\displaystyle v$ is the velocity of the object

$\displaystyle c$ is the speed of light

$\displaystyle L$ is the observed length

Plugging in values

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

$L=3.57\textup{ m}$ $\displaystyle L=3.57\textup{ m}$

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Example Question #11 : Quantum And Nuclear Physics

A $\displaystyle 3m$ long rod is traveling at .75c $\displaystyle .75c$ in relationship to an observer along it's long axis. Determine the observed length.

Possible Answers:

None of these

3.98m $\displaystyle 3.98m$

2.98m $\displaystyle 2.98m$

4.5m $\displaystyle 4.5m$

1.98m $\displaystyle 1.98m$

Correct answer:

1.98m $\displaystyle 1.98m$

Explanation:

Using

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

Plugging in values

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

L=1.98m $\displaystyle L=1.98m$

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Example Question #1 : Principles Of Special Relativity

A 363ft $\displaystyle 363ft$ tall rocket is traveling at .57c $\displaystyle .57c$ in relationship to an observer along it's long axis. Determine the observed length.

Possible Answers:

175ft $\displaystyle 175ft$

401ft $\displaystyle 401ft$

None of these

320ft $\displaystyle 320ft$

298ft $\displaystyle 298ft$

Correct answer:

298ft $\displaystyle 298ft$

Explanation:

Using

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

Plugging in values

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

L=298ft $\displaystyle L=298ft$

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AP Physics 2 : Principles of Special Relativity

Study concepts, example questions & explanations for AP Physics 2

All AP Physics 2 Resources

Example Questions

Example Question #1 : Principles Of Special Relativity

Example Question #1 : Principles Of Special Relativity

Example Question #11 : Quantum And Nuclear Physics

Example Question #1 : Principles Of Special Relativity

All AP Physics 2 Resources

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