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Problem 26 Easy Difficulty

A cubical box is 0.75 $\mathrm{m}$ on a side. (a) What are the dimensions of the box as measured by an observer moving with a speed of 0.82$c$ parallel to one of the edges of the box? (b) What is the volume of the box, as measured by this observer?

Answer

a) 0.43 $m \times 0.75 m \times 0.75 m$
b) 0.24 $\mathrm{m}^{3}$

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Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Jared E.

University of Winnipeg

Video Transcript

according to one standing Still, observer still is the shape of the box, according to an observer that is moving parallel to the side of the box. These in the shape of the box because he is moving with respect to the side of the box. Therefore, you measured the contracted length and not the properly before he seems the box as a parallelogram. To complete el, we have to use the next contraction equation. So l is close to l zero times square. Root off one mind really divided by C Square to L equals to 0.75 times the square root off one minus zero point, a two time seat divided by C squared. The PSI factor simplifies and we get a contracted length of approximately zero point 43 meters. Now, according to the Observer, that is moving with respect to the box, it will have a different value. The value's off the box, according to the Observer, is given by 0.75 times zero going 75 times 0.43 which is approximately 0.24 cubic meters

Brazilian Center for Research in Physics
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Jared E.

University of Winnipeg