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$\cdot$ A cube of metal with sides of length $a$ sits at rest in thelaboratory with one edge parallel to the $x$ axis. Therefore, inthe laboratory frame, its volume is $a^{3} .$ A rocket ship flies pastthe laboratory parallel to the $x$ axis with a velocity $v .$ To anobserver in the rocket, what is the volume of the metal cube?

$$=\overline{\frac{a^{3}}{\gamma}}$$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

University of Washington

University of Sheffield

McMaster University

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

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A cube of metal with sides…

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A cube with a mass of $48 …

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The volume of a cube is fo…

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Volume The change in the v…

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Use the following formulas…

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The volume of a cube is gi…

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Find the volume of the fo…

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Solve each problem.Vol…

All right, so in this problem, we have a cube of side length, eh? And a new observer flies past it with the velocity V parallel to one of the sides of the cube. And we want to know what the new volume of the Cube is going to be. So what we need to notice is that, um length contraction on ly happens in the direction parallel to the motion. So basically two sides of the cube, the two sides perpendicular to the motion will retain a new area of a squared. And then the side that the motion is parallel to will get a new length. It'll get linked, contracted so they will get multiplied by the square of one minus. V squared over C squared. So another way, writing this is just a cube square one minus v squared over C squared

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