Chapter 36: Q. 22 (page 1059)

A cube has a density of $2000 k g / m^{3}$ while at rest in the laboratory. What is the cube’s density as measured by an experimenter in the laboratory as the cube moves through the laboratory at $90 %$ of the speed of light in a direction perpendicular to one of its faces?

Short Answer

Expert verified

$ρ = 4600 k g / m^{3}$ .

Step by step solution

Given Information

We have given that, a cube has a density of $2000 k g / m^{3}$ .

The cube moves through the laboratory at $90 %$ of the speed of light in a direction perpendicular to one of its faces.

Simplify

At rest, the cube has a density of $2000 k g / m^{3}$ . That is, a cube with dimensions of $l m \times l m \times l m$ has a mass of $2000 k g$ . The cube's dimension in the direction of motion is contracted as the cube moves at a speed of $0.9 c$ :

localid="1650133944245" $L' = \sqrt{1 - {(\frac{v}{c})}^{2}} 1 L' = \sqrt{1 - \frac{{(0.9 \cdot c)}^{2}}{c^{2}}} 1 L' = \sqrt{1 - 0.81 \cdot} (1 m) L' = 0.436 m$

Because the other dimensions are unaffected, the new density is:

localid="1650133299285" $ρ = \frac{2000 k g}{1 m \times 1 m \times 0.436 m} ρ = 4600 k g / m^{3}$

Therefore, Cubes density is $ρ = 4600 k g / m^{3}$ .

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A cube has a density of $2000 k g / m^{3}$ while at rest in the laboratory. What is the cube’s density as measured by an experimenter in the laboratory as the cube moves through the laboratory at $90 %$ of the speed of light in a direction perpendicular to one of its faces?

Short Answer

Step by step solution

Given Information

Simplify

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A cube has a density of 2000kg/m3while at rest in the laboratory. What is the cube’s density as measured by an experimenter in the laboratory as the cube moves through the laboratory at 90%of the speed of light in a direction perpendicular to one of its faces?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Classical Mechanics

Measurements

Waves Physics

Electricity and Magnetism

Translational Dynamics

Study anywhere. Anytime. Across all devices.

A cube has a density of $2000 k g / m^{3}$ while at rest in the laboratory. What is the cube’s density as measured by an experimenter in the laboratory as the cube moves through the laboratory at $90 %$ of the speed of light in a direction perpendicular to one of its faces?