Q. 18 At what speed, in m/s,聽would a ... [FREE SOLUTION]

Chapter 36: Q. 18 (page 1059)

At what speed, in $m / s,$ would a moving clock lose role="math" localid="1649531760117" $1.0 ns$ in $1.0$ day according to experimenters on the ground?
Hint: Use the binomial approximation.

Short Answer

Expert verified

The speed of a moving clock is $46 m / s .$

Step by step solution

Given Information

We have to find the speed in $m / s$ for a moving clock lose $1.0 ns$ in $1.0$ day according to experimenters on the ground using binomial approximation.

Simplify

The ground's frame is $S$ .

The moving clock frame is $S' .$

$鈭� t = 1.0 d + 1.0 n s 鈭� t' = 1.0 d = 86400 s$

We have: $鈭� t = y 鈭� t' .$

When calculating powers of sums of 1 and a small number x, the binomial approximation comes in handy.

Now, we use binomial approximation for $y :$

localid="1649844482103" $\frac{鈭� t}{鈭� t'} = 1 + \frac{v^{2}}{2 c^{2}} \frac{鈭� t}{鈭� t'} - 1 = \frac{v^{2}}{2 c^{2}} 2 c^{2} (\frac{鈭� t}{鈭� t'} - 1) = v^{2} v = c \sqrt{2 (\frac{鈭� t}{鈭� t'} - 1)} v = c \sqrt{2 (\frac{1.0 n s}{1.0 d})} v = (3 脳 10^{8} m / s) \sqrt{(\frac{2 (1.0 脳 10^{- 9} s)}{86400 s})} v = 46 m / s$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

At what speed, in $m / s,$ would a moving clock lose role="math" localid="1649531760117" $1.0 ns$ in $1.0$ day according to experimenters on the ground?
Hint: Use the binomial approximation.

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

Radiation

Modern Physics

Atoms and Radioactivity

Particle Model of Matter

Classical Mechanics

Wave Optics

Study anywhere. Anytime. Across all devices.

91影视

At what speed, in m/s,would a moving clock lose role="math" localid="1649531760117" 1.0nsin 1.0day according to experimenters on the ground?Hint: Use the binomial approximation.

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

Radiation

Modern Physics

Atoms and Radioactivity

Particle Model of Matter

Classical Mechanics

Wave Optics

Study anywhere. Anytime. Across all devices.

At what speed, in $m / s,$ would a moving clock lose role="math" localid="1649531760117" $1.0 ns$ in $1.0$ day according to experimenters on the ground?
Hint: Use the binomial approximation.