/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q5-88GP A science-fiction tale describes... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q5-88GP (page 109)

A science-fiction tale describes an artificial 鈥減lanet鈥� in the form of a band completely encircling a sun (Fig. 5鈥�50). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate livable), and that the ring rotates quickly enough to produce an apparent gravity of gas on Earth. What will be the period of revolution, this planet鈥檚 year, in Earth days?

Short Answer

Expert verified

The period of revolution is 9 days.

Step by step solution

01

Find the period of revolution, this planet’s year, in Earth days

According to Newton鈥檚 second law, the centripetal force acting on the objects on this planet must be equal to\(mg\). Therefore

\(\begin{aligned}mg &= \frac{{m{v^2}}}{r}\\g\; &= \;\frac{{{v^2}}}{r}\\v &= \;\sqrt {rg} \end{aligned}\)

The period is given by:

\(T = \frac{{2\pi r}}{v} = \frac{{2\pi r}}{{\sqrt {rg} }} = 2\pi \sqrt {\frac{r}{g}} \)

Let the distance from the Sun to the Earth be \(r = 149.6 \cdot {10^6}\;{\rm{km}}\).Therefore, the period is given by:

\(T = 780000\;{\rm{s}} = 9{\rm{ days}}\)

So, the period of revolution is 9 days.

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

Most popular questions from this chapter

The source of the Mississippi River, is closer to the centre of the Earth than is its outlet in Louisiana (because the Earth is fatter at the equator than at the poles). Explain how the Mississippi can flow "uphill."

A 0.55-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have?

A pilot performs an evasive maneuver by diving vertically at 270 m/s. If he can withstand an acceleration of 8.0 g鈥檚 without blacking out, at what altitude must he begin to pull his plane out of the dive to avoid crashing into the sea?

Calculate the force of Earth鈥檚 gravity on a spacecraft 2.00 Earth radii above the Earth鈥檚 surface if its mass is 1850 kg.

(a)Show that if a satellite orbits very near the surface of a planet with period \({\bf{T}}\), the density (= mass per unit volume) of the planet is \({\bf{\rho = m/V = }}\frac{{{\bf{3\pi }}}}{{{\bf{G}}{{\bf{T}}^{\bf{2}}}}}\) (b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of \({\bf{85}}{\rm{ }}{\bf{min}}\). Approximate the Earth as a uniform sphere.
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Fields in Physics

Read Explanation

Nuclear Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Classical Mechanics

Read Explanation

Mechanics and Materials

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.