Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 65

What is the acceleration of the Earth in its orbit? (Assume the orbit is circular.)

Short Answer

Expert verified
Answer: The approximate acceleration of Earth in its orbit around the Sun is 5.932 × 10^-3 m/s².

Step by step solution

01

Determine the radius of the Earth's orbit

The average distance from the Earth to the Sun, which represents the radius of the Earth's orbit, is approximately 93 million miles or 1 Astronomical Unit (AU). To use the centripetal acceleration formula, we should convert this distance to meters: 1 AU ≈ 1.496 × 10^11 meters
02

Find the Earth's orbital speed

The Earth takes about 365.25 days to complete one orbit around the Sun. To find the speed (v), we can use the formula: v = (2πr) / T, where r is the radius of the Earth's orbit and T is the period of revolution (time taken for one complete orbit). First, convert the time to seconds: 365.25 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute ≈ 3.156 × 10^7 seconds Now, plug in the values to find the speed: v = (2π × 1.496 × 10^11 meters) / (3.156 × 10^7 seconds) ≈ 2.978 × 10^4 m/s
03

Calculate the centripetal acceleration

Now that we have the radius of the Earth's orbit (r) and its orbital speed (v), we can use the centripetal acceleration formula: a = v^2 / r Plug in the values to find the acceleration: a = (2.978 × 10^4 m/s)^2 / (1.496 × 10^11 meters) ≈ 5.932 × 10^-3 m/s^2
04

Express the result

The acceleration of the Earth in its orbit, assuming it is circular, is approximately 5.932 × 10^-3 m/s².

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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 motor of a fan turns a small wheel of radius \(r_{\mathrm{m}}=\) \(2.00 \mathrm{~cm} .\) This wheel turns a belt, which is attached to a wheel of radius \(r_{f}=3.00 \mathrm{~cm}\) that is mounted to the axle of the fan blades. Measured from the center of this axle, the tip of the fan blades are at a distance \(r_{\mathrm{b}}=15.0 \mathrm{~cm} .\) When the fan is in operation, the motor spins at an angular speed of \(\omega=1200\). rpm. What is the tangential speed of the tips of the fan blades?

A particular Ferris wheel takes riders in a vertical circle of radius \(9.0 \mathrm{~m}\) once every \(12.0 \mathrm{~s} .\) a) Calculate the speed of the riders, assuming it to be constant. b) Draw a free-body diagram for a rider at a time when she is at the bottom of the circle. Calculate the normal force exerted by the seat on the rider at that point in the ride. c) Perform the same analysis as in part (b) for a point at the top of the ride.

Determine the linear and angular speeds and accelerations of a speck of dirt located \(2.0 \mathrm{~cm}\) from the center of a CD rotating inside a CD player at 250 rpm.

A small block of mass \(m\) is in contact with the inner wall of a large hollow cylinder. Assume the coefficient of static friction between the object and the wall of the cylinder is \(\mu\). Initially, the cylinder is at rest, and the block is held in place by a peg supporting its weight. The cylinder starts rotating about its center axis, as shown in the figure, with an angular acceleration of \(\alpha\). Determine the minimum time interval after the cylinder begins to rotate before the peg can be removed without the block sliding against the wall.

A race car is making a U-turn at constant speed. The coefficient of friction between the tires and the track is \(\mu_{\mathrm{s}}=1.20 .\) If the radius of the curve is \(10.0 \mathrm{~m},\) what is the maximum speed at which the car can turn without sliding? Assume that the car is performing uniform circular motion.
See all solutions

Recommended explanations on Physics Textbooks

Radiation

Read Explanation

Electricity

Read Explanation

Electricity and Magnetism

Read Explanation

Dynamics

Read Explanation

Electrostatics

Read Explanation

Electromagnetism

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.

Sign-up for free