The radius of the earth’s orbit around the sun (assumed to

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

Problem 28E Chapter 3

University Physics | 13th Edition

  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

4 5 0 254 Reviews
24
1
Problem 28E

The radius of the earth’s orbit around the sun (assumed to be circular) is 1.50 X 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of the earth toward the sun, in m/s2? (c) Repeat parts (a) and (b) for the motion of the planet Mercury (orbit radius = 5.79 X 107 km, orbital period = 88.0 days).

Step-by-Step Solution:

Solution 28E Step 1: Equation for speed in centripetal motion, v = distance /time = 2 r / T Where, 2 r - circumference of the circular path T - Time taken to cover this circular path Step 2: a) In the case of earth, radius of earth’s orbit, r - 1.50 × 10 km 1 km = 1000 m Therefore, r - 1.50 × 10 × 1000 m = 1.50 × 10 m 11 Therefore, the circumference of the orbit of the earth, C = 2 r = 2 × 3.14 × 1.50 × 10 m 11 C = 9.42×10 m11 Step 3: a ) Time required to cover this orbit, T = 365 days We know that, 1 day = 24 hours Therefore, 365 days = 365 × 24 hours = 8760 hours 1 hour = 60 minutes Therefore, 8760 hours = 8760 × 60 minutes = 525600 minutes 1 minute = 60 seconds Therefore, 525600 minutes = 525600 × 60 seconds = 3.1536 × 10 seconds 7 Step 4: 11 7 a) Speed or magnitude of velocity of earth, v = (9.42×10 m) / (3.1536 × 10 seconds) v = 2.987 × 10 m/s 4 Step 5: 2 b) E quation for centripetal acceleration, a = v /r Where, v - magnitude of velocity of centripetal motion r - radius of the orbit In the case of earth, v = 2.987 × 10 m/s (from step 4) and r = 1.50 × 10 m 11 Therefore, a = (2.987 × 10 m/s) / (1.50 × 10 m) = (8.922 × 10 m /s ) / (1.50 × 10 m) 8 2 2 11 -3 2 a = 5.948 × 10 m/s Radial acceleration of earth towards the sun is, a = 5.948 × 10 m/s -3 2

Step 6 of 9

Chapter 3, Problem 28E is Solved
Step 7 of 9

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 28E from chapter: 3 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This textbook survival guide was created for the textbook: University Physics, edition: 13. This full solution covers the following key subjects: EARTH, orbit, radius, sun, days. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. Since the solution to 28E from 3 chapter was answered, more than 1839 students have viewed the full step-by-step answer. The answer to “The radius of the earth’s orbit around the sun (assumed to be circular) is 1.50 X 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of the earth toward the sun, in m/s2? (c) Repeat parts (a) and (b) for the motion of the planet Mercury (orbit radius = 5.79 X 107 km, orbital period = 88.0 days).” is broken down into a number of easy to follow steps, and 81 words.

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

The radius of the earth’s orbit around the sun (assumed to

×
Log in to StudySoup
Get Full Access to University Physics - 13 Edition - Chapter 3 - Problem 28e

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to University Physics - 13 Edition - Chapter 3 - Problem 28e
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here