1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question
Question answers 1-3
Background:
Newton formulated the Universal Law of Gravitation: F =
R2
GmM
where,
F
the gravitational force between two masses.
the gravitational constant, G = 6.67 x 101" N- m/kg?
the mass of one object
mass of other object
distance between the center of the objects
%3D
G =
m
M =
R =
Also, we learned that weight, w=mg. Equating weight with Newton's Law of Gravitation
GmM
we get: mg =
R2
or canceling m:
GM
g =
R2
This can be used to calculate the acceleration of gravity on any planet/object/body.
Objective:
Investigate several phenomena using Newton's Universal Law of Gravitation. Understand
the difference between accuracy and precision.
Procedure:
Perform the indicated calculations. The following information can be used for the
calculations.
Mass of Sun
Mass of Earth
1.99 x 1030 kg
5.98 x 1024 kg
7.36 x 1022 kg
2 x 1030 kg
1.90 x 1027 kg
Earth-Sun distance
1.50 x 10" m
6.38 x 10° m
1.74 x 10 m
Radius of Earth
Mass of Moon
Radius of Moon
Mass of neutron star
Radius of neutron star
Mass of Jupiter
Earth-Jupiter distance (in-line)
12,000 m
6.3 x 10" m
Error and Uncertainty:
All measurements contain error and thus uncertainty. We can calculate errors depending on
the nature of the experiment. We define two main types of uncertainty:
Precision is how well independent measurements (E, and E2) match. Precision can be
quantified using the formula: Percent Difference = -
E, - E
-x100
(E, + E)/2
Percent difference is used when there is not an accepted value; it is used to compare two
independent quantities.
Accuracy is how close a measurement (E) is to an accepted value (A). Accuracy can be
quantified using the formula: Percent Error =|A-E/Ax100
Percent error is used to compare a quantity/measurement to an accepted value.
Transcribed Image Text:Background: Newton formulated the Universal Law of Gravitation: F = R2 GmM where, F the gravitational force between two masses. the gravitational constant, G = 6.67 x 101" N- m/kg? the mass of one object mass of other object distance between the center of the objects %3D G = m M = R = Also, we learned that weight, w=mg. Equating weight with Newton's Law of Gravitation GmM we get: mg = R2 or canceling m: GM g = R2 This can be used to calculate the acceleration of gravity on any planet/object/body. Objective: Investigate several phenomena using Newton's Universal Law of Gravitation. Understand the difference between accuracy and precision. Procedure: Perform the indicated calculations. The following information can be used for the calculations. Mass of Sun Mass of Earth 1.99 x 1030 kg 5.98 x 1024 kg 7.36 x 1022 kg 2 x 1030 kg 1.90 x 1027 kg Earth-Sun distance 1.50 x 10" m 6.38 x 10° m 1.74 x 10 m Radius of Earth Mass of Moon Radius of Moon Mass of neutron star Radius of neutron star Mass of Jupiter Earth-Jupiter distance (in-line) 12,000 m 6.3 x 10" m Error and Uncertainty: All measurements contain error and thus uncertainty. We can calculate errors depending on the nature of the experiment. We define two main types of uncertainty: Precision is how well independent measurements (E, and E2) match. Precision can be quantified using the formula: Percent Difference = - E, - E -x100 (E, + E)/2 Percent difference is used when there is not an accepted value; it is used to compare two independent quantities. Accuracy is how close a measurement (E) is to an accepted value (A). Accuracy can be quantified using the formula: Percent Error =|A-E/Ax100 Percent error is used to compare a quantity/measurement to an accepted value.
1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star.
2. Forces cause accelerations, and thus velocity. Using Newton's Law of Gravitation, the
GM
orbital velocity (speed) of an object can be shown to be: v =
R
Where M is the
mass of the body being orbited and R is the average distance from the body. A) Calculate
Earth's orbital velocity around the Sun. B) How fast is Earth traveling in m.p.h.? C)
Calculate Earth's orbital velocity using a second method. (Hint: The Earth orbits the
Sun in approximately a circle every 365 days. Speed = Distance/Time. Distance = the
circumference of Earth's orbit = 2rR and Time is number of seconds in a year.) D)
Compare the orbital velocities (speeds) from Parts A and C by calculating the percent
difference of the two velocities and comment (are they about the same?).
Earth
M (Sun)
3. Astrologers claim that when Jupiter is 'lined-up' with the Earth and Sun, its gravitational
pull on humans is significant, and thus affects our life. A) Calculate the gravitational pull
from Jupiter on a human (m=70 kg) when Jupiter is 'in-line' with the Earth and Sun. B)
Calculate the gravitational pull from a skyscraper on a human walking through any
downtown, or city center (ASsume a skyscraper has a mass of 1.2 x 10° kg, and the
distance between the center of masses is 175 m). C) Calculate the pull from a large cliff
(M=8.8 x 107 kg and R=14 m). D) How many times bigger are the answers in B and c
than the answer in part A? Comment on these results.
m = 70 kg
A)
M (Jupiter)
m = 70 kg
B)
R
M (skyscraper)
m = 70 kg
C)
M (cliff)
Transcribed Image Text:1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star. 2. Forces cause accelerations, and thus velocity. Using Newton's Law of Gravitation, the GM orbital velocity (speed) of an object can be shown to be: v = R Where M is the mass of the body being orbited and R is the average distance from the body. A) Calculate Earth's orbital velocity around the Sun. B) How fast is Earth traveling in m.p.h.? C) Calculate Earth's orbital velocity using a second method. (Hint: The Earth orbits the Sun in approximately a circle every 365 days. Speed = Distance/Time. Distance = the circumference of Earth's orbit = 2rR and Time is number of seconds in a year.) D) Compare the orbital velocities (speeds) from Parts A and C by calculating the percent difference of the two velocities and comment (are they about the same?). Earth M (Sun) 3. Astrologers claim that when Jupiter is 'lined-up' with the Earth and Sun, its gravitational pull on humans is significant, and thus affects our life. A) Calculate the gravitational pull from Jupiter on a human (m=70 kg) when Jupiter is 'in-line' with the Earth and Sun. B) Calculate the gravitational pull from a skyscraper on a human walking through any downtown, or city center (ASsume a skyscraper has a mass of 1.2 x 10° kg, and the distance between the center of masses is 175 m). C) Calculate the pull from a large cliff (M=8.8 x 107 kg and R=14 m). D) How many times bigger are the answers in B and c than the answer in part A? Comment on these results. m = 70 kg A) M (Jupiter) m = 70 kg B) R M (skyscraper) m = 70 kg C) M (cliff)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Unit conversion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON