Chapter 1 5 Physics 210 Problems - My Solutions
Dr. Hulan E. Jack Jr.
Serway, Faughn and Vuille: College Physics 8th Edition , Thomson Brooks/Cole, Vol I(ISBN #) 978-049511374-3
THE PROBLEM STATEMENT
Ch 1 5. Newton's law of universal gravitation is represented by
F = - GMm/r2 ,
where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units
kg· m/s2 ( mass . meter/second2) What are the SI units of the proportionality constant G?
Page 1 of 3
Physics 210 Problems - My Solutions
Dr. Hulan E. Jack Jr.
Ch 1 5. Newton's law of universal gravitation is represented by
F = - GMm/r2 ,
where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units
kg· m/s2 ( mass . meter/second2) What are the SI units of the proportionality constant G?
BRAINSTORMING - Definitions, concepts , principles and Discussion
We want the dimensions of G. Hence, we should first solve for G algebraically.
G = F r2 /mM
(1)
Let’s the Dimensions of G
Dimensions: mass = M,
r=L
s=T
F = ma a=L/T2
So F =ma = ML/T2
ML
ML 2
( 2 ) L2
L
2
( F )r 2
G
 T
 T 2
Mm
MM
M
ML 2
ML
L
T 2 2 L2
2
ML L2
T
 T 2 

M
T2 M2
T 2M 2

ML L2
M L3
L3


T 2 M 2 M 2 T 2 MT 2
G= 
L3
m3

MT 2
kg * s 2
Replace F,r, and M and m with their respective Dimensions.
Clear fraction in numerator by multiplying and dividing by T 2 .
Simplify.
Express dimensions in SI units.
Page 2 of 3
Physics 210 Problems - My Solutions
Dr. Hulan E. Jack Jr.
Ch 1 5. Newton's law of universal gravitation is represented by
F = - GMm/r2 ,
where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units
kg· m/s2 ( mass . meter/second2) What are the SI units of the proportionality constant G?
Basic Solution (Minimum Expected from the student)
NOTE: In this case the solution was generated in the above
Brainstorming page. You need not rewrite it here. Simply circle it
on the above page and label it “MY SOLUTION”
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