F=g*m1*m2/r^2 related question

  • Thread starter Mikasun1108
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In summary, the weight of a man on the moon can be calculated by dividing his weight on Earth by 6, and the mass of the moon can be estimated using the formula for surface gravity. Using the given data and assuming a spherical shape, the mass of the moon is approximately 1.22 x 10^23 kg.
  • #1
Mikasun1108
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8
Homework Statement
The weight of a man on the moon is 1/6 of his weight on Earth. If a man is at the surface of the moon whose diameter of its cross-section is approximately 4.47x10^6, what is the mass of the moon?
Relevant Equations
F=gm1m2/r^2
Thanks for the help! :)
Edit: My answer is 1.25 x 10^7 ( I do not think it is correct, I'll try to think some more and update my answer)
Do we need to get the mass of the man? or is this problem actually solvable?
-sun1108
 
Last edited:
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  • #2
2r=4.47 10^6 meter
 
  • #3
Mikasun1108 said:
Homework Statement:: The weight of a man on the moon is 1/6 of his weight on Earth. If a man is at the surface of the moon whose diameter of its cross-section is approximately 4.47x10^6, what is the mass of the moon?
Relevant Equations:: F=gm1m2/r^2

Thanks for the help! :)
-sun1108
We need to see your best attempt to solve this yourself.
 
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  • #4
PeroK said:
We need to see your best attempt to solve this yourself.
Ook, sorry I didn't put my attempt I wasn't sure about my answer. Ill make sure to write it.
 
  • #5
Mikasun1108 said:
Edit: My answer is 1.25 x 10^7 ( I do not think it is correct, I'll try to think some more and update my answer)
Looks like an error with the orders of magnitude. Maybe a conversion problem.
Please post your steps,
 
  • #6
haruspex said:
Looks like an error with the orders of magnitude. Maybe a conversion problem.
Please post your steps,
Oh right i think i might have place a 667 instead of 6.67. Thanks for the feedback.
I tried doing it again this time I got 1.213 X 10^23 kg
Working: m2= Fr^2/Gm1
Assuming mass is 60kg weight in moon will be 97.2 N
So m2= 97.2N(4.985225 x 10^12m)/6.67 x 10^-11 Nm^2kg^-2(60kg)
m2= 1.213 x 10^23kg
 
  • #7
Mikasun1108 said:
Oh right i think i might have place a 667 instead of 6.67. Thanks for the feedback.
I tried doing it again this time I got 1.213 X 10^23 kg
Working: m2= Fr^2/Gm1
Assuming mass is 60kg weight in moon will be 97.2 N
So m2= 97.2N(4.985225 x 10^12m)/6.67 x 10^-11 Nm^2kg^-2(60kg)
m2= 1.213 x 10^23kg
When I search online, the mass of the Moon is given as ##7.35 \times 10^{22} kg##.
 
  • #8
PS that said, the diameter of the Moon is given as ##3.5 \times 10^6 m##.
 
  • #9
Using the data you were given, your answer is approximately correct. If I use ##g = 9.81 m/s^2## for Earth, I get ##M = 1.25 \times 10^{23}kg##
 
  • #10
PeroK said:
PS that said, the diameter of the Moon is given as ##3.5 \times 10^6 m##.
Oh! so re #2, it was not meter but perhaps milli mile ?
[EDIT]
Wrong comment. I confused diameter with radius.
 
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  • #11
anuttarasammyak said:
Oh! so re #2, not meter but mile ?
##m## is metres.
 
  • #12
Mikasun1108 said:
Relevant Equations::[/B] F=gm1m2/r^2
[tex]GmM_E/6R_E^2=GmM_M/R_M^2[/tex]
[tex]\frac{\rho_M}{\rho_E} =\frac{1}{6}\frac{ R_E}{R_M} [/tex]
where ##\rho_M,\rho_E## are average density of Moon and the Earth with assumption that both have sphere shape. In observation
[tex]\frac{\rho_M}{\rho_E} =0.6[/tex] and [tex]\frac{ R_E}{R_M} =3.6[/tex]
 
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  • #13
PeroK said:
When I search online, the mass of the Moon is given as ##7.35 \times 10^{22} kg##.
So sorry for the very late reply, I haven't been opening my account, thank you so much for your feedback.
I apologize for the very late update: I tried doing the question again later, but then I still arrived at the same answer. Here is my working.
 

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  • #14
I just put the numbers in a spreadsheet:

GDRgM
6.67E-11​
4.47E+06​
2.24E+06​
1.635​
1.22E+23​

The first column is the gravitational constant. The second is the given diameter of the Moon. The third is the radius of the Moon (##R = D/2##). The fourth is the Moon's surface gravity, which I calculated as ##\frac{ 9.81}{6} \ m/s^2##.

The final column, the estimated mass of the Moon, I calculated using the formula for surface gravity ##g = \frac{GM}{R^2}##.
 
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  • #15
PeroK said:
I just put the numbers in a spreadsheet:

GDRgM
6.67E-11​
4.47E+06​
2.24E+06​
1.635​
1.22E+23​

The first column is the gravitational constant. The second is the given diameter of the Moon. The third is the radius of the Moon (##R = D/2##). The fourth is the Moon's surface gravity, which I calculated as ##\frac{ 9.81}{6} \ m/s^2##.

The final column, the estimated mass of the Moon, I calculated using the formula for surface gravity ##g = \frac{GM}{R^2}##.
Yeyy, so my answer is correct :). Thank you so much for your help and prompt reply, I truly appreciate it :)
 

Related to F=g*m1*m2/r^2 related question

1. What is the formula for calculating gravitational force?

The formula for calculating gravitational force is F = G * m1 * m2 / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

2. What is the unit of measurement for gravitational force?

The unit of measurement for gravitational force is Newtons (N).

3. How does the distance between two objects affect gravitational force?

The distance between two objects is inversely proportional to the gravitational force between them. This means that as the distance increases, the force decreases and vice versa.

4. What is the significance of the gravitational constant in the formula?

The gravitational constant (G) is a universal constant that represents the strength of the gravitational force between two objects. It is used to calculate the force of gravity between any two masses in the universe.

5. Can the formula for gravitational force be used for objects other than planets?

Yes, the formula for gravitational force can be used for any two objects with mass, regardless of their size or composition. It is a fundamental law of physics that applies to all objects in the universe.

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