Question regarding the Moon and Earth and height and weight

[.NoStyle]

Hi guys, I'm stuck on a problem with my homework:


#44. How far above the surface of the Earth does an object have to be in order for it to have the same weight as it would have on the surface of the moon? (Neglect any effects from the Earth's gravity for the object on the moon's surface or from the moon's gravity for the object above the earth.)

Does anyone have any suggestions on what to do? Would this involve using the Universal Gravitational Constant? Thank you

 

[berkeman]

What is the equation for the gravitational force between two objects (like the Earth and a person, or the moon and a person)?

 

[.NoStyle]

Hi Berkeman,

The UGC is:

F=(G*m1*m2)/r^2

where G = 6.674X10^-11Nm^2/kg^2

Thank you

 

[berkeman]

Hi Berkeman,

The UGC is:

F=(G*m1*m2)/r^2

where G = 6.674X10^-11Nm^2/kg^2

Thank you

Good. So now do you see how you can solve the question? What masses do you need to know, and which ones do you not need to know? Why?

 

[Paul L]

<< solution deleted by berkeman >>

If you need more help, take a look at the attached picture, but try for yourself first! ;)

<< attachment deleted by berkeman >>

 

[berkeman]

<< solution deleted by berkeman >>

If you need more help, take a look at the attached picture, but try for yourself first! ;)

<< attachment deleted by berkeman >>

Paul, we do not allow complete solutions to be posted for homework/coursework problems. That is one reason that we require these types of questions to be posted in the Homework Help forums. The original poster (OP) must do the bulk of the work, and our help is confined to hints and suggestions like the ones I posted above.

 

[.NoStyle]

Good. So now do you see how you can solve the question? What masses do you need to know, and which ones do you not need to know? Why?

I'm not familiar with this formula, so I'm not sure if I use Earth's
radius or the moon's radius. Also, I don't know how this will determine
the height I would need to be at for a particular to weigh the same as
on the moon.

Thanks berkeman

 

[.NoStyle]

well, I could see having two radii and subtracting one from the other to determine the height?

 

[berkeman]

I'm not familiar with this formula, so I'm not sure if I use Earth's
radius or the moon's radius. Also, I don't know how this will determine
the height I would need to be at for a particular to weigh the same as
on the moon.

Thanks berkeman

The R is not the radius of the mass -- it is the distance away from the center of mass that you are. So if you are on the surface of the Earth, you would use Rearth. If you are on the surface of the moon, you would use Rmoon. If you are moving away from the Earth and getting lighter and lighter, you use the radius distance between you and the center of the Earth. Does that make it clearer to you?

 

[.NoStyle]

The R is not the radius of the mass -- it is the distance away from the center of mass that you are. So if you are on the surface of the Earth, you would use Rearth. If you are on the surface of the moon, you would use Rmoon. If you are moving away from the Earth and getting lighter and lighter, you use the radius distance between you and the center of the Earth. Does that make it clearer to you?

Yes thanks a lot berkeman :)