What Does 'Earth Radii' Mean in This Homework Problem?

[CinderBlockFist]

What exactly is meant by Earth radii?

In my homework problem, it is asking, "How many Earth radii must the same object be from the center of Earth if it is to weigh the same as it does on the Moon?"

Well, I found out how far the distance the object has to be from the earth, but is this the same as Earth radii? If it is not what exactly is it asking for?

 

[christinono]

What exactly is meant by Earth radii?

In my homework problem, it is asking, "How many Earth radii must the same object be from the center of Earth if it is to weigh the same as it does on the Moon?"

Well, I found out how far the distance the object has to be from the earth, but is this the same as Earth radii? If it is not what exactly is it asking for?

I would think it is that distance (from object to Earth's center) divided by the radius of the earth, which is, I think, 6.38 x10^6 m, or something like that.

 

[CinderBlockFist]

ok thanks leme try it out, see if it is the correct answer, if not, It's all your fault! jk man, thanks for the quick response. brb.

 

[CinderBlockFist]

crap its wrong =\

 

[Cantari]

Radii is the plural of radius...

 

[christinono]

Maybe you're doing the first part of the problem wrong. Show your work and I'll see if I can help...

 

[CinderBlockFist]

The mass of the object is 7.645 kg. The object has to weigh 12.499 N.

So what i did was plugged those two variables into w = mg

and i get 12.499 N = (7.645 kg) x g

so i got gravitational acc. has to be 1.634 m/s^2



Now I pluged it into the formula gravitational acc. = (Gravitational constant)(Mass of earth)/r^2 to find the radius distance of the object.

i got r = 1.5623 x 10^ 7 m.

so i added r to radius of Earth to get 2.1993 x 10^7 m, then divided by the radius of Earth to get 3.45 Earth radii, which was incorrect. Where did i go wrong?

 

[christinono]

Where did you get the 12.499 N from? Was it given in the question?

 

[CinderBlockFist]

yea that's given

 

[CinderBlockFist]

maybe i wasnt supposed to add the Earth's radius in the last part,is it already included for my value for r?

 

[christinono]

The mass of the object is 7.645 kg. The object has to weigh 12.499 N.

So what i did was plugged those two variables into w = mg

and i get 12.499 N = (7.645 kg) x g

so i got gravitational acc. has to be 1.634 m/s^2



Now I pluged it into the formula gravitational acc. = (Gravitational constant)(Mass of earth)/r^2 to find the radius distance of the object.

i got r = 1.5623 x 10^ 7 m.

so i added r to radius of Earth to get 2.1993 x 10^7 m, then divided by the radius of Earth to get 3.45 Earth radii, which was incorrect. Where did i go wrong?

I got 6.56 x 10^16 m. Divided by the radius of the earth, i get 1.03 x 10^10.

 

[christinono]

Sorry, i used the wrong constant. I used the k constant instead of the G constant. let me try it again...

 

[CinderBlockFist]

are you adding the radius of the earth, to the value of r that was in the denominator? or just leaving r , as is?

 

[christinono]

The mass of the object is 7.645 kg. The object has to weigh 12.499 N.

So what i did was plugged those two variables into w = mg

and i get 12.499 N = (7.645 kg) x g

so i got gravitational acc. has to be 1.634 m/s^2



Now I pluged it into the formula gravitational acc. = (Gravitational constant)(Mass of earth)/r^2 to find the radius distance of the object.

i got r = 1.5623 x 10^ 7 m.

so i added r to radius of Earth to get 2.1993 x 10^7 m, then divided by the radius of Earth to get 3.45 Earth radii, which was incorrect. Where did i go wrong?

OK. I got the same r value: 1.5623 x 10^ 7 m.
But I'm pretty sure that's the TOTAL radius, meaning it's the distance from the center of the Earth. In this case, you don't have to add the radius of the Earth to that r value. You just divide r by the radius of the earth. I got
2.45.

 

[CinderBlockFist]

Oh crap i got it! i wasnt supposed to add the Earth's radius. THe correcta nswer is 2.45. THanks chris, u da man!

 

[christinono]

no problem