Acceleration due to gravity - Help with equation. Thanks

In summary, the conversation is about calculating the expected value of acceleration (g) using the formula g = G Me/r^2, where G is a constant and Me and r are the mass and radius of Earth. The correct calculation involves using the value of G (6.67300 × 10-11 m3kg-1s-2) and squaring the radius. The resulting value should be close to 9.81 m/s^2, which is the acceleration due to gravity on Earth.
  • #1
nukeman
655
0

Homework Statement



Here is the problem:

GIven the formula below, calculate the expected value of the accerlation, G (in m/s^2). THe mass and radius of Earth are 5.974x10^24 kg and 6.37 x 10^6 m, respectively.

Formula to use: g = G Me/r^2

How do I solve for g ? I keep messing up on calculation.

Thanks


Homework Equations





The Attempt at a Solution

 
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  • #2
'g' is already the subject of the formula, so you just need to substitute the numbers into the equation.
 
  • #3
rock.freak667 said:
'g' is already the subject of the formula, so you just need to substitute the numbers into the equation.

Oh. So, it would then turn into:

g = G 5.974x10^24 / 6.37 x 10^6

?

So, would the answer be? 9.378x10^29

? That can't be rigbht
 
  • #4
nukeman said:
Oh. So, it would then turn into:

g = G 5.974x10^24 / 6.37 x 10^6

?

So, would the answer be? 9.378x10^29

? That can't be rigbht

Well 'G' is a constant such that G=6.67300 × 10-11 m3kg-1s-2

And you are dividing by 106,so you can't really get back 1029. Redo the calculation with the value of 'G' in it.
 
  • #5
rock.freak667 said:
Well 'G' is a constant such that G=6.67300 × 10-11 m3kg-1s-2

And you are dividing by 106,so you can't really get back 1029. Redo the calculation with the value of 'G' in it.

im real sorry, but you lost me with G

How do I do the calculation with Value G in it?
 
  • #6
nukeman said:
im real sorry, but you lost me with G

How do I do the calculation with Value G in it?

g=GM/r2

Just replace the letters with the numbers given.
 
  • #7
How do I calculate this? First, is this correct?

6.6726 x 10-11N-m^2/kg^2 x 5.974x10^24 / 6.37 x 10^6
 
  • #8
nukeman said:
How do I calculate this? First, is this correct?

6.6726 x 10-11N-m^2/kg^2 x 5.974x10^24 / 6.37 x 10^6

Your units are the same throughout, so you can leave out the units in the calculation. You also forgot to square the radius 'r'.

g= (6.67x10-11)(5.974x1024)/(6.37x106)2
 
  • #9
I tried it 2 diferent ways.

first answer: 9.37833595 x 10^24

next: 9.8200

??
 
  • #10
nukeman said:
next: 9.8200

This is more or less correct.
 
  • #11
rock.freak667 said:
This is more or less correct.

Is there anyway you can check, or I can be sure?

:)
 
  • #12
nukeman said:
Is there anyway you can check, or I can be sure?

:)

Well we know that on Earth, g=9.81 m/s2, so your answer should be around that number. (Depending on how accurate your values are)
 
  • #13
rock.freak667 said:
Well we know that on Earth, g=9.81 m/s2, so your answer should be around that number. (Depending on how accurate your values are)

Great, good enough for me :)

Thanks VERY much for your help, really appreciate it!
 

Related to Acceleration due to gravity - Help with equation. Thanks

1. What is the equation for acceleration due to gravity?

The equation for acceleration due to gravity is a = GM/r2, where G is the universal gravitational constant, M is the mass of the larger object, and r is the distance between the two objects.

2. How do you calculate the acceleration due to gravity?

To calculate the acceleration due to gravity, use the equation a = GM/r2, where G is the universal gravitational constant (6.674 x 10^-11 m^3 kg^-1 s^-2), M is the mass of the larger object, and r is the distance between the two objects.

3. What is the value of acceleration due to gravity on Earth?

The value of acceleration due to gravity on Earth is approximately 9.8 m/s^2, which is the same for all objects regardless of their mass. This value can vary slightly depending on location and altitude on Earth.

4. How does the mass of an object affect its acceleration due to gravity?

The mass of an object does not affect its acceleration due to gravity. All objects experience the same acceleration due to gravity, regardless of their mass. However, the larger an object's mass, the greater the force of gravity acting on it.

5. How does distance affect the acceleration due to gravity between two objects?

The acceleration due to gravity between two objects decreases as the distance between them increases. This is because the force of gravity is inversely proportional to the square of the distance between the two objects.

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