Calculating Earth's Mass Using Algebra

In summary, I was able to solve the problem using a Newton calculator online. I would just like to know how to solve this without a plug and play. Here is what I have done. I multiplied M1 by both sides and ended up with 3.2568*10^-24x. I then divided each side by 19.6 to get 6.0181*10^24. This is the answer I was looking for.
  • #1
surferbarney
4
0
Trying to calculate the mass of earth. I am given the mass of the second object (2.00 kg) and the attraction between the Earth and the mass is 19.60 N.

I understand the concept and have successfully (I think) solved the problem using a Newton calculator online. I would just like to know how to solve this without a plug and play. Here is what I have

F= (6.67*10^-11) * [(M1*2.00)/(6.40*10^6)^2] = 19.60 N

I arrived at M1 = 6.016*10^24

How can i set this up to solve using algebra?

Thanks
 
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  • #2
How much algebra do you know? If you know any algebra, the setup should be straight forward.
 
  • #3
Well i haven't done algebra since freshman year of college circa 2003
 
  • #4
##6.67*10^{-11}*\frac{M_1*2}{(6.40*10^6)^2}=19.60##

Well, what do YOU think are the steps you need to take to isolate the M1 on one side of the equation?
Start at the beginning. What's the first thing you could do?
 
  • #5
mutltiply M1 by both sides...

6.67*10^-11 * (2/(6.40*10^6)^2)

= 3.2568*10^-24x = 19.60

I think i got it
 
  • #6
Slow down, and think again. If you multiply the left side by M1, you should end up having M1*M1 somewhere in there, while on the right side there'd be 19.60*M1.

This is different from what you wrote, and doesn't help you much, as the goal is to have just one instance of isolated M1, not M1 squared or any higher order.
You already have M1 in the numerator in the original equation. You need to get rid of all the numbers on the same side where M1 is. If there's a value(on that side) in the numerator, divide both sides by it. If in the denominator, multiply both sides.
 
  • #7
cant you just use the 3.2568*10^-24 x = 19.60 and then divide each side by 19.6

this gives you 6.0181*10^24 which the study guide says is correct

Did i just get lucky and stumble across the solution or is the solution wrong

Thanks for all our time
 
  • #8
You keep saying one thing, and then doing another.
You'll get the answer if you divide both sides by 3.2568*10^-24, not by 19.6. You will get the right answer just from churning the numbers willy-nilly, as you know what you should get and there aren't that many options. But this is not algebra.

For example, you've somehow got rid of M1, and put an x in there completely arbitrarily. Why did you do that, if you're looking for M1?

The best approach to see the algebra at work would be to forget about the numerical values for a moment, and try to rearrange the equation ##F=G\frac{M1*M2}{R^2}## so that M1 is on one side, and all the rest of it is on the other. Then plug in the numbers.
 
  • #9
What distance is that 6.4 * 106? Where did you get it?
Ah, it must be the distance between the surface and the Earth's core - in that case, are you certain you can calculate the Earth's mass like that? Do not presume without analysing.
 

FAQ: Calculating Earth's Mass Using Algebra

What is the equation used to calculate Earth's mass using algebra?

The equation used to calculate Earth's mass is M = gR²/G, where M is the mass of Earth, g is the gravitational constant, R is the radius of Earth, and G is the universal gravitational constant.

What is the value of the gravitational constant (g) used in the equation?

The value of the gravitational constant used in the equation is 6.67 x 10^-11 m^3/(kg*s^2). This value is constant for all objects in the universe and is crucial in calculating the mass of Earth.

What is the radius of Earth (R) used in the equation?

The radius of Earth used in the equation is approximately 6,371 kilometers. This value is the average distance from the center of Earth to its surface and is also crucial in calculating its mass.

How is the universal gravitational constant (G) determined?

The universal gravitational constant is determined through experiments and observations of the gravitational force between two objects with known masses and distances. It is a fundamental constant in physics that helps to explain the behavior of gravity in the universe.

What is the unit of measurement for Earth's mass calculated using algebra?

The unit of measurement for Earth's mass calculated using algebra is kilograms (kg). This is the standard unit for mass in the International System of Units (SI) and is used to measure the mass of all objects, including Earth.

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