How Do You Calculate the Mass Difference Between Two Planets Based on Gravity?

[kasiu]

1. The mass of a robot is 5370 kg. This robot weighs 3520 N more on planet A than it does on planet B. Both planets have the same radius of 1.33 x 10^7 m. What is the difference MA - MB in the masses of these planets?




2. attached picture



3. I was wondering what to do with the 3520 N. Do I find a ratio of weight between the planets and then multiply the original weight by that ratio? Do I need to use (G*mass/radius^2)? I'd appreciate some pointers or hints. I don't need the solution, just help with setting up the equation and understanding what I am looking for.

 

[dynamicsolo]

3. I was wondering what to do with the 3520 N. Do I find a ratio of weight between the planets and then multiply the original weight by that ratio? Do I need to use (G*mass/radius^2)? I'd appreciate some pointers or hints. I don't need the solution, just help with setting up the equation and understanding what I am looking for.

I'd say a comparison ratio for the weight of the robot on the two different planets would be a better place to start.

 

[kasiu]

So,
would I set it up like this:

W_subB + 3520 N = M * (g_subB)
Or
M * (g_subA) = W_subB +3520 N
So, would I solve for the acceleration of planet A to get g_subA and then use 5370 Kg for my M (mass) and solve for W_subB

 

[dynamicsolo]

So,
would I set it up like this:

W_subB + 3520 N = M * (g_subB)
Or
M * (g_subA) = W_subB +3520 N
So, would I solve for the acceleration of planet A to get g_subA and then use 5370 Kg for my M (mass) and solve for W_subB

Yeah, I'm going to take back what I said: because of the types of information provided, a comparison ratio won't really help. Write out both weights in terms of the appropriate Mg in one of those equations. Insert the appropriate expressions for g on each planet. You will now be able to factor your equation, with one of the terms being the difference between the planetary masses, which you can solve from there. (I thought initially that the problem set-up would be nicer...)

 

[kasiu]

How would I find weight?
Would I use the equation attached?

 

[kasiu]

so:
(5370*acceleration due to gravity) + 3520 N = 5370 * gravity...
that's not right I can see, but how do I find the weight.
I can't solve for acceleration because I don't have the weight of the planet...
I feel confused :(

 

[dynamicsolo]

How would I find weight?
Would I use the equation attached?

Your attachment still hasn't been cleared yet. You have

M * (g_subA) = W_subB +3520 N , so replace W_subB also:

M * (g_subA) = M * (g_subA) +3520 N .

How do you find g on each planet? (You mentioned this in your earlier post.) If you put that in for g_subA and g_subB, what do you get?

 

[kasiu]

I know that the equation has to equal (mass of planet A)-(mass of planet B)

 

[kasiu]

do i get the acceleration?

 

[kasiu]

G(Ma)(m)/d^2 - G(Mb)(m)/d^2= N* r^2/Gm

Would I use that

 

[dynamicsolo]

I know that the equation has to equal (mass of planet A)-(mass of planet B)

It won't be equal to it, it will let you solve for that.

do i get the acceleration?

How do you find the gravitational acceleration at the surface of a planet? (Have you already written this?)

 

[kasiu]

so acceleration= F/m
or
a=g=6.67e-11* mass/distance^2

 

[kasiu]

ooooooh!
I get it so,

Ma-Mb =N* r^2/Gm
So, what I posted before was right :)
thank you so much!

I understand it now!
:):):)
wow, that took me a while
finally my brain made some connections
thanks once again!

 

[dynamicsolo]

so acceleration= F/m
or
a=g=6.67e-11* mass/distance^2

The distance in this application is the distance from the surface of the planet to its center, that is, the planet's radius. (Why that is so is due to a theorem of Newton's you may have discussed by now...)

You can save a little writing and use the universal gravitation constant G, instead of writing 6.67e-11, for now.

So you can now use that, for each planet, in this equation:

M * (g_subA) = M * (g_subA) +3520 N .

 

[dynamicsolo]

ooooooh!
I get it so,

Ma-Mb =N* r^2/Gm
So, what I posted before was right :)
thank you so much!

I understand it now!
:):):)
wow, that took me a while
finally my brain made some connections
thanks once again!

Provisionally glad to hear it! The equation should be Ma-Mb = (3520 Newtons) * r^2/Gm , m being the robot's mass. (I wasn't sure what your N was supposed to be -- that's the force unit, not a value itself.) So you do need all the info in the problem... You'll get a pretty big number (in kg).