Find Fg for G, M, m, and r: 5.21*109 mkg/s2

[Ellen W.]

Homework Statement

Find F_g if G=6.67*10^-11m³ kg^-1s^-2, M=2.6*10²³ kg, m=1200kg, and r = 2000m

Homework Equations

F_g= -GMm/r²

The Attempt at a Solution

F_g=-GMm/r²

F_g=- (6.67*10^-11m³kg^-1s^-2)(2.6*10²³ kg)(1200kg)/(2000m)²

F_g=- (6.67*10^-11m³kg^-1s^-2)(2.6*10²³ kg)(1200kg)/4000000 m²

F_g= - 2.08*10¹⁶ kg m³ s^-2/4000000m²

F_g= - 5,202,600,000 mkg/s²

F_g= - 5.21*10⁹ mkg/s²

First, I'm not sure how to deal with the units here. I added the exponents across and subtracted if they had the same unit below them but I'm not sure I ended up with the right units. Also, I don't know if you can have a negative number in scientific notation. Lastly, I don't even know if the problem was solved correctly.

Thank you for any help, I'm beyond rusty at math like this.

 

[Bystander]

mkg/s2

Look like a unit of force to you?

don't know if you can have a negative number in scientific notation

Can you think of any reason there shouldn't be negative numbers?

 

[Qwertywerty]

First, I'm not sure how to deal with the units here. I added the exponents across and subtracted if they had the same unit below them but I'm not sure I ended up with the right units.

I would think it best to leave the units out of the calculations . The formula will eventually work out to give you the Unit of force - Newton(N) .

Also, I don't know if you can have a negative number in scientific notation. Lastly, I don't even know if the problem was solved correctly.

Yes you can . Scientific notation only helps to make working with large numbers easier - It doesn't have any relation with the sign of a number . -120000 = -1.2*10⁵ .

Also , you seem to have worked out your answer probably .

Hope this helps .

 

[micromass]

I would think it best to leave the units out of the calculations . The formula will eventually work out to give you the Unit of force - Newton(N) .

No! Never leave out the units! Aside from needing units to be formally correct, the units provide a very neat way of checking your answers.

 

[Qwertywerty]

No! Never leave out the units! Aside from needing units to be formally correct, the units provide a very neat way of checking your answers.

Just to be clear , I was talking about using units during steps .

However , if this is what you intended to reply to , point well taken .

 

[HallsofIvy]

I am puzzled as to why this was titled "Algebra Question". Other than the "physics" involved in the given formula, this is purely arithmetic.

 

[FallenLeibniz]

Your units are correct. The unit for Force is a Newton, which is defined as one kilogram times one meter per second squared (mass times acceleration).

 

[insightful]

An interesting problem. Realistically though, what could that massive object be?

 

[haruspex]

An interesting problem. Realistically though, what could that massive object be?

It's not the mass in itself that's remarkable, it's less massive than the earth. The difficulty is combining that with a distance of 2000m.
Strictly speaking, there is not enough information. We have to assume that M is a sphere composed of concentric uniform spherical shells, with an outer radius less than 2000m.
Maybe there was more text in the original question.

 

[insightful]

An interesting problem. Realistically though, what could that massive object be?

My first thought was "neutron star" but, although the density is right, it doesn't have enough total mass to be one.