Explaining Fg = mg: Net Force, Mass and Acceleration

[pointintime]

Homework Statement

we can say that the force of gravity is equal to mass times acceleration were the acceleration is equal to gravity sense gravity is an acceleration because of Newtons second law force = mass times acceleration

hence Fg = mass times acceleration
Fg = mass times gravity

Fg = mg

however Newtons second law states that the net force acting on an object is equal to it's mass times it's acceleration so what allows us to say that

Fg = mg
because certainly not for every single situation the

net force is going to equal to the force of gravity

please explain...

what allows us to say

Fg = mg

Homework Equations

net force = mass times acceleration

The Attempt at a Solution

Thank You!

 

[Pengwuino]

When you say Fg, do you mean $$F_g$$? As in the force of gravity? If not, and you mean the force of gravity multiplied by gravitational acceleration Fg = mg, then that is not correct. It's simply F=mg.

 

[pointintime]

i mean in the force of gravity

 

[LeonhardEuler]

If the net force on the object is not F_g, then the object's acceleration is not g, so there is no contradiction because the second law refers to the object's acceleration. g is just the "acceleration due to gravity" in the sense that it is the component of the acceleration caused by the gravitational force.

 

[pointintime]

so then I'm not sure how to do this problem

Calculate the acceleration due to gravity on the Moon. The Moon's radius is about 1.74 E 6 m and its mass is 7.35 E 22 kg.

I know I just use this equation

a = r^-2 G m

were m is the mass of the moon but

Fg = r^-2 G m M

were M is the the mass of the object the moon orbits were does it go

Fg = r^-2 G m M
?

why can we just simply set this equal to Mg??

Fg = r^-2 G m M = M a

and that's how we get this

a = r^-2 G m

 

[LeonhardEuler]

why can we just simply set this equal to Mg??

I think I might see why you are confused. g is the acceleration due to gravity on the Earth's surface. It is different on other planets and higher in space above the Earth. g is not the acceleration due to gravity on the Moon.

 

[pointintime]

Do I do it like this

net force = M a = r^-2 G m M

or

r^-2 G m M = M g

am I solving for how fast M accelerates towards the moon?

 

[LeonhardEuler]

r^-2 G m M = M g

If you are solving a problem on the Moon's surface, why would you use 'g', the acceleration due to gravity on the surface of the Earth?