Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 311

Gravitational Field Strength

Is gfs a scalar or vector?

I know there is direction involved, but the direction is in two ways, yeah? Example a 90kg man standing on Earth. Each attracts the other. So what direction would we give for the gfs? 10N/kg upwards? 10N/kg downwards?

For the man, and Earth, respectively, their weight would be;

W=mg
W=90kg*10N/kg
W=900N downwards

w=mg
W=6*10^24kg*10N/kg
W=6*10^25kg  upwards  **EDIT**; should that be upwards or downwards?

But what if we're just looking at the gfs?

It seems that most websites, when posing w=mg problems, are content to state the gfs in terms of magnitude alone, i.e, 10N/kg, or 9.8N/kg, yet we're told it's a vector quantity.

From the internet; "The direction of g is always towards the center of the body creating the gravitational field."

But, in the case of the man standing on Earth, both bodies create the field, yeah? The man pulls Earth, Earth pulls the man, yeah?

Last edited by paulb203 (2024-10-27 00:53:42)

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KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 239

Re: Gravitational Field Strength

I guess this is related to "Newton's universal law of gravitation".
F=K*m1*m2/(d^2) = W = m*g

if 'm1' is the mass of earth, 'm2'=m is of a person on its surface and 'd' is the distance between the earth center and its surface, we may say:
g = K*m1/(d^2)
This explains why g, at the equator, is lower than at the North/South poles.

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Bob

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Registered: 2010-06-20

Posts: 10,618

Re: Gravitational Field Strength

If I was doing a calculation involving the forces acting on the man then I would show this downwards. I've never seen a question where I'm expected to consider the forces acting on the Earth but if I did then the man's attraction on the Earth would be upwards.

Bob

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paulb203

Member

Registered: 2023-02-24

Posts: 311

Re: Gravitational Field Strength

Thanks, KerimF, thanks, Bob

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paulb203

Member

Registered: 2023-02-24

Posts: 311

Re: Gravitational Field Strength

We do tend to think of ourselves standing on the planet, pushing down on it with a force of several hundred Newtons due to the gfs (and it pushing up on us). But what if we imagine standing at the north pole, considering someone standing at the south pole. From our perspective, the planet is on top of them, pushing down on them with a force of...

What would that force be?

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