# Newtons Law of Gravitation

• Averforde

#### Averforde

Hello, Is there any research available as to whether Newtons Law F = mg should include horizontal surface area as a factor (ie the surface area of opposing masses). Example a pole weighing exactly the same seems heavier when held at one end horizontally to the ground, compared to holding it vertically or upright from the ground.

Regards

Mark

No.

When you hold a pole horizontally from the end, you have to apply a torque to it, so the forces are much larger.

Welcome to PF!

Hello Mark! Welcome to PF!
… a pole weighing exactly the same seems heavier when held at one end horizontally to the ground, compared to holding it vertically or upright from the ground.

In future, try holding it in the middle!

I think OP is onto something. Sometimes, when I'm lying in my bed I feel so heavy that it seems impossible to get up.

have you tried rolling off the bed (onto a walking-legs dog)?

No, the OP, unfortunately, is almost definitely not onto something. Observations of the gravitational force felt by something near the surface of the Earth (assuming Newtonian mechanics, not General Relativity) are dependent only on mass, not cross sectional area.

And, despite the title says, this isn't Newton's Universal Law of Gravitation, this is Newton's Second Law, which is about as unrelated as anything can be when Newton's Second Law (plus the relativistic correction to it) is involved.

If two body of different mass fall from a height at same time which body will reach the Earth quickly

If two body of different mass fall from a height at same time which body will reach the Earth quickly

Do you mean "which will reach the Earth more quickly?" Depends on their shape, but if we assume air resistance is negligible, they'll both reach the ground at the same time. This is well-known and there's even a (probably false) story about Galileo dropping two balls of different masses from the Leaning Tower of Pisa.

I think that Averforde might be saying that if we hold a rod then the force on it might be less (or might be other way, i have totally forgotten my result and calculation),though negligible, than that of if we put it horizontally (rotated by its MIDDLE). Which you can find out Newtons gravitation law. But then his question says otherwise.

Example a pole weighing exactly the same seems heavier when held at one end horizontally to the ground, compared to holding it vertically or upright from the

When you are holding the pole upright, you are pushing up on it with a force that is equal to the force of gravity pulling it down.

But suppose you're holding the pole horizontally by the end. Let's assume you're using two hands and the pole is sticking out to the left, just to be definite.

Now the pole is imbalanced - the left end wants to tip down towards the ground, raising the right end up. So your right hand is pushing DOWN on the right end of the pole, and your left hand is pushing up to counteract the downwards force from the weight of the pole and your right hand. And yes, you're working a lot harder, because your left and right hands are working against each other.

As a previous poster has pointed out, you can make this effect go away by grabbing the pole at the middle. Now there's no tendency to tip and both your hands can push the pole up without wasting effort fighting against each other.

If feel constrained to point out that "F= mg" is NOT "Newton's Law of Gravitation". Newton's law of Gravitation is
$$F= -\frac{GmM}{r^2}$$
where F is the force with which two objects attract each other, m and M are the masses of the two objects, r is the distance between the centers of the two objects, and G is the "universal gravitation constant". That reduces to "F= -mg" when M is the mass of the Earth and r is the radius of the Earth so that F is the force with which the Earth attracts and object on its surface.

Firstly, thanks to those who actually gave me an explantion on my query. As to those who got a bit upset, I confess I am no scholar on the subject nor do I even have a degree in the field, I am just interested in it, that's all. I apologise for getting the formula or topic wrong I just thought this fourm might be a good way of having explained observations I notice from time to time. I sure was not trying to commit some sort of heresy by rocking the foundation of your existence, as you know it (remember scientists can be wrong as can theories!).

Nevertheless, I also thought of holding it in the middle but I assumed that in relative terms, a pole's gravitation pull (if that is what you call it) may vary so insignificantly based on its position that it may not be noticable, hence my query on actual research and not just observation. I have also done the vacuum test at school many years ago, but wondered if assumably the size of vacuum chambers on Earth are relatively limited, that even ones that have been used for detecting an objects fall may also not be able to show a minute difference based on surface area.

As I said, I am just looking for some sort of evidence rather than theory into the phenomena

Direct consequence of the General Theory of Relativity: on relatively small scales, this cross-sectional surface are won't matter. Probably on relatively large scales, too. And the General Theory of Relativity is quite well tested.