Newtons Law of Gravitation

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

russ_watters
Mentor
No.

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

tiny-tim
Homework Helper
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!

A.T.
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.

tiny-tim
Homework Helper
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.

Nugatory
Mentor
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.

HallsofIvy
$$F= -\frac{GmM}{r^2}$$