Why don't I weigh more at the poles

[russ_watters]

BUT, do we live in an Einsteinian Relativity world or not?

Yes we do, but it isn't always relevant. For situations where the energy involved isn't nuclear, the equivalence of matter and energy produces immeasurably tiny changes in mass. Recently, there was a thread asking about the relativistic mass change in burning oil, and I calculated it was something like 1/100,000,000th %.

Some nuclar reactions have mass conversions to energy on the order of .1%. Still pretty small, but a lot more than in a chemical reaction. That tells you that nuclear reactions are really powerful compared to chemical reactions.

Do we measure weight on Earth differently than in space?

Weight is properly measured with a spring-scale, anywhere.

I guess I still don't understand why we don't factor in Potential Energy and Kinetic energy etc in questions of this sort.
I guess that Relativity doesn't come in unless we are talking of things nearer the speed of light or nearer the scale of nuclear processes?
Bligh

Yes, that's correct. If you are unsure, do the calculations yourself. They are easy. Here's that other thread I was talking about, with an example for the energy released in burning oil (just plug the energy into e=mc^2 to find the equivalent mass): https://www.physicsforums.com/showthread.php?t=170280

 

[D H]

Weight is properly measured with a spring-scale, anywhere.

There is no way to measure "weight" if one defines "weight" as the "force exerted on an object by gravity". Balance scales measure mass. Spring scales measure the total of all forces acting on a body except for gravity: in short, everything but weight. Using a spring scale in a jet pulling 6Gs would yield a markedly different result than using the same scale on the ground, even though the object's "weight" is the unchanged.

This whole thread has been talking about many different things: mass, weight (force of gravity), weight (what a scale measures), the Earth's gravitational potential, and geopotential. Note: the potential fields are typically represented in units of Joules/kg.

The geopotential includes the Earth's gravitational and a potential resulting from the Earth's rotation. Both the geopotential and gravitational potential are "real". The Earth's rotation affects the shape of the Earth and of the oceans that cover the Earth. The mean sea surface is an equipotential surface of the geopotential, not the gravitational potential.

Taking the gradient of the gravitational potential yields the acceleration due to gravity. Multiplying this by the mass of some object yields its "weight". As noted above, this is not what a scale measures. Taking the gradient of the geopotential yields an acceleration as well. The additive inverse of this acceleration is what a spring scale measures: the force that must be applied to an object to make it stationary with respect to the rotating Earth.

 

[MadMax]

Didn't read the whole thread, so not sure if it was mentioned... but at the start people were mentioning "centrifugal force". There is no such thing. There is only a centripetal force which pulls us towards the centre of the earth. This is countered by a reaction force from the surface of the earth, and the net force is exactly the force needed to keep us in our geostationary orbit on the surface of the earth.

 

[AlephZero]

All this was sorted out pretty well by Newton - see Principia Book 3, Proposition 20, Problem 4.

This was "big science" at the time, because sailors were trying to use clocks as navigation tools to find longtitude, and had discovered that pendulum clocks ran at different speeds at different latitudes. There was a big debate about whether this was caused by changes in "gravity" (i.e. what we would now call the resultant of gravity and centripetal effects) or by the clock pendulums expanding at the equator because the climate was hotter. There was no agreed scale of temperature and no accurate thermometers, so nailing down the temperature effects was a serious experimental problem.

Newton takes about 3 pages to list all the experimental data he has on the subject, gives a table showing the length of a pendulum with period 1 sec at various latitudes between the equator and the poles according to his theory, and concludes that "if the experimental observations are correct, the Earth is higher under the equator than at the poles, by an excess of about 17 miles".

Been there, done that.

 

[laurelelizabeth]

I have wondered this sort of thing too. When they calculated the gravity of Earth (F=Gm1m2/r^2), they must have taken into account the spinning of the Earth (F=mv^2/r) so the Fnet would really be Gm1m2/r^2-mv^2/r

I'm assuming they took that into account otherwise they wouldn't have been able to send spaceships anywhere, right?

 

[bligh]

Laurel. I was trying to think in terms of Potential E and Kinetic E of an isolated mass (me) at Equator and Pole with Gravity one force, Centrifug force another etc. I think the moderator told me there is no way to have a strain gauge in space to measure weight of an isolated mass there, or something similar.
Anyway, I am an amateur physicist. One year college 1958 or so.
I do enjoy reading physics, however. Lay type Quantum stuff. Enjoyed Bagott's "the meaning of quantum mechanics"
Anyway, with enough energy you could launch almost anyone?
B

 

[laurelelizabeth]

Sorry i didn't make myself clear -- i meant that they must have taken into account centripetal force from the Earth spinning when figuring out the gravitational constant (G), because otherwise their calculations would be wrong about other things -- like the distance to the moon, in which case they couldn't have orbited the moon. :)