Posted on 02/08/2005 3:50:43 AM PST by PatrickHenry
Funniest headline of the year. Figures it's from Berserkeley.
Not near as funny as the post from the creationist about the whales had gills till they moved onland and developed lungs so they could breathe out of the water ...
If you lift one at a time, the force is constant as the product of the masses is the same, however, if you lift both, you have a three body problem.
M1 * Me /= M2 * Me
set Earth's mass at 1,000,000,000,000,000,000,000,000,000,000 kilograms
set object1's mass at 1kg
set object2's mass ate 5kg
the classic formula for gravity is: f(grav) ~ (m1+m2)/d2
you can see that, if m1 is the mass of the Earth in both trials, and m2 is 1kg in one trial and 5kg in the other, there shall be an infinitessimal difference in the amount of gravity between the earth and test object one and the earth and test object two.
It will be so small a difference that the basic value of 9,8m/s2 shall not be altered in any practical way.
ah, I see.
cute :)
???? I was agreeing with you :-)
a question on your symbol usage: is the asterisk standing for multiplication or addition?
I find it very unlikely to stand for multiplication:
Fg ~ 1,000,000,000,000,000,000kg X 5kg/(d X d)
is a hell of a big shift from
Fg ~ 1,000,000,000,000,000,000kg X 1kg/(d X d)
when, in reality, we know that the difference is trivial.
if it is addition, just use "+" and be done with it.
Actually, I think I made an error. If picked up one at a time, the 2# rock will fall faster?
But Mass of the earth is not constant if you get your rocks off of the ground.
It should be multiplication. The force on a 5kg weight is indeed 5 times as great as the gravitational force on a 1 kg weight. Since F = ma, which can be rearranged to a = F/m, however, the acceleration, which is the quantity that really determines how the weights fall, will be nearly the same. That is, for a 5 pound weight, both the force and the mass are 5 times greater than that for a 1 pound weight. Therefore the force divided by the mass should be nearly the same in both cases. Implicit in this treatment is the assumption that the mass as determined by gravitational force is the same mass as determined by accelerating an object. In physics speak, we are assuming that the gravitational and inertial masses have the same value. The fact that they do has been confirmed experimentally to a precision on the order of a couple of tenths of a percent. Theoretically, the theory of general relativity is based on the equivalence principle which maintains that there is no difference between a gravitational field and any other type of acceleration. This implies that the inertial and gravitational masses must indeed be identical. If they are not, then relativity is in serious trouble as is most of our current understanding of the universe.
mass and gravity are independent? really? hrmn... lets play with the equation a bit... using a constant test object of 10kg, a constant drop height of 10m, and two planets of widely divergent mass.
Mass of Planet One = Mp1 = 30,000,000,000,000,000,000,000kg
Mass of Planet One = Mp2 = 5,000,000,000,000,000,000,000kg
Mass of Test Object = Mto = 10kg
Distance of fall = d = 10m
The math suggests that mass is cardianally relevant to gravity
you are trying to make my head hurt, again.
If you have two objects of different masses and measure the gravitational acceleration of these masses due to a third body, you will measure the same acceleration for both masses. In your example, the acceleration of planets 1 and 2 due to the 10 kg test mass will indeed be the same (and immeasurably small). Don't forget that gravity is a two-way attraction. The 10 kg mass exerts the same force on the planet as the planet does on the 10 kg mass. In your example, the force exerted by the 10 kg mass on planet one is six times greater than the force exerted by the test mass on planet two. The mass of planet one is also six times greater than the mass of planet two. If you calculate the acceleration of each planet, you will find that for planet two, it's F/m, where F is the force exerted on planet one by the test mass and m is the mass of planet two. For planet one, this acceleration is then 6F/6m = F/m. Physically speaking, this is exactly the same situation as the one in which there are two test masses being attracted by the same planet. In that case, the acceleration of the planet will be different depending on which test mass is under consideration, but the acceleration of the two test masses is equivalent. In your last example, it is the acceleration of the planets that is equivalent. The test mass undergoes different accelerations depending on which planet is under consideration.
Sorry for the headaches. LOL
ok, done a little research/refresher
G, the proportion (not the force), is a universal constant
quote: "The constant of proportionality G is known as the universal gravitational constant. It is termed a "universal constant" because it is thought to be the same at all places and all times, and thus universally characterizes the intrinsic strength of the gravitational force."
the force of gravity (Fg) is directly proportional to the product(ok, that's multiplication) of the masses in question
the force of gravity is inversely proportional to the square of the distance separating the centers of the masses in question.
maybe I'm just thick in the head, but it persists in looking like a 5kg mass would fall 10m on Earth marginally faster than would a 1kg mass, all other factors being set as equal.
Fg1 = GM1Me/r2 = M1 * a1
a1 = GMe/r2
Fg2 = GM2Me/r2 = M2 * a2
a2 = GMe/r2
a1=a2
For the case the two objects are dropped at the same time.
I see you found your physics texts.
You are more knowledgeable than I am in the area of physics so I will defer to your opinion.
The point I was was making, and that you obviously understood, was that most people would believe that the heavier object would fall noticeably faster and that it is just 'common sense' that it do so. I find that 'common sense' really gets in the way of science education. It would be nice if the education system could encourage students to think a little more critically.
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