The connection between Anti-Science and Anti-Education views.

If I do this for you.... will you just admit that you are wrong?

1) For F = GMm/r² I will plug in the numbers for the Gravitation constant, the mass of the Earth and radius of the Earth to get the force of gravity for each object (which I have already given).

Under Newton's Laws

1) F = ma

2) F = G(Mm)/(r^2)

3) The meaning of the word "force" is the same in both of these equations. There is nothing to reconcile and no contradiction.You can plug in the number for yourself/

So... A 5kg mass will experience a gravitational force of 49N and will accelerate at 9.8 m/s/s.
A 10kg mass will experience a gravitational force of 98N and will accelerate at 9.8 m/s/s.

The two masses have the same acceleration (and hit the ground at the same time). The math all works out correctly (you can check it if you want) and there is no contradiction. If you don't accept this, than plug in the numbers into the equations above and show me where they don't work.

Under your logic

1) You accept that a 10kg object has double the force as a 5 kg object. But then you don't. But then you claim there is more than one definition of the word "force" (which isn't true above as I show).

2) You calculate a different acceleration for each object. This violates Galileo's claim (which you accepted) that two objects of different masses will fall at the same rate.

There are contradictions in your thinking. Newton's laws work without contradiction.

This also shows why math (which makes it so clear) is better than a bunch muddled words. As soon as you do the math, you can see whether you have it right or not.

1. Using Newton's law of gravitation to calculate the gravitation force of each object

G = 6.67408 × 10-11 m3 kg-1 s-2
r = 6,378,100 m
M = 5.972 × 10^24 kg (Mass of earth)

https://www.google.com/search?sxsrf=ALeKk03nSWn6kbVe7CX6g4I6yiVzENdyGQ%3A1586733465132&ei=maGTXojUB-TC1QGB3oOoCQ&q=6.67408e-11+*+5.972e24+*+5+%2F+%286%2C378%2C100%5E2%29&oq=6.67408e-11+*+5.972e24+*+5+%2F+%286%2C378%2C100%5E2%29&gs_lcp=CgZwc3ktYWIQA0oJCBcSBTEyLTY5SggIGBIEMTItN1CmaFjVgAFgtYQBaANwAHgAgAFRiAHbA5IBATeYAQCgAQGqAQdnd3Mtd2l6&sclient=psy-ab&ved=0ahUKEwjIhKvkguToAhVkYTUKHQHvAJUQ4dUDCAw&uact=5

https://www.google.com/search?sxsrf=ALeKk00mMGyG3PZR8ndOmXu-LA_8HZ_b5Q%3A1586733482609&ei=qqGTXvXqJPaLytMP29yyiAg&q=6.67408e-11+*+5.972e24+*+10+%2F+%286%2C378%2C100%5E2%29&oq=6.67408e-11+*+5.972e24+*+10+%2F+%286%2C378%2C100%5E2%29&gs_lcp=CgZwc3ktYWIQA0oJCBcSBTEyLTcxSggIGBIEMTItNVD5sQNY57MDYLPoA2gAcAB4AIABV4gB3QKSAQE1mAEAoAEBqgEHZ3dzLXdpeg&sclient=psy-ab&ved=0ahUKEwj159XsguToAhX2hXIEHVuuDIEQ4dUDCAw&uact=5

So for Newton's laws of Gravitation.

The Gravitational force for a 5kg object is 49N. The gravitation force for the 10kg object is 98N

And for Newton's second law.

For the 5kg object the Gravitational force is 49N (from above), the acceleration is 9.8 m/s. For the 10kg object the Force is 98N.

49N = (9.8m/s/s) * 5kg (Yes!)
98N = (9.8m/s/s) * 10kg (Yes!)

The forces are different (one is double the other). The accelerations are the same. Newton wins!

I have also figured out how to show mathematically that a 10kg cannonball falls faster than a similar 5kg ball from the same height.

It involves applying critical thinking regarding the equations.

livinglava wrote:

I have also figured out how to show mathematically that a 10kg cannonball falls faster than a similar 5kg ball from the same height.

It involves applying critical thinking regarding the equations.

That isn't reality.

We have shown experimentally that a 10kg cannonball and a 5kg cannonball fall at the same rate. We have shown this repeatedly on Earth (including in just about every Physics classroom). We have shown this on the Moon.

If your mathematics is getting a different result that what happens in reality, then your mathematics are wrong (by definition). The mathematics of Isaac Newton get the correct answer (to a degree where any difference is not measurable at this scale).

That is the point.

The 5Kg weight experiences a gravitational force of 49N and accelerates at a rate of 9.8 m/s/s

The 10Kg weight experiences a gravitational force of 98N and accelerates at a rate of 9.8 m/s/s

Clearly, if you are getting the wrong answer, then you are doing the math wrong.

I very patiently showed you, step by step, how to calculate the answer using Newtons Law's the correct way.

One of the keys to critical thinking is being able to admit when the facts don't support your position, and to change your mind when this happens. This is a key to science and something you learn when you study Physics in a University.

1. I showed my work here https://able2know.org/topic/546372-5#post-6988323. I believe this is pretty clear. I think the problem is that you are being stubborn.

2. It is acceleration that "accounts for the difference in falling rate". The acceleration is equal, so the two cannonballs will fall at the same rate and land at the same time.

I don't know why you think the 10kg object falls faster than the 5Kg. You admitted pages ago that the fall at the same rate. But please proceed. I am still waiting patiently for you to show any amount of critical thinking (i.e. the ability to see the flaws in your own understanding)

Quote:

The 5Kg weight experiences a gravitational force of 49N and accelerates at a rate of 9.8 m/s/s

The 10Kg weight experiences a gravitational force of 98N and accelerates at a rate of 9.8 m/s/s

Let me be an example of Critical thinking (since I am defending science here).

These are the results of my calculations using Newton's laws. You can prove me wrong in one of two ways:

1. By showing that the calculations in either case don't match Newton's second law (F = ma).

2. By showing that the calculations in either case don't match very closely (allowing for precision in the Gravitational Constant) Newtons law of Universal Gravitation (F = GMm/(r^2))

Do either of these things, and I will admit that I am wrong because I will be wrong.

You are being ridiculous.

This is where I leave this discussion... unless you have something interesting to say.

Do you want to know why the 10kg object falls faster than the 5kg one? Hint: it is implicit in part of Newton's equation. Do you know which part?

Show me the results of your calculations then. The result of my calculations are:

The 5Kg object experiences a force of gravity of 49N and falls with an acceleration of 9.8 m/s/s.

The 10Kg object experiences a force of gravity of 98N and falls with an acceleration of 9.8 m/s/s.

What are the results of your calculations?

Quote:

Do you want to know why the 10kg object falls faster than the 5kg one? Hint: it is implicit in part of Newton's equation. Do you know which part?

Don't ask stupid questions? Just make your point.

Do you realize that in reality the 10kg falls no faster than the 5kg object (unless you are going to play tricks with air friction or something).

This is easy to test with experiment. You are literally fighting with reality.

In this case, the equation predicts that the rates of falling for the two objects will be slightly different, but in practice the difference might not be enough to detect with the human ear.