Exploring Newton's Law of Universal Gravitation

[TheBlackNinja]

High guys,

I've always had problems with this law at the way it was explained.But now I've seen lewin explaining that way that bothers me: In terms of sensations.At 1:50

http://youtu.be/M_8w-dD4RBE

What I think is that we "feel" the pull only because we are made of multiple particles and the pull is not applied at them -exactly- the same way, because if it was the case their relative positions wouldn't change and there is no way we could feel the force.And for a single particle the notion doesn't even exist.So as long as the particles involved are all accelerated the same way, you can't tell if you're accelerating or not.

Is that right?

 

[TurtleMeister]

Yes, that is right, IMO. But I don't really see a conflict in what you're saying and what Lewin is saying. Your description is just more explicit.

 

[TheBlackNinja]

Yes, that is right, IMO. But I don't really see a conflict in what you're saying and what Lewin is saying. Your description is just more explicit.

Lewin said that while he is in an accelerating horse, standing people may conclude that he is feeling a pull because of the second law.And that reasoning is ok because they are on a inertial reference.And he observes the standing people accelerating and concludes, by the second law, the there must be a force acting into them, but he says that that reasoning is flawed because the people are not feeling any forces(he is not on a inertial reference frame).
But what I said is that:1: he only feels the accelerating force from the horse because its only applied to his particles that are in contact with the horse so his set of particles relative positions(among themselves) is changing.2 so the fact that the standing people are not feeling the pull doesn't tell that there is no force acting on them.

I think the idea that I'd like to be explained is why the principle of equivalence is not valid for any force, rather than only gravity.Because I think that's the case only because we deal with multi particles objects.In a gravitational field, when its weak enough we can say that for a long multi particle body the force acts on each particle exactly the same way, so the body physically can't tell if he is accelerating or not.But single particles can't tell of they are accelerating anyway

 

[TurtleMeister]

Yes, I understand what you are saying:

$F = m\,a$ (m "feels" the force of acceleration, non gravitational)

$F_g = \frac{GMm}{r^2}$ (m does not "feel" the force of acceleration, disregarding tidal effects)

And I agree with what you are saying. But I think the point that Lewin is trying to make is that while he is accelerating on the horse, he cannot make accurate judgements based on Newton's laws, because his frame of reference is non-inertial. I do not think his lecture is about the equivalence principle. But your point is well taken by me.

 

[TheBlackNinja]

Yes, I understand what you are saying:

$F = m\,a$ (m "feels" the force of acceleration, non gravitational)

$F_g = \frac{GMm}{r^2}$ (m does not "feel" the force of acceleration, disregarding tidal effects)

And I agree with what you are saying. But I think the point that Lewin is trying to make is that while he is accelerating on the horse, he cannot make accurate judgements based on Newton's laws, because his frame of reference is non-inertial. I do not think his lecture is about the equivalence principle. But your point is well taken by me.

He made an explicit association between force and feeling.Whatever he was trying to say he was wrong, I think.

 

[TurtleMeister]

He made an explicit association between force and feeling.Whatever he was trying to say he was wrong, I think.

Why would he be necessarily wrong? He, and the people in the audience, are not single particles. And the accelerations he is talking about are not necessarily gravitational. He was not wrong in the point he was trying to make, which is the requirement that Newton's laws be only applicable in an inertial frame of reference.

 

[TheBlackNinja]

Why would he be necessarily wrong?

Because he told that if you're not "feeling" a force, then there is no force acting on you.

 

[TurtleMeister]

Because he told that if you're not "feeling" a force, then there is no force acting on you.

Hmm, I'll have to go back and watch it again. I don't remember that.

 

[Fewmet]

Because he told that if you're not "feeling" a force, then there is no force acting on you.

Isn't he, rather, saying that if you are not feeling the force you can treat you reference frame (like the lecture hall) as sufficiently case to being inertial?

He calculates the centripetal effect and shows it to be so small compared to g, and asserts that is true for the the other centripetal effects he cites. He is not asserting that those forces don't exist. He also says that we cannot prove the first law because we can never know if our reference frame is truly inertial (which I took to mean there may well be indetectably small accelerations). Again, that suggests he acknowledges the existence of forces we do not feel rendering a frame noninertial.

 

[TurtleMeister]

Isn't he, rather, saying that if you are not feeling the force you can treat you reference frame (like the lecture hall) as sufficiently case to being inertial?

He calculates the centripetal effect and shows it to be so small compared to g, and asserts that is true for the the other centripetal effects he cites. He is not asserting that those forces don't exist. He also says that we cannot prove the first law because we can never know if our reference frame is truly inertial (which I took to mean there may well be indetectably small accelerations). Again, that suggests he acknowledges the existence of forces we do not feel rendering a frame noninertial.

Good observation. I think Ninja is just being a little nit-picky. You could also say that he is wrong at 27:40. He uses the equation $\frac{1}{2}\!gt^2=h$ to determine how long it will take an apple to hit the earth. But as the apple falls, g is constantly changing. As the apple moves closer to the earth, g will increase. So he is wrong. But you would be nit-picky to make that accusation because h is only 100 meters. It's a very close approximation. But Ninja's point is well taken. However, I don't think anyone is necessarily wrong here.

 

[vjraghavan]

Newton's laws can be deceptively simple. To understand the point being made by the first law one has to study properly about frames of reference and why & how to set them up before applying the Newton's laws.

I don't want to spoil the learning by explaining it further here. Reading Halliday Resnikc and Walker would do the trick. If you are a physics/math/engineering major doing a course in classical mechanics I strongly suggest you read Int to Mech by Klepper and Kolenkow (MIT Press). That will clear you doubts.

Cheers

 

[Drakkith]

What I think is that we "feel" the pull only because we are made of multiple particles and the pull is not applied at them -exactly- the same way, because if it was the case their relative positions wouldn't change and there is no way we could feel the force.And for a single particle the notion doesn't even exist.So as long as the particles involved are all accelerated the same way, you can't tell if you're accelerating or not.

Is that right?

That is 100% correct. If a force had no gradient because it was equally strong at all distances from it, you would NOT be able to tell you were accelerating by "feeling" it. Take a skydiver for example. The change in the force of gravity from 20,000 ft to ground level is very very small, and unnoticeable without using measuring instruments. To a skydiver, once he jumps out of a plane he wouldn't know he was accelerating except for the fact that he encounters air resistance. Thus you get the sensation of "free fall", which happens to be exactly the same as floating in space away from any object.

In contrast, sitting in a vehicle that suddenly accelerates is easily felt because the force acts first on the seat, then on the back of the driver or passenger, then gradually the rest of their bodies. The force acts THROUGH these, unlike gravity which acts ON these at the same time.