# B Time of free fall does depend on mass

1. Sep 17, 2016

### parshyaa

Months ago I have seen walter lewins first lecture on dimensions, there he made a comment that scientist are trying to prove that time taken to reach ground when a object is dropped does depends on mass (in small amount) but it depends on mass, how they have thaught that it depends on mass , formula says T = C√(h/g) and T is only proportional to height or distance , then how there can be a relation between mass and time, what made them to make a research on this, answer from a researcher in this field will be great.

2. Sep 17, 2016

### CWatters

Im a bit rusty but this sounds like you are referring to the possibility that gravitational and inertial mass could be different.

For example we can write...

GMm/r^2 = ma

Where m on the left is the gravitational mass and m on the right is the inertial mass. Normally we assume these are the same so the mass m cancels. That makes the acceleration a independent of m. But what if it's not exactly the same.

3. Sep 17, 2016

### parshyaa

Okk , wohoo you made me think a lot , how can we say that a same particle can have two masses.

4. Sep 17, 2016

### 256bits

Why wouldn't it?
An incorrect assumption is that the only one of the masses under mutual gravitational.
Both masses move towards one another.

5. Sep 17, 2016

Staff Emeritus
This is guesswork, and it's because the OP didn't ask a good question.

A good question: "In the video at this link, at 4:58, Prof. X says Y. Can you explain how Y and Z can both be true?"
A bad question: "In one of his videos, Prof. X says something that might have been Y. I don't understand/"

6. Sep 17, 2016

### mrspeedybob

It is generally expected that inertial and gravitational mass are equivalent. The reason people are looking for a difference is because that would be big news. It's human nature to want to set yourself apart from the crowd. What better way to do that then proving that physics is radically different then everyone thought? So, people keep rechecking old theories with ever greater and greater acuracy, hoping to prove them wrong and find new physics. Sometimes, very rarely, it works, and progress is made. :-)

7. Sep 17, 2016

### sophiecentaur

This classical treatment may be all that's involved. The OP doesn't make it clear.
Can the OP give a link to the particular lecture that they are quoting from?

8. Sep 17, 2016

### parshyaa

, go to this link and you will get walter lewin's first lecture , he discusses all this at the end of video

9. Sep 17, 2016

### parshyaa

time :36.16 minutes

10. Sep 17, 2016

Staff Emeritus
Lewin says that people are checking on what we think we know by performing ever more sensitive experiments.

11. Sep 17, 2016

### parshyaa

Why they are checking , formula simply shows that time depends on height only then why do we check for mass

12. Sep 17, 2016

Staff Emeritus
Because physics is an experimental science, and we want to verify that the formulas we use are correct to the best of our ability.

13. Sep 17, 2016

### parshyaa

Ok how can you say that they are only verifying their formula

14. Sep 17, 2016

### TurtleMeister

In Newtonian mechanics (two body problem):

The universality of free fall is always true. The time of free fall is affected by the mass of both bodies.

The acceleration of body A is affected only by the mass of body B, and the acceleration of body B is affected only by the mass of body A.

If the mass of free falling body A is changed, it's acceleration will not change, but the time of free fall will change.

If I'm understanding the op post correctly you may find the above statements confusing or even contradictory, but they are all true. I puzzled over this for a long time. It's one of those things where once you get it, it will be an aha moment. Until you understand why the above statements are all true, I think it would be unwise to try and understand the concepts of active, passive, and inertial mass.

15. Sep 17, 2016

Staff Emeritus
I could repeat what I said, only louder, but I don't think it would help.

16. Sep 18, 2016

### sophiecentaur

What are you trying to say? You seem to be suggesting 'something' is wrong but you are not specifying just what is wrong.

17. Sep 18, 2016

### David Lewis

In General Relativity, a force is felt when a body accelerates in spacetime, suggesting inertial and gravitational mass might be two ways of looking at the same thing.

18. Sep 18, 2016

### TurtleMeister

The formula that you are referring to has limitations. It is usually used for measurements near the earth surface where the value of h is limited. g is not necessarily a constant. It changes with a change in the value of h, thus the limitation. In addition to the value of g being affected by the value of h, it is also affected by the value of the combined masses of both bodies. So to get a more precise value for T we should check for mass also.

19. Sep 18, 2016

### sophiecentaur

Because that's the way that Physics is done. If there is no experimental evidence (and that includes finding that something is NOT a factor) then a theory is not acceptable.
Dimensional Analysis is very powerful at generating ideas and theories but it is not enough because the formula that it's applied to may not actually be correct.

20. Sep 18, 2016

### TurtleMeister

A more accurate equation for free fall time can be derived from Kepler's third law:

This equation has the advantage that it accounts for both the distance R and the masses M and m. But it also has the disadvantage that M and m are considered to be point masses. So you would need to account for the physical size of the bodies.

Last edited: Sep 18, 2016
21. Sep 19, 2016

### Pet Scan

That is a unique rendering of Kepler's Law for free fall I've not seen. However, if I'm not mistaken Kepler eqn. for period of circular orbital motion should be equivalent to the oscillation period of m through a frictionless hole in the center of large Mass, M, if it has uniform mass density. In that case the free fall period would place m at center of mass, M in 1/4th the period, making the numerical constant merely pi/2 in your above eqn. Where does the extra factor of sq.rt. 2 come from?

Last edited: Sep 20, 2016
22. Sep 20, 2016

### votingmachine

There seems to be an obvious mistake in what he says.

He says:
Time (is proportional to) height^a x Applemass^b x Earthmass^c

And then he claims the dimensional analysis proves this must be wrong. But any math would say that PROPORTIONAL means EQUAL WITH A CONSTANT.

So:
Time (is proportional to) Y

means:
Time = kY

And k may have any units. We do not require Planck's constant to be dimensionless (it isn't). Or the Ideal Gas constant to be dimensionless (it isn't). So when he takes a proportionality, and does dimensional analysis, he is not being careful. All he really can conclude is that the dimensions of the constant must cancel everything except the time unit.

I apologize if I've missed an important point, but I skipped to the point in the lecture where the problem is discussed.

23. Sep 20, 2016

### sophiecentaur

Afaiaa, Kepler's laws were not to do with free fall and didn't involve Mass, at all but with the geometry and timing of planetary motion. They were arrived at in order to explain observed data and they did not involve any Physics as such. Newton was the one to do that. Here's one of many links.
Kepler's law refers to 'swept areas' and, for Simple harmonic oscillation through a hole in the Earth, the swept area is zero.
I really can't see where all this is going. Is there any doubt about the Classical Physics involved here? Lewin's wording was a bit loose and I think he was just being mischievous and showing the risks of relying on Dimensional Analysis. He wanted to make his students think a bit harder and not just to take notes and learn them off by heart.
The thread is causing a number of people to worry about the validity of fundamental stuff and that is a shame.

24. Sep 20, 2016

### parshyaa

Sorry for this thread ,but he said that time of free fall does depends on mass , if any budy proved this then he will get a nobel prize and scientists are buisy to crack this. Suppose they have proved that yes it does depends on mass , then what will happen to the formula for time t, what is wrong in arguing that inertial mass and gravitational mass can be different[then this argument will raise a question how can a object have two mass] , oh god I am confused and making others too

25. Sep 20, 2016