# Free fall acceleration help

Tags:
1. Feb 11, 2016

### Gazi

how two objects hit the ground at same time regardless of their weight of masses.
what is the reason of Acceleration is always constant via gravitational force for both of them. F=mg
F1/m1=F2/m2

2. Feb 11, 2016

### pervect

Staff Emeritus
When you phrase it in terms of forces, you are implicitly asking about Newtonian gravity and not General Relativity. According to Newtonian gravity, it's just a coincidence that all matter, regardless of what it's made of, falls at the same rate. Another way of saying this is that the inertial mass is always equal to the gravitational mass.

In terms of General Relativity, the theory is that the equivalence of gravitational and inertial mass is not just a coincidence, but it's postulated as part of the theory. One way of stating this is that gravity is an inertial force. Pursuing this line of thought eventually leads to the idea that falling objects are moving along special curves called geodesics, and that this motion is the natural force-free motion that all objects share.

3. Feb 11, 2016

### Gazi

I took a look web site, it says, all freely-falling bodies experience the same acceleration, that is, a = -g
Mass of gravitational = Mass of inertial.
There is no obvious reason why the inertial mass m that governs the response of a body to an applied force... http://www.britannica.com/science/inertial-mass
i guess there is no brief explanation for the situation.

4. Feb 12, 2016

### Ibix

In terms of Newton's theory of gravity, there is no explanation. It's just one of those things.

In terms of Einstein's theory of gravity, gravity isn't a force. Instead it is a curving of spacetime. Objects all act the same way because they're moving through the same curved spacetime. Their own mass doesn't come in to it.

5. Feb 12, 2016

### A.T.

Note that the definition of an "object" is arbitrary. You can consider two equal apples falling side by side as two objects, you might also consider them as just one object called "pair of apples", that has twice the weight of a single apple.

6. Feb 12, 2016

### MikeGomez

Galileo would ask you to explain how it would make sense any other way. Let’s say the larger rock falls faster and the smaller rock falls slower. If we tie the two rocks together the small rock falling slower would slow down the large rock.

But another way to think about it is that the combination of the two rocks makes a rock that is larger than either of the original rocks, so the two rocks tied together should fall faster than the original rocks.

So should the (tied together larger rock) fall faster or slower than the original rocks?

What A.T. said in post #5 is correct. What you decide to call an object is arbitrary.

7. Feb 12, 2016

### DrStupid

I wouldn't call it a coincidence because Newton set inertial and gravitational mass equal because all bodies are falling identical.

8. Feb 12, 2016

### Gazi

if gravity isn't a force, how objects act the same way,... moving through curved space time? if there is no force, no motion

9. Feb 12, 2016

### Ibix

That's not true even in Newtonian physics. Things move in straight lines at constant speed.

The same is true in general relativity. The only difference is that near massive bodies, the concept of a straight line doesn't really make sense. Spacetime is curved and you can't move in a straight line through it without applying a force (if you can even define "straight line" unambiguously). Objects in free fall near massive bodies move along curved paths because massive bodies curve spacetime.

10. Feb 12, 2016

### pervect

Staff Emeritus
If you've got a ball of, say lead, and you split it into two parts, it's not a coincidence that the two parts fall at the same rate. But there's no a-priori reason that a ball of copper, a ball of lead, and a feather (ignoring air resistance, obviously) should all fall at the same exact rate according to Newton's theory. We observe that they do, and this leads to the principle of equivalence, one of the foundational principles of GR.

11. Feb 12, 2016

### DrStupid

Both, Newtonian mechanics and general relativity are designed to result in identical trajectories for all free falling objects and both Newton and Einstein did it for the same reason: because we observe that in nature.

12. Feb 12, 2016

### Gazi

i need to fix my last sentence, it would be if there is no force, no acceleration which is gravity. Newton's first law says, if an object is moving along, untouched by a force of any kind, it will continue to move along in a perfectly straight line at a constant speed...

13. Feb 12, 2016

### Ibix

Yes. But Newtonian gravity doesn't forbid some kind of Unobtanium whose "gravitational charge" is $\kappa m$ but whose inertial mass is $m$, and the fix to Newtonian gravity is easy. But you can't fix GR in the same way since the geodesic equation doesn't directly depend on the mass of the free falling particle, which means that "no Unobtanium" is a prediction of GR - at least that's my understanding.

14. Feb 12, 2016

### Ibix

Yes. But Newton made three assumptions that turned out to be incorrect - that time is a separate thing from space, that it is an absolute thing that everyone agrees on, and that space obeys the rules of Euclidean geometry. That last is why things move in straight lines when not accelerated. But in GR spacetime is non-Euclidean, so objects move along curves through spacetime. You may wish to search these forums for posts by @A.T. who has produced a nice animation describing this.

15. Feb 12, 2016

### PeroK

All laws and formulas have a context in which they are true. Newton's. First law is, in fact, only valid in inertial reference frames. It's not valid in an accelerating reference frame. If you are accelerating then you see objects moving in curves not straight lines.

Someone at rest in a gravitational field is effectively in an accelerating reference frame. That is the approach of general relativity.

In classical mechanics, of course, gravity must be considered a force. But not in GR.

16. Feb 12, 2016

### Gazi

17. Feb 12, 2016

### jbriggs444

GR = General Relativity. Our best current model for gravitation.

18. Feb 12, 2016

### ZapperZ

Staff Emeritus
19. Feb 12, 2016

### Gazi

F1/m1=F2/m2=F3/m3..............= gravity.
formulas don't explain the reason why all object fall at same time.

20. Feb 12, 2016

### ZapperZ

Staff Emeritus
They don't! They only fall at almost the same time when the OTHER body has a mass significantly bigger than all the others.