# Free Fall question

1. Jan 9, 2009

### aaron35510

In free fall, there is no air resistance, so the only force acting upon the object of free fall would only be its weight.

Now the question is, if an object keeps accelerating due to free fall, wouldn't it eventually reach the speed of light? For example, earth's g=9.81 m/s^2, so over a course of time, it would eventually accelerate to the speed of light (considering the fact that the object would never hit the ground.)

So since Einstein proclaimed that NOTHING that has mass can travel at the speed of light, wouldn't this prove him wrong?

2. Jan 9, 2009

### Delphi51

The same situation exists in a particle accelerator. As the speed increases, the mass increases (and has been measured for particles near the speed of light). As the speed approaches the speed of light, it gets very large indeed and so the acceleration approaches zero. There are some other problems with accelerators - notably EM radiation draining away the kinetic energy - but it certainly appears that c cannot be reached.

3. Jan 10, 2009

### Mephisto

yes. the short answer is that intuition simply breaks down for particles traveling near speed of light, and the acceleration is not constant 9.8 anymore. You have to use different equations that correct for relativistic effects.

4. Jan 10, 2009

### A.T.

g=9.81 is only valid near earth's surface. It varies with distance. Even in Newtonian mechanics nothing falling towards the earth could reach more than the earth's escape velocity, which is not even close to the speed of light.

Yes. And if apples where flying up from the ground to the tree it would prove Newton wrong. But neither one was observed so far.

5. Jan 10, 2009

### rcgldr

What about the case of a neutron falling into a black hole? Wouldn't the increase in mass also correspond to an increase in gravity, so maintaining or increasing the rate of acceleration? Or the case of a positron and electron collision?

6. Jan 10, 2009

### A.T.

Increase in mass also corresponds to an increase in inertia. Even in Newtonian mechanics the mass of a body is irrelevant for its acceleration by gravity.

There really are better ways to accelerate stuff than by gravity, but nothing will accelerate stuff beyond the speed of light.

7. Jan 10, 2009

### tim_lou

speed is ill-defined unless you specify what the observer is. If the observer is falling in the block hole with the particle, he/she would not measure anything greater than c. For anyone outside the horizon, you simple can't measure the speed (i.e. there is no well defined speed).

8. Jan 10, 2009

### aaron35510

so in this case, how do you calculate the relativistic acceleration of a free falling object?

9. Jan 10, 2009

### jshuford

Plus, aren't neutrinos mass-less particles anyway?