Gravitational forces and constant acceleration

[UrbanXrisis]

Why isn't it true that an object tends to move with a velocity that is proportional to the force on it? For example, when an object falls, there must be a gravitational force on it, and this gravataional force in the downward direction gets larger and larger as the object falls and gets closer to the earth. Wouldn't this cause the velocity to get larger and larger as the object falls, so the object undergoes a constant acceleration because the force gets larger at a constant rate as the objecct falls?

 

[bross7]

Well it does increase for a time. But don't forget that there is air resistance when free falling which slows down the rate of acceleration.

 

[ponjavic]

UrbanXrisis
Why isn't it true that an object tends to move with a velocity that is proportional to the force on it?

If you mean a net force then of course the velocity will not be proportional. The net force is an accelleration and especially if the accelleration is constant the velocity increases while the accelleration is the same, thus they are not proportional.

For a simple mathematical example take a ball falling from v=0m/s
The accelleration is G(m1m2)/r^2

say it would fall for one second
it would move g/2=4.41m and the velocity would now be 9.82m/s
the velocity has increased a lot

how has the gravitational force been changed?
if r before was (i'm guessing the distance from the center of the Earth to the ball could be 10km or whatever) it now is 9.999km this means that the gravitational force has been changed with 0.001^2=0.000001 while the the velocity has changed infinite times (0-9.82) so it is not proportional

This is the reason we say that g is constant, it changes so little...

so the object undergoes a constant acceleration because the force gets larger at a constant rate as the objecct falls?

constant accelleration means constant force :/
so truly neither the accelleration nor the force (which is the same F=mg) is constant but increases/decreases so little it can be called constant

excuse any errors, it's still morning in sweden, if you have any questions ask away :P

 

[HallsofIvy]

Why isn't it true that an object tends to move with a velocity that is proportional to the force on it?

No, it moves with an acceleration that is proportional to the force on it.
You are asking why that is true- one very real reason is that force is defined as "rate of change of momentum" not momentum itself.

For example, when an object falls, there must be a gravitational force on it, and this gravataional force in the downward direction gets larger and larger as the object falls and gets closer to the earth. Wouldn't this cause the velocity to get larger and larger as the object falls, so the object undergoes a constant acceleration because the force gets larger at a constant rate as the objecct falls?

Are you assuming that the distance is so great that (1/r²) comes into play? In that case, there would be an increasing acceleration, not and constant acceleration.

In the case that distance involved is small so that the force stays approximately the same ("surface of the earth" problems), then the acceleration would be approximately the same.