When an object is tossed up from the ground

[Ranku]

When an object is tossed up from the ground, is it in freefall on the way up? When the object is returning to the ground, the cancellation between gravitational and inertial forces makes the object weightless. How does the cancellation of the forces work on the way up ? - given that there was an initial external force imparted on it.

 

[Dale]

When an object is tossed up from the ground, is it in freefall on the way up?

It is in freefall whenever gravity is the only significant force acting on it. So from the moment it leaves your hand to the moment it hits the ground, regardless of whether it is moving up, down, or neither at any moment in between.

 

[Mister T]

When an object is tossed up from the ground, is it in freefall on the way up?

Yes.

When the object is returning to the ground, the cancellation between gravitational and inertial forces makes the object weightless.

No. Can you tell us what you mean by an inertial force?

- given that there was an initial external force imparted on it.

That initial force disappears as soon as the object is released.

Suppose you are inside a box, and there are no openings in the box so you cannot see what's going on outside the box. You could feel, and confirm with measurements, the presence of that initial force. But as soon as the initial force goes away, you are in freefall. You will feel no different on the way up, at the apex, or on the way down. There would be no experiment you could perform within the box that would determine when you switched from moving upward to moving downward.

 

[Ranku]

No. Can you tell us what you mean by an inertial force?

Freefall implies the equality of gravitational and inertial mass, whereby gravitational force cancels equal and opposite arisen inertial force, rendering the object force-free and weightless.

 

[Mister T]

Freefall implies the equality of gravitational and inertial mass,

Okay.

whereby gravitational force cancels equal and opposite arisen inertial force, rendering the object force-free and weightless.

No. In classical physics the gravitational force is the only significant force exerted on an object in free fall.

Again, I ask you, what do you mean by the term "inertial force"? And more specifically, what inertial force do you suppose is exerted on an object that's in free fall?

 

[A.T.]

Freefall implies the equality of gravitational and inertial mass, whereby gravitational force cancels equal and opposite arisen inertial force, rendering the object force-free and weightless.

You seem to confuse free falling frames of reference with free falling objects.

 

[Ranku]

No. In classical physics the gravitational force is the only significant force exerted on an object in free fall.

Again, I ask you, what do you mean by the term "inertial force"? And more specifically, what inertial force do you suppose is exerted on an object that's in free fall?

It's all clearly laid out in 'Gravitation and Cosmology' by Steven Weinberg in the chapter 'The Principle of Equivalence' (pg. 67 & 68): "The principle of equivalence rests on the equality of gravitational and inertial mass. The equivalence principle says that the cancellation of gravitational by inertial force (and hence their equivalence) will obtain for all freefalling systems."

 

[A.T.]

It's all clearly laid out in 'Gravitation and Cosmology' by Steven Weinberg in the chapter 'The Principle of Equivalence' (pg. 67 & 68): "The principle of equivalence rests on the equality of gravitational and inertial mass. The equivalence principle says that the cancellation of gravitational by inertial force (and hence their equivalence) will obtain for all freefalling systems."

freefalling systems = free falling frames of reference
See post #6

 

[Ranku]

freefalling systems = free falling frames of reference

Freefalling systems contain freefalling objects, whose gravitational and inertial mass are equivalent.

 

[A.T.]

Freefalling systems contain freefalling objects,

Reference frames aren't containers for certain objects. You can analyze any object from any frame.

 

[Ranku]

This discussion is going nowhere.

 

[PeroK]

This discussion is going nowhere.

It's been in freefall for some time.

 

[Ranku]

it's in circular freefall.

 

[A.T.]

This discussion is going nowhere.

Your question is based on confusing frames and objects. Clear that up, and the issue resolves itself.

 

[PeroK]

it's in circular freefall.

Like the Earth around the Sun? Maybe that's not so bad.

 

[Ranku]

Like the Earth around the Sun? Maybe that's not so bad.

At least no hard landing .

 

[Ibix]

It's all clearly laid out in 'Gravitation and Cosmology' by Steven Weinberg in the chapter 'The Principle of Equivalence' (pg. 67 & 68): "The principle of equivalence rests on the equality of gravitational and inertial mass. The equivalence principle says that the cancellation of gravitational by inertial force (and hence their equivalence) will obtain for all freefalling systems."

A free-falling frame of reference, in Newtonian physics, is an accelerating frame. Thus there is an "inertial" or "fictitious" force acting in the direction opposite to the acceleration (the one that presses you back into a car seat when you press the accelerator). But there's also a real force acting in the direction of acceleration - that is, gravity. The two always cancel, which is a result of the $m$ in $F=GMm/r^2$ being the same as the one in $F=ma$.

That's just one of those things in Newtonian physics - there's no problem if $F=GMkm/r^2$, where $k$ is a constant that depends on (for example) what a falling body is made of. In this case the inertial mass would be $m$ and the gravitational mass would be $km$. It's just that, experimentally, we find that $k=1$ always. The equivalence principle, as written by Weinberg, is simply the claim that not only is $k=1$ for every pair of masses we've ever tested, it's 1 for every pair of masses, full stop. This was a key realisation on the route to describing gravity as spacetime curvature, since if the effect of gravity on a test body is only due to the geometry of spacetime then it can't depend on (for example) what the body is made of.

 

[A.T.]

A free-falling frame of reference, in Newtonian physics, is an accelerating frame. Thus there is an "inertial" or "fictitious" force acting in the direction opposite to the acceleration (the one that presses you back into a car seat when you press the accelerator). But there's also a real force acting in the direction of acceleration - that is, gravity. The two always cancel, ...

@Ranku The "always" part is key here. The inertial force and gravity cancel for all objects analyzed in the Newtonian freefalling frame, not just for freefalling objects. The non-freefalling object just have some other forces aside from these two.

 

[jbriggs444]

The two always cancel,

The two always cancel because we chose to use an accelerating reference frame with just enough acceleration to make them cancel -- i.e. the one in which they do cancel.

 

[Ibix]

The two always cancel because we chose to use an accelerating reference frame with just enough acceleration to make them cancel -- i.e. the one in which they do cancel.

Yes - but imagine doing this in a Coulomb field with two particles with different charge-to-mass ratios. You can pick an accelerating frame in which either one is stationary, but the other one is always accelerating. The point about gravity is that the "charge-to-mass ratio" is always one, so the accelerating frame in which one is stationary is also the frame in which the other is stationary.

 

[jbriggs444]

Yes - but imagine doing this in a Coulomb field with two particles with different charge-to-mass ratios. You can pick an accelerating frame in which either one is stationary, but the other one is always accelerating. The point about gravity is that the "charge-to-mass ratio" is always one, so the accelerating frame in which one is stationary is also the frame in which the other is stationary.

Agreed, when you find an acceleration that cancels gravity for one object, it cancels gravity for all objects, regardless of composition or complexity.