What happens with the puck in a non inertial board?

[Manny46]

I'm not being extremely exact here, but suppose there's a puck in a board where there's very little friction. Both puck and board are at rest. Suppose the board starts from rest to some decent speed, so there's definitely this acceleration, by virtue of which (and also less friction), puck slides backward if that board is moving forward or in other words (pucks) remains at same place by virtue of inertia. And after a few seconds when the board reaches a decent speed, it keeps at it. Thereby, it becomes again an inertial frame.
Now what happens to the puck now when the board reaches constant pace?
1. Will it too acquire that speed?
2. Will it fall off the board as it keeps traveling backwards (as board moves forward)?

Here friction is bare minimum and has a very minuscule effect. Board is long enough to have puck on it for whatever backward slide it faces.

Obviously, when there's sufficient friction, it acquires the same speed as the board, but what happens when the friction is sufficiently less or bare minimum?

 

[Drakkith]

If the friction is small enough and the board is not big enough, the puck falls off the edge of the board. If friction and the board are large enough, then the puck and the board both accelerate in opposite directions (puck forward, board backward) until their velocities are equal.

 

[Manny46]

If the friction is small enough and the board is not big enough, the puck falls off the edge of the board. If friction and the board are large enough, then the puck and the board both accelerate in opposite directions (puck forward, board backward) until their velocities are equal.

Now here's the thing, board is large enough, less friction and board comes to a constant speed, what happens then?
Also if the friction is large enough, won't puck stay where it is?

 

[Drakkith]

Now here's the thing, board is large enough, less friction and board comes to a constant speed, what happens then?

Either there is sufficient space and friction to keep the puck on the board, or there is not. I can't answer what happens if you increase the space while decreasing the friction without knowing the size of the board, the magnitude and time of the acceleration, the force of friction, and other details.

Also if the friction is large enough, won't puck stay where it is?

Yes, it is possible that static friction is large enough to keep the puck pinned to the board, such that the board and the puck both accelerate at the same rate.

 

[Manny46]

Either there is sufficient space and friction to keep the puck on the board, or there is not. I can't answer what happens if you increase the space while decreasing the friction without knowing the size of the board, the magnitude and time of the acceleration, the force of friction, and other details.

I mean without going for the numerical details, my question is w.r.t. board achieving a constant speed (of course board is long enough, less friction here), will the puck keeps moving backward when the board moves forward at a constant speed or it goes along with it with the same speed?

 

[Drakkith]

The puck will accelerate as long as any friction is present. If the board is large enough, the puck will eventually reach the same speed as the board.

 

[lightarrow]

I mean without going for the numerical details, my question is w.r.t. board achieving a constant speed (of course board is long enough, less friction here), will the puck keeps moving backward when the board moves forward at a constant speed or it goes along with it with the same speed?

When the board reaches constant speed (however it's not clear if you "assume" this simply because you stop pushing/pulling the board with an external force and then you neglect the tangent reaction of the puck on it, or because you "imposes" a constant board's velocity with some apparatus) then you can use an inertial reference system where the board is stationary: now you notice that the puck is moving on the board with some friction and no other tangent force on it, so it will necessary have to stop, before or less, even if the friction is extremely small; so it will have to become stationary with respect to the board.

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lightarrow

 

[sophiecentaur]

@Manny46 : You keep shifting the goalposts. The answer will always depend on the actual circumstances.
If there is no force on the puck (from any source) it will be 'left behind' by the board. Any force between board and puck can accelerate the puck and it may accelerate for long enough to reach the speed of the board, ending up on a spot on the board where it remains stationary in the frame of the board.

 

[Manny46]

@Manny46 : You keep shifting the goalposts. The answer will always depend on the actual circumstances.
If there is no force on the puck (from any source) it will be 'left behind' by the board. Any force between board and puck can accelerate the puck and it may accelerate for long enough to reach the speed of the board, ending up on a spot on the board where it remains stationary in the frame of the board.

Oh I apologize for not being precise enough, but I get your point. Thanks

 

[Manny46]

When the board reaches constant speed (however it's not clear if you "assume" this simply because you stop pushing/pulling the board with an external force and then you neglect the tangent reaction of the puck on it, or because you "imposes" a constant board's velocity with some apparatus)

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lightarrow

Here I definitely assume some engine working on it in a very controlled manner. Like, let's say a car which accelerates from 0 to 60 mph in some seconds, and then it stays at 60. Something to that effect. Though got your point.

 

[A.T.]

...will the puck keeps moving backward when the board moves forward at a constant speed or it goes along with it with the same speed?

When the board reaches constant speed, its rest frame becomes inertial. What then happens relative to the board, is the same that would happen relative to the ground, given the same initial conditions.

 

[sophiecentaur]

Here I definitely assume some engine working on it in a very controlled manner. Like, let's say a car which accelerates from 0 to 60 mph in some seconds, and then it stays at 60. Something to that effect. Though got your point.

If you apply Newton's First Law of motion strictly, then the answer is very straightforward. If there is any force between board and puck, the puck will be accelerating, if the board is not accelerating, there can be a force until the puck acquires the speed of the board, then the force will be zero. Ignore intuition and apply the rules strictly.

 

[Manny46]

If you apply Newton's First Law of motion strictly, then the answer is very straightforward. If there is any force between board and puck, the puck will be accelerating, if the board is not accelerating, there can be a force until the puck acquires the speed of the board, then the force will be zero. Ignore intuition and apply the rules strictly.

Yeah that helps, basically if there's a friction and when the train stops accelerating it becomes an inertial frame where Newton's laws work. Now that due to train's acceleration, puck acquired some velocity backwards (if train moves forward) and now due to friction it comes to rest (w.r.t. train). As this is an inertial frame, puck will remain at rest (w.r.t. train) as there's no force acting on it we assume.
I was just not applying the rules correctly. Sorry, for bothering all of you here for my silly misreading.

 

[lightarrow]

Yeah that helps, basically if there's a friction and when the train stops accelerating it becomes an inertial frame where Newton's laws work. Now that due to train's acceleration, puck acquired some velocity backwards (if train moves forward) and now due to friction it comes to rest (w.r.t. train). As this is an inertial frame, puck will remain at rest (w.r.t. train) as there's no force acting on it we assume.

Forgive me for asking: my reply didn't address exactly the same?
Thanks.

lightarrow

 

[Mister T]

Now what happens to the puck now when the board reaches constant pace?
1. Will it too acquire that speed?

Only if there's friction between them.