How Do Moving Frames Affect the Observation of a Puck's Path?

[Oblio]

I am standing (yes, the question actually goes like this!) on a level floor at the origin of an inertial frame S and kick a frictionless puck due north across the floor.

a.) Write down the x and y coordinates of the puck as functions of time as seen from my inertial frame. (use x and y axes pointing east and north respectively). now consider two more observers, the first at rest in a frame S' that travels with constant velocity v due east releative to S, the second at rest in a frame S'' that travels with constant acceleration due east relative to S. (all three frames coincide at the moment i kick the puck and S'' is at rest relative to S at that same moment.

b.) find the coordinates x',y' of the puck and describe the puck's path as seen from S'.

C.) do the same for S''.
Which of the frames is inertial?


Ok, well I know the puck is obviously not traveling east at all, so the x coordinate will stay at 0 from 'my reference frame'. I'm not sure where to start for a formula for the y-coordinate from his reference frame for a.)

For b.) Since S' is not accelerating, the puck will appear to just move west.

c.) S'' which is not inertial, will make S appear to move south west? How do i start finding the coordinates?

thanks!

 

[learningphysics]

For a, remember the puck is frictionless... no force acting on it horizontally... so no accleration...

b) careful... remember the puck is moving north in S's frame of reference.

c) how do you get south west?

One thing that the question doesn't state... the velocity of frame S'' with respect to frame S when the 3 frames coincide... that will affect the answer to part c). Did they give this velocity in the question? Are we to assume that the velocity of S'' is 0 when the 3 frames coincide?

The position of the puck seen by an observer is the position of the puck - position of the observer... (measuring all the coordinates in the S frame)

 

[Oblio]

How does this look for a.)?
x(t) = y + vt+ (F/2m)t^2

 

[Oblio]

and no velocity is given at all...
I'm not sure how to get ACTUAL coordinates without the values...

 

[learningphysics]

How does this look for a.)?
x(t) = y + vt+ (F/2m)t^2

I don't think they want you to consider the time spent hitting the puck which is negligible... I think they only care once the puck has left your foot...

You know x(t)=0... since it's only going north. Once the puck has left your foot... assume the puck has velocity vp... what is y(t)

Do they give information like the mass of the puck?

 

[Oblio]

no mass is given either..

So, its y-coordinate will just be vxt

 

[learningphysics]

no mass is given either..

So, its y-coordinate will just be vxt

Yeah, y(t) = vp*t (using a different variable from v, to not get it mixed up with the frame S' velocity v)

 

[Oblio]

introducing momentum?

 

[learningphysics]

introducing momentum?

no sorry... by vp I just meant velocity of the puck.

 

[Oblio]

ok ok i get it!

 

[Oblio]

do you think they want actual values for the coordinates?

 

[learningphysics]

do you think they want actual values for the coordinates?

No, I suspect they just want expressions.

 

[Oblio]

and the expression will need to express the sort of parabolic motion the puck will appear to make?

 

[learningphysics]

and the expression will need to express the sort of parabolic motion the puck will appear to make?

yes... get the x and y coordinates in terms of time... in the 3 frames...

then you can then express y in terms of x... that equation will give you the path... for example:

if x = t and y = t^2... you can substitute t from the first equation into the second... giving

y = x^2... that means that the object follows a parabolic path.

 

[learningphysics]

Find the coordinates of the two other observers... as seen by you.

Then the coordinates of the puck - coordinates of the observer... that's the coordinates that particular observer sees.

 

[Oblio]

maybe I'm missing something , but how do you get coordinates of frames; where all the info about such frames is that they are moving in a certain direction, either constant or accelerating?

 

[learningphysics]

maybe I'm missing something , but how do you get coordinates of frames; where all the info about such frames is that they are moving in a certain direction, either constant or accelerating?

Yeah, just use variables (they gave v as the velocity of S' relative to S)... for example the coordinates of frame S' relative to S are...

x(t) = v*t
y(t) = 0

For the coordinates of S'', just use a for acceleration... maybe v0 for initial velocity...

 

[Oblio]

just thinking about it in my head, from S', won't S appear to move both in the y and x
directions? instead of just x?

 

[learningphysics]

just thinking about it in my head, from S', won't S appear to move both in the y and x
directions? instead of just x?

why? S' is just moving east. so S will appear to move west... but the puck will appear to move in both directions...

 

[Oblio]

I was thinking the puck. My bad.

 

[Oblio]

how did you know that coor. of puck - coor. of observer = coor. of what is seen?

 

[learningphysics]

how did you know that coor. of puck - coor. of observer = coor. of what is seen?

what is the displacement vector from the second observer in S' to the puck? this is the same displacement vector in any frame... from the second observer to the puck...

ie: in any frame the displacement between two objects at a particular is the same (ignoring relativity)...

In the S' frame... the second observer takes himself as being at the origin... So coordinates of puck in S' frame - (0,0) = displacement vector... ie: coordinates of puck in S' frame = displacement vector...

 

[Oblio]

neither S` nor S`` have y coordinates though...

 

[Oblio]

and if the puck is vt and S`is vt, ... you get a coordinate of 0?

 

[learningphysics]

neither S` nor S`` have y coordinates though...

yeah, but remember at t = 0, all 3 observers are at the same place... so the observer in S' will have coordinates y = 0... the observer in S'' will have coordinates y = 0...

Think of the observer in S'... as the origin of frame S'... and the observer in S''... as the origin of frame S''.

 

[learningphysics]

and if the puck is vt and S`is vt, ... you get a coordinate of 0?

careful... they are different velocities... that's why I used vp instead... but also, the puck is moving in the y direction...

coordinates of puck as seen by the observer in S:

x(t) = 0
y(t) = vp*t

coordinates of the observer in S' as seen by the observer in S:
x(t) = v*t
y(t) = 0

coordinates of puck as seen by observer in S' (now I subtract)
x(t) = 0 - v*t = -v*t
y(t) = vp*t - 0 = vp*t

 

[Oblio]

i think i cna finish it, thanks again learningphysics!

 

[learningphysics]

i think i cna finish it, thanks again learningphysics!

no prob.