Rotating pendulum. Find absolute acceleration

[kulig15]

Homework Statement

I have to find current absolute acceleration in attached picture in points 1,2,3,4 and draw vectors.
The picture is rotating pendulum. The rest data show attached picture:

Homework Equations

aabs = arel + au + acor

acor=2*angular velocity X vrel

The Attempt at a Solution

This is my first attempt:

My teacher said that it is wrong attempt.

Regards
M.K.

 

[paisiello2]

Can you define all the terms you are using?

 

[BvU]

Hello Kulig and welcome to PF.

I can't be the only one puzzling about what is the situation here. Is this a top view, or a side view ? Does all the water have the same v ? How can that be ?

 

[haruspex]

I assume the water is in a loop of tubing, or if the plane of rotation is horizontal perhaps some annular trough. So it is free to flow around the loop, yes?
First, let's suppose it is not free to flow, so treat the water as a solid. Which direction would the accelerations be in then?

 

[kulig15]

Hello and Thanks for the reply.

This is a side view. You have to imagine the rotating pendulum with something like a pipe with water. This water has some v and i have to find current absolute acceleration of water in those four points of pipe.


Thanks in advance,
Kulig

 

[kulig15]

Hello guys!

This is my second attempt. Can somebody check it? And if it is wrong, can someone try do another one picture?

http://guzik24x7.twomini.com/281zjug.jpg



Thanks in advance,

Regards,
Kulig15

 

[haruspex]

The first thing you need to think about is how the water will move in the pipe. Fix on a small section of the water. How will that move around the axis? Remember, the water is not a solid. To answer this, I think you need to make an assumption about what the water was doing before the arm started to rotate. I would guess it was stationary. Hint: put some water in a cup, sprinkle something on top so that you can what's going on... a few tealeaves perhaps.. then rotate the cup. What does the water do?

 

[kulig15]

The water in pipe has some static V equals Vwater

 

[haruspex]

The water in pipe has some static V equals V_water

Oh, you're saying that the V_water in the diagram is the circulatory speed of the water relative to the pipe? That wasn't clear. (A curved arrow for it would have been clearer.)
In that case, the approach is to consider the two motions separately then add up the accelerations:
a. The motion of the water relative to the pipe.
b. The motion of the pipe about the axis.
Draw the acceleration vectors for each of those, for each of the four points.

Unsure how to interpret your second diagram. I see the central point of rotation, O. Are the two dashed circles the trajectories of points 1 and 3?
Gravity is not relevant - nothing is falling under gravity, is it? The system might as well be moving in a horizontal plane.
You show two accelerations of ω²r pointing away from O. In uniform circular motion, the acceleration is towards the centre of rotation.

 

[kulig15]

I try everything. I just read some books and it is what I think... I am tired of this pendulum. Coould you please draw these vectors? Because every my solution is wrong. I sent two times to my doctor and i have last one chance.


Thanks in advance,

Kulig15

 

[haruspex]

I try everything. I just read some books and it is what I think... I am tired of this pendulum. Coould you please draw these vectors? Because every my solution is wrong. I sent two times to my doctor and i have last one chance.


Thanks in advance,

Kulig15

The process on this forum is to give hints and nudges, not to provide solutions.
Let's start with something simple. Forget the water for moment. Consider the bit of pipe at point 1. Which way is that accelerating? What about the pipe at 2, 3 and 4?

 

[kulig15]

OK, I will try. I hope that we can do it until friday night. Could You give me some tips? For sure for point one has some centripetal acceleration connected with r? But could You tell me what Vrel?
And If I want get Acor i have to use my given data ω and Vrel again. Could you help me establish what is coriolis acceleration for these points?


Thanks in advance, I hope that i WIll do it until Saturday :<
Regards,
Mariusz

 

[kulig15]

I found some time today to make a little drawing (in paint :D).

So I guess i found vectors of centripetal acceleration water (in these 4 points) and whole pendulum.

I don't know how will look vector of relative acceleration for these 4 points and vector of Coriolis acceleration.

So i need to find:
*acor = 2ω X Vrel
*arelative
Can someone confirm my attempt?
http://guzik24x7.twomini.com/second_solution.png

 

[kulig15]

And this is proposition with coriolis acceleration.

Is it good?


http://guzik24x7.twomini.com/third_solution.png

 

[haruspex]

I found some time today to make a little drawing (in paint :D).

So I guess i found vectors of centripetal acceleration water (in these 4 points) and whole pendulum.

I don't know how will look vector of relative acceleration for these 4 points and vector of Coriolis acceleration.

So i need to find:
*acor = 2ω X Vrel
*arelative
Can someone confirm my attempt?
http://guzik24x7.twomini.com/second_solution.png

Yes, this is much better. The OP does ask for the net acceleration, though, which will be the resultant of the blue and orange vectors.
You have correctly shown all the orange vectors the same length, but as far as I can tell you've also made all the blue vectors the same length. They won't be.
Forget Coriolis - that's a 'fictitious' force which only arises when you use a non-inertial reference frame.

 

[kulig15]

Ok then. My teacher said that we have to use Coriolis Acceleration to establish absolute acceleration. What about relative acceleration for these four points? They are perpendicular to their relative velocity?

Thanks for help!
Regards,
Mariusz Kuligowski

 

[kulig15]

What is more i guess we use a non-inertial reference frame because water in pipe is moving relative to the whole pendulum (So there is Coriolis Acceleration). In sum for sure i need to use Coriolis acceleration (Even because lecture was connected with Coriolis Force). So the one that i need to find is Relative acceleration of water in these four points.


Thanks!

 

[haruspex]

What is more i guess we use a non-inertial reference frame because water in pipe is moving relative to the whole pendulum (So there is Coriolis Acceleration). In sum for sure i need to use Coriolis acceleration (Even because lecture was connected with Coriolis Force). So the one that i need to find is Relative acceleration of water in these four points.


Thanks!

There is only a Coriolis force if you choose a non-inertial reference frame. You never need to choose such a frame, so there is no case in which you have to consider a Coriolis force.
It may be that you were instructed to solve the problem in a non-inertial frame.
In the present case, I presume your non-inertial frame would be that of the pendulum? Even then, I'm not sure how you would apply Coriolis.
To be honest, I still harbour a suspicion that I don't have the correct interpretation of the apparatus. Why "pendulum"? That suggests rotation in a vertical plane, with gravity being relevant somehow. But if the water fills a sealed pipe in the plane of rotation I don't see how that's relevant. It might as well be horizontal, and gravity free.

 

[kulig15]

It is gravity and horizontal free. You have to imagine for example pendulum from old clock. You can call it whatever you want. This pendulum is moving like a hand of a cloack and and the end of it is something like a pipe with water with const velocity. I guess it is non-inertial system because there are 2 systems: in pipe and whole pendulum. Can you help me find relative acceleration (not centripetal) in these 4 points?