Loop-the-loop track, connection height with time?

[Arslan32]

So at school we had to make our own experiment, and we tried to make a loop-the-loop.
We let a marble go from some height.
But now we've got a problem.
We had a sensor on the top of the loop, to see how long it does to go to the top of the loop.
But it didn't make sense.
So I had to fake the results(the time)
I need to know what the connection is between the height and the time it'll arive at the top.

Edit:
This is our set-up:
http://imagizer.imageshack.us/v2/xq90/34/iqqk.jpg

We just simply put a light sensor at the top of the loop, if the marble goes through the top the light sensor will notice a drop in voltage. So we'll know at which time i'll reach the top. This is between 0,20 and 0,40 seconds.

But, the connection between the total distance (or speed) and the time doesn't make sense if we use our real results.
Could you explain to me what the connection is between the the total distance ( or speed) and time? Like lineair. That would be really great.

Homework Statement

Diamater of the loop-the-loop:29m
Height values are:
0,30
0,32
0,53
0,57
0,60
0,64
0,68
0,70
0,74
0,77
0,82
0,87

Homework Equations

What is the link between the height and the time it will arive at the top?

The Attempt at a Solution

I've tried to make a diagram, but it's weird.
I also tried to fake the results (the time), but with no avail.
I have to know what the connection is of the height and time it will arive at the top.
It gave me a real headache

Ty for your time, and sorry for my bad english.

 

[BvU]

Hello Arslan, and welcome to PF.

The fact that "it does not make sense" can be the consequence of all kinds of things:
Misunderstanding (wrong idea about "sense"), some error in the measurements, misinterpretation, whatever.
If great discoverers would have done what you plan to do now, we wouldn't have a big part of the scientific knowledge we have today.

The fact that it does not make sense can never be a reason to start faking things. That only wastes your time, time of others and utlimately your credibility and perhaps even your career. You might also miss out on a Nobel prize...

Under 1) Show your setup, show your measurements,
tell us what you already know (under 2.)
Tell us what you've done. No need to tell that "it's weird", "no avail", "I have to know". That is NOT showing us your attempt, it is only telling what you think of it. And we have no idea if you were right or not.

If we can help, we will help. Give us something to help you with.

All in good spirit.

Oh, and doesn't your school have a code of honour or something equivalent that you pledged to adhere to?

 

[CWatters]

How about showing us your original data so we can see if it "makes no sense"?

Diamater of the loop-the-loop:29m
Height values are:
0,30
0,32
0,53
0,57
0,60
0,64
0,68
0,70
0,74
0,77
0,82
0,87

If the diameter is 29cm how can you have a height of >29cm?

You haven't provided the speed at which the ball enters the loop so it's not possible to answer your question. I think you also need to know the mass of the ball.

 

[Arslan32]

Thanks for your answers. I really appreciate it.

Hello Arslan, and welcome to PF.

The fact that "it does not make sense" can be the consequence of all kinds of things:
Misunderstanding (wrong idea about "sense"), some error in the measurements, misinterpretation, whatever.
If great discoverers would have done what you plan to do now, we wouldn't have a big part of the scientific knowledge we have today.

The fact that it does not make sense can never be a reason to start faking things. That only wastes your time, time of others and utlimately your credibility and perhaps even your career. You might also miss out on a Nobel prize...

Under 1) Show your setup, show your measurements,
tell us what you already know (under 2.)
Tell us what you've done. No need to tell that "it's weird", "no avail", "I have to know". That is NOT showing us your attempt, it is only telling what you think of it. And we have no idea if you were right or not.

If we can help, we will help. Give us something to help you with.

All in good spirit.

Oh, and doesn't your school have a code of honour or something equivalent that you pledged to adhere to?

Well it's for school, and we want a good mark. The results didn't came out as we expected. It just randomply popped from 0,20 seconds to 0,28 seconds to 0,24 seconds if we let the marble go through the loop at a higher height.

This is our set-up:
http://imagizer.imageshack.us/v2/xq90/34/iqqk.jpg We just simply put a light sensor at the top of the loop, if the marble goes through the top the light sensor will notice a drop in voltage. So we'll know at which time i'll reach the top. This is between 0,20 and 0,40 seconds.

But, the connection between the total distance (or speed) and the time doesn't make sense if we use our real results.
Could you explain to me what the connection is between the the total distance ( or speed) and time? Like lineair. That would be really great.

How about showing us your original data so we can see if it "makes no sense"?If the diameter is 29cm how can you have a height of >29cm?

You haven't provided the speed at which the ball enters the loop so it's not possible to answer your question. I think you also need to know the mass of the ball.

Yeah, if the height is <29 cm, it doesn't reach the top of the loop.
We just had that in our report just to show that the equation h=2.5r is right.
The balls has no speed in the beginning, so EK=0.
We simply hold the marble at, let's say, 80 cm. Then we let it go, to see in how much seconds it reaches the top of the loop.
At 0,80 cm, the time it reached the top was 0,39 seconds.
At 0,70 cm, the time it reached the top was 0,32 seconds.
But at 0,75 cm, the time it reached the top was 0,35 seconds.
See, what I'm trying to say? This doesn't make sense.

 

[BvU]

Beautiful experiment. Good opportunity to learn a lot of useful things. Not just physics, either. (And your english is very good!)

So by now we have a list of 12 Heights in the first post plus three combinations height-time in post #4. Funny that 0.75 m and 0.8 m were not in the original list. Is there an explanation for that ?

height   Δt
0.3	    ?
0.32	
0.53	
0.57	
0.6	
0.64	
0.68	
0.7	  0.32
0.74	
0.77	
0.82	
0.87	   ?
plus (?)
0.75      0.35
0.8       0.39

Then: the times in the second column are in fact time differences. We understand your sensor to stop the timing is at the top of the loop. Where is the sensor that starts it ?

And: In your original post you do not give any relevant equations. No idea at all? Because further on you mention kinetic energy and there is a h=2.5r that appears suddenly (out of the blue?).

Grade 10 (I am on a different continent) means you have already learned about acceleration, but not about rotation yet ?

 

[Arslan32]

Beautiful experiment. Good opportunity to learn a lot of useful things. Not just physics, either. (And your english is very good!)

So by now we have a list of 12 Heights in the first post plus three combinations height-time in post #4. Funny that 0.75 m and 0.8 m were not in the original list. Is there an explanation for that ?

height   Δt
0.3	    ?
0.32	
0.53	
0.57	
0.6	
0.64	
0.68	
0.7	  0.32
0.74	
0.77	
0.82	
0.87	   ?
plus (?)
0.75      0.35
0.8       0.39

Then: the times in the second column are in fact time differences. We understand your sensor to stop the timing is at the top of the loop. Where is the sensor that starts it ?

And: In your original post you do not give any relevant equations. No idea at all? Because further on you mention kinetic energy and there is a h=2.5r that appears suddenly (out of the blue?).

Grade 10 (I am on a different continent) means you have already learned about acceleration, but not about rotation yet ?

Haha, thanks for your reply man.
We already have given our report digitaly, but I said in my report that our results aren't correct.
I said that we tried a lot, but it simply didn't make sense.
We had to come up, and make our own first experiment. We didn't find this on the internet or anywhere else.
This is a pretty hard subject.
So I guess he wouldn't mind.

Still, I find this interesting.

I made this painting with paint
http://imagizer.imageshack.us/v2/xq90/541/kp56.jpg

Licht sensor, means (you probably guessed it right) light sensor.
That's where our light sensor was.
And knikker means marble (in dutch).
The angle of the loop-the-loop was 20 degrees.

The light sensor was attached to a computer. So when we dropped the marble, we simaltaneuly pressed enter on the computer so it would start counting.
When the marble past the light sensor it gave a drop in voltage, as you can see on the following picture:
http://imagizer.imageshack.us/v2/xq90/855/cbh1.png

So we can see in how much seconds it made it to the top of the loop-the-loop

I also understand every equation regarding this subject.
Like Vminimum in the top is the square of ( g x r ).

Still, I couldn't figure out what the connection was between the height (or speed) and time :(

I simply calculated the speed with this: v = s/t.
I calculated the distance with this:
http://imagizer.imageshack.us/v2/xq90/69/xedj.png

I just added those 2 together, so I got the total distance the marble made to the top.
s, total = h/cos 20 + 0,5 * pi * d.

I uploaded my faked results special for you (attachments)

Btw, You don't have to answer my question. I know it's very long and it can give you a head ache.
I'll understand that.

 

[BvU]

Well, well, partner in crime...
Nice stuff they have in the Netherlands. Turns out we are on the same continent anyway. I should have seen that from the 220 V sockets in the picture and the "doos2" under the plant! So grade 10 means class 2 ? (not the same as second class in english )

One long post deserves at least some reply, so here goes:

By now I am inclined to think that the "doesn't make sense" is mainly due to the time measurement. Hitting Enter on the keyboard of an ordinary PC has to be processed, which takes some time. It is not a good way to start a stopwatch that has to measure such short times.

As an experimenter, I would say: experiment has to be repeated with more "lichtsensoren"
(the outcome of research is very often that "more research has to be done, with more resources of course )

Concerning the theory: I'm not all that reassured by your

I also understand every equation regarding this subject.
Like Vminimum in the top is the square of ( g x r ).

especially the last bit.

You will get quite a bit of "les" in motion under a constant force later on, but a small sample in advance can't hurt:

gravity pulls down the marble with a force mg. If the incline would be straight and under 20^o the force along the slope would be mg * sin(20^o).
Isaac Newton has a very important relationship named after him (for good reason), that Force = mass times acceleration. So the acceleration along the slope is g * sin(20^o) and it is constant as long as the marble is on the slope. That causes the speed to increase continuously with g * sin(20^o) m/s per second. For a constant speed v, you have s = v t (if you start at 0 at t=0).
For a constant acceleration a you have v = a t. And (you know or will learn) s = s₀ + v₀ t + 1/2 a t². Let s₀ =0 (start of length of path measurement) and v₀=0 (lies still when t=0).

The length of the slope is h / sin(20^o).
The acceleration is g * sin(20^o) so this formula gives
h / sin(20^o) = 1/2 g * sin²(20^o) t² that you can rework to get t² = (2h)/(g sin²(20^o) )
Fill in h = 0.8 m, g = 9.81 m/s² and for t you get 1.2 seconds.

That is just an estimate:

• The marble doesn't just move (slide) it also needs to get rolling. That slows it down a bit
• Your slope is not straight

In 1.2 seconds, with an acceleration of g sin(20^o) the speed is already 4 m/s.

Bottom of the ramp, no more acceleration.
Now we come to your loop-the-loop with, say 4 m/s. Half a turn is another 0.45 m, so 0.11 seconds -- if the speed wouldn 't be reduced considerably because gravity is holding it back again.

Another equation regarding this subject is mg Δh = m/2 Δ(v²) so to go 0.29 m higher up the Δ(v²) = 2.8, leaving a v of 3.2 m/s at the highest point .

To loop the loop a downward force at the highest point of m v²/r is needed (circular motion constant (oops) speed). So the 3.2 m/s makes that much more than mg and the marble won 't fall.

Far too much to read, let alone digest. Any further urgent questions ? If not, then: "veel succes".

 

[Arslan32]

Well, well, partner in crime...
Nice stuff they have in the Netherlands. Turns out we are on the same continent anyway. I should have seen that from the 220 V sockets in the picture and the "doos2" under the plant! So grade 10 means class 2 ? (not the same as second class in english )

One long post deserves at least some reply, so here goes:

By now I am inclined to think that the "doesn't make sense" is mainly due to the time measurement. Hitting Enter on the keyboard of an ordinary PC has to be processed, which takes some time. It is not a good way to start a stopwatch that has to measure such short times.

As an experimenter, I would say: experiment has to be repeated with more "lichtsensoren"
(the outcome of research is very often that "more research has to be done, with more resources of course )

Concerning the theory: I'm not all that reassured by your especially the last bit.

You will get quite a bit of "les" in motion under a constant force later on, but a small sample in advance can't hurt:

gravity pulls down the marble with a force mg. If the incline would be straight and under 20^o the force along the slope would be mg * sin(20^o).
Isaac Newton has a very important relationship named after him (for good reason), that Force = mass times acceleration. So the acceleration along the slope is g * sin(20^o) and it is constant as long as the marble is on the slope. That causes the speed to increase continuously with g * sin(20^o) m/s per second. For a constant speed v, you have s = v t (if you start at 0 at t=0).
For a constant acceleration a you have v = a t. And (you know or will learn) s = s₀ + v₀ t + 1/2 a t². Let s₀ =0 (start of length of path measurement) and v₀=0 (lies still when t=0).

The length of the slope is h / sin(20^o).
The acceleration is g * sin(20^o) so this formula gives
h / sin(20^o) = 1/2 g * sin²(20^o) t² that you can rework to get t² = (2h)/(g sin²(20^o) )
Fill in h = 0.8 m, g = 9.81 m/s² and for t you get 1.2 seconds.

That is just an estimate:

• The marble doesn't just move (slide) it also needs to get rolling. That slows it down a bit
• Your slope is not straight

In 1.2 seconds, with an acceleration of g sin(20^o) the speed is already 4 m/s.

Bottom of the ramp, no more acceleration.
Now we come to your loop-the-loop with, say 4 m/s. Half a turn is another 0.45 m, so 0.11 seconds -- if the speed wouldn 't be reduced considerably because gravity is holding it back again.

Another equation regarding this subject is mg Δh = m/2 Δ(v²) so to go 0.29 m higher up the Δ(v²) = 2.8, leaving a v of 3.2 m/s at the highest point .

To loop the loop a downward force at the highest point of m v²/r is needed (circular motion constant (oops) speed). So the 3.2 m/s makes that much more than mg and the marble won 't fall.

Far too much to read, let alone digest. Any further urgent questions ? If not, then: "veel succes".

Thanks for your very long post, with very much usefull information.

It gave me a head ache though:p
Where are you from?

Yeah well, due our goverments budget cut on education our school can't afford expensive recources:P
I'm now in the 6th class (Atheneum), and I hope to go to a university next year.

Physics is pretty hard.

Doos 2 means Box 2 btw :p

But OT:
Are you sure those are the formulas we've to use to calculate the theoratical speed?
That's a very good explanation man.
Thanks :D
I understand it ;)

 

[BvU]

Aspirin helps agains headaches.
Class 6 means you're in your final year, so I wish you good luck with your exams !
And remember: "eerlijk duurt het langst"...
I still think your 0.2 to 0.4 seconds is rather too short for the time to get from letting go to the top of the loop, but it's up to you to check that someway or other.

Must confess I'm quite curious to find out how this all is being looked upon by teacher, so I would be much obliged if you could post the outcome (with, perhaps, the right answers) later on...

Good luck again !