How am I supposed to draw this diagram?

[InSpiRatioNy]

Homework Statement

I won't need to give the detail, i just want to know an example of a diagram like the one I need to draw:

Q: An experiment is performed to track an object under the influence of a constant force. At regular intervals the position of the object is measured. (The data is displayed in the table)

So first we had to plot the data in the graph and draw a best fit curve thought the data (It's a x(m) vs time(s)) plan... I've done that, the part I'm confused about now is What are "error bars"?? it said "Make sure to include the error bars.

And the 2nd part: To experimentally determine the acceleration of the object you need to re-plot the data in a different form. Determe what the plot should consist of (x vs ?) and create the new plot on the next page (We're given a 100% bank graph paper except for x(m) axis).

And how do determine new errors, or errors at all?

Homework Equations

None, there won't be any

The Attempt at a Solution

I don't suppose it would be anything looking like a best fit curve, would it?

 

[tiny-tim]

… the part I'm confused about now is What are "error bars"?? it said "Make sure to include the error bars.

Hi InSpiRatioNy!

For error bars, estimate the error of each measurement, and instead of a dot, draw a small vertical line connecting the measured value ± the error.

And the 2nd part: To experimentally determine the acceleration of the object you need to re-plot the data in a different form. Determe what the plot should consist of (x vs ?) and create the new plot on the next page (We're given a 100% bank graph paper except for x(m) axis).

You're going to plot something else along the "y" axis, so that the "best-fit" curve will be a "best-fit" line …

'cos that's easier to draw!

 

[InSpiRatioNy]

Hi InSpiRatioNy!

For error bars, estimate the error of each measurement, and instead of a dot, draw a small vertical line connecting the measured value ± the error.


You're going to plot something else along the "y" axis, so that the "best-fit" curve will be a "best-fit" line …

'cos that's easier to draw!

For the 1st part: hmm... They only gave me values e.g. (x(m) 0.528, 2.581, 4.161, etc. and t(s) 0.349, 0.751, 09.48, etc. and the last, which I haven't used: delta t(s) 0.051, 0.042,0.055, etc.) so do I still have to caculate anything or do I just draw a line from the point that the curve didn't cover to the best fit curve?

For the 2nd part: So do I use the same figures that I used for the best fit curve or something? is it going to be x(m) vs. delta t(s) this time??


Thanks for your help!

 

[tiny-tim]

For the 1st part: hmm... They only gave me values e.g. (x(m) 0.528, 2.581, 4.161, etc. and t(s) 0.349, 0.751, 09.48, etc. and the last, which I haven't used: delta t(s) 0.051, 0.042,0.055, etc.) so do I still have to caculate anything or do I just draw a line from the point that the curve didn't cover to the best fit curve?

Well, they specifically ask for error bars, so I suppose you'll have to guess an error … 1% or 5%, say …

For the 2nd part: So do I use the same figures that I used for the best fit curve or something? is it going to be x(m) vs. delta t(s) this time??

(what's ∆t(s)? )

No, you'll be using the square, or the square-root, or the log, or something like that, for at least one of the axes.

You're looking for a best-fit line for acceleration, so what do you think would give you a straight line?

 

[InSpiRatioNy]

Well, they specifically ask for error bars, so I suppose you'll have to guess an error … 1% or 5%, say …



(what's ∆t(s)? )

No, you'll be using the square, or the square-root, or the log, or something like that, for at least one of the axes.

You're looking for a best-fit line for acceleration, so what do you think would give you a straight line?

Okay, I get the first bit for sure now. I'm not really sure where does delta t (s) come in, but I got those figures.

Though there is another part of the question which I am confused about, the third part: "Determine and plot the error bars in your new plot (the one from part 2 of the question) Explain how you determine the new errors" How do you determine it? It sounds like it's not really up to guessing.

In case of confusion, the only details at beginning of the question is: "An experiment is performed to track an object under the influence of constant force. At regular intervals the position of the object is measured." Then they give a whole chart of values from s(m), t(s), and delta t(s)

 

[tiny-tim]

"Determine and plot the error bars in your new plot (the one from part 2 of the question) Explain how you determine the new errors"

If you change from x to x², the error doubles; if you change from x to √x, the error halves.

Generally, if you change from x to xⁿ:
(x + ∆x)ⁿ = xⁿ(1 + ∆x/x)ⁿ ~ xⁿ(1 + n∆x/x), when ∆x/x is small,
so the error (as a proportion of the measurement) is multiplied by n.

(I've looked at http://en.wikipedia.org/wiki/Error_bar, and it seems that maybe you are supposed to calculate an error of one standard deviation, which you should be able to get from the data given.)​

 

[InSpiRatioNy]

hm... I'll try to figure it out... This is racking my brains, I never learned anything related before! Oh and one more thing, I haven't noticed before it said "Make sure your new graph is large enough to actually determine the equation of the line" so hehe I guess it's a line.

 

[tiny-tim]

Oh and one more thing, I haven't noticed before it said "Make sure your new graph is large enough to actually determine the equation of the line" so hehe I guess it's a line.

hehe …

told you! ​

 

[InSpiRatioNy]

Oh btw, that reminds me, I've been so worried about the error thing, I haven't figure out x vs what for the second graph! Well, it's getting very late for me, and I can't think, so do you mind if I get at least another clue about that (sorry, I don't really remeber old stuff, and it's due so soon!).

Thanks.

 

[tiny-tim]

Oh btw, that reminds me, I've been so worried about the error thing, I haven't figure out x vs what for the second graph! Well, it's getting very late for me, and I can't think, so do you mind if I get at least another clue about that (sorry, I don't really remeber old stuff, and it's due so soon!).

Thanks.

If it's very late (which time-zone are you in?), then get some sleep! :zzz:

It'll all be clear in the morning. ​

 

[InSpiRatioNy]

*sniff* I hope it will.
I'm off now :)

 

[InSpiRatioNy]

Urgh... I still can't figure out what that is...

 

[tiny-tim]

Urgh... I still can't figure out what that is...

just got up :zzz: … yawn! …

for a graph that will give a straight-line for speed, plot x against t,

for a graph that will give a straight-line for acceleration, plot v against t.

 

[InSpiRatioNy]

Thanks, I figured it the other way around... it all makes sense, or why would we be give delta t(s) ? It's just I thought that they wouldn't ask a question that was dead obvious hehe Well, you confrimed my theory right! ;)

I'll just explain before it get confusing: for the things I'm studying (stuff about time dilation and others are an influence) delta t(s) is the velocity!
I was just so packed up yesterday that I didn't realize that the delta t is the velocity! It's was just obvious! But then again, things about graphing and time dilation keeps getting me confused, the worse of it: I forget the basics... >:(

Anyways, Thanks so much for your help! Yay! I'm almost done with this set of horribly complicated homeworks!

 

[InSpiRatioNy]

grrr... My trouble with this looonnngg question isn't over: I've determined all the errors, but there here comes the stupid part. What is the acceleration of this object? Show how you determine it, and THEN the experimental error for the acceleration?

I'm not so sure how to do it, I thought I might need the equation of my newly plotted graph, but then I realized that it would be useless. But I've got so many valuse of x(m) and delta t(s) I just don't know what formula or value should I use!

Well, that's the last bit of the question so once I get this done, I won't be bothering anyone about this anymore.

Thanks!

 

[tiny-tim]

Hi InSpiRatioNy!

The acceleration will be the slope (the tan of the angle) of the best-fit line in the v against t graph.

 

[InSpiRatioNy]

Okay! I'll try it after I get some good night sleep! Thanks!

 

[InSpiRatioNy]

I won't be wrong if I use simple algebra to get it instead right? Cause I don't have the angle...

 

[tiny-tim]

I won't be wrong if I use simple algebra to get it instead right? Cause I don't have the angle...

I'm not following you …

you have drawn a v against t graph, and a best-fit line on that graph …

all you do now is measure the angle that that line makes with the t-axis.

 

[InSpiRatioNy]

okay thanks :)