# Homework Help: How am I supposed to draw this diagram?

1. Nov 17, 2008

### InSpiRatioNy

1. The problem statement, all variables and given/known data
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???

2. Relevant equations
None, there won't be any

3. The attempt at a solution
I don't suppose it would be anything looking like a best fit curve, would it?

2. Nov 17, 2008

### tiny-tim

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!

3. Nov 17, 2008

### InSpiRatioNy

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??

4. Nov 17, 2008

### tiny-tim

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?

5. Nov 17, 2008

### InSpiRatioNy

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)

6. Nov 17, 2008

### tiny-tim

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.)​

7. Nov 17, 2008

### 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.

8. Nov 17, 2008

### tiny-tim

hehe …
told you! :tongue2:

9. Nov 17, 2008

### 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.

10. Nov 17, 2008

### tiny-tim

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

It'll all be clear in the morning.

11. Nov 17, 2008

### InSpiRatioNy

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

Last edited: Nov 17, 2008
12. Nov 17, 2008

### InSpiRatioNy

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

13. Nov 18, 2008

### tiny-tim

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.

14. Nov 18, 2008

### 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!!

15. Nov 18, 2008

### 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!

16. Nov 18, 2008

### 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.

17. Nov 18, 2008

### InSpiRatioNy

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

18. Nov 18, 2008

### InSpiRatioNy

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

19. Nov 19, 2008

### tiny-tim

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.

20. Nov 19, 2008

### InSpiRatioNy

okay thanks :)