Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Accuracy of a meter stick

  1. Sep 12, 2009 #1

    Pengwuino

    User Avatar
    Gold Member

    I was grading my labs and in this lab, we used a meter stick and a wooden protractor. A group finally wrote in their write up that they believed the error was due to the inaccurate nature of the equipment. This begs the question, what sort of tolerances do you see in the manufacture a typical wooden meterstick and protractor that you'd find in a university physics department?
     
  2. jcsd
  3. Sep 12, 2009 #2

    russ_watters

    User Avatar

    Staff: Mentor

    Did they really mean the inaccuracy of the meter stick or the imprecision of humans being able to use it? I'd be surprised if most meter sticks had worse than a 1mm accuracy over their full length.

    How far off were their results? Have they compared their meter stick to any others to check the accuracy?
     
  4. Sep 12, 2009 #3

    Pengwuino

    User Avatar
    Gold Member

    They had decent results, they were simply finding the result of adding two vectors, A + B = C on the sidewalk and they were off about 5%. I'm more concerned with how they view equipment. It always stuck in my head when I was in the first or second year of my undergrad and I was in a lab and our professor asked what we could do to make more accurate measurements. Of course, what do we say? "Electronic equipment" (we were using ol fashion measuring stuff, i forget which though :). The professor then replied "How do you know electrical equipment is more accurate".

    They did mean the inaccuracy of the meter stick. I think they even mentioned twice about needing more accurate equipment for smaller errors. They also mentioned human error so I don't feel they're mixing up the two. I was hoping to find online some manufacturers tolerances but finding them isnt as easy as I thought. I wanted to mention it on this students report but I suppose demonstrating in the lab will be good enough to prove the point.
     
  5. Sep 12, 2009 #4

    nvn

    User Avatar
    Science Advisor
    Homework Helper

    Pengwuino: Commercial measuring devices tend to be very poor quality. So I would say the meter stick and protractor could easily have an accuracy error of +/-0.3 %. Or, for very poor quality, maybe up to +/-0.5 %.
     
  6. Sep 12, 2009 #5

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    To add to what Russ said: There is also a human error in interpretation. Suppose you made draw two solid circles on a sheet of paper separated by some known distance. You make copies of this, hand these out to your class, have them measure the distance between the circles, and compare the results. You will probably see a bimodal distribution because some students will assume you meant center to center while others will assume you mean the edge to edge. Some will round, some won't. There are lots of places that human error and human (mis)interpretation can slip in, even in a simple assessment such as this.
     
  7. Sep 12, 2009 #6

    FredGarvin

    User Avatar
    Science Advisor

    I remember from my undergrad physics labs that the rule of thumb we used was usually the uncertainty/inaccuracy was 50% of the smallest increment. That didn't include parallax error.
     
  8. Sep 12, 2009 #7

    Pengwuino

    User Avatar
    Gold Member

    Worse case scenario, that's 0.5% of the 5% error they recorded. Definitely not something that can be attributed to equipment error.

    None of this woudl be the case since there was no copying or possible way of misinterpreting the instructions (that wouldn't result in outrageous errors).
     
  9. Sep 12, 2009 #8

    Pengwuino

    User Avatar
    Gold Member

    This is where I always have to think abit about what's in question. 0.5mm is the precision in the measurement. However, the accuracy... how would we figure out the accuracy?
     
  10. Sep 12, 2009 #9

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    What were they measuring? Not just vectors, how were the things they were measuring drawn? You mentioned vectors on a sidewalk. How does that differ from measuring circles on a paper, conceptually? What they did measure versus what you wanted them to measure might well have been two different things.
     
  11. Sep 12, 2009 #10

    Pengwuino

    User Avatar
    Gold Member

    Using a piece of chalk and a meter stick, they went outside and drew a 1.413m vector North. Then, from that tip, they measured a vector due east at 0.468m or something. They used a metal L thingy, forget the name, that allowed them to draw the second vector perpendicular to it. They then used the meter stick to draw and measure the resultant vector. A 5% error meant a ~8cm error which is well above equipment error in my mind.
     
  12. Sep 12, 2009 #11

    nvn

    User Avatar
    Science Advisor
    Homework Helper

    Pengwuino: If I understand your reply in post 7, you are saying there is still a 4.5 % error unaccounted for. I think a significant amount of the remaining 4.5 % could be attributed to [strike]protractor[/strike] metal L square misalignment, and to the chalk equipment error. [strike][...] Protractor[/strike] L square misalignment, extrapolated over a large distance, would seem to be a major culprit, creating a significant percentage of the error in a linear distance measurement, I would think. This could be calculated.
     
    Last edited: Sep 13, 2009
  13. Sep 12, 2009 #12

    Pengwuino

    User Avatar
    Gold Member

    The protractor wasn't used to measure the length of the new vector. It's strictly an issue with the meter stick.
     
  14. Sep 13, 2009 #13

    Bystander

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Kids & chalk? That's arctan(1-2cm over the lengths of the legs of the square) error in the angle.
     
    Last edited: Sep 13, 2009
  15. Sep 13, 2009 #14

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    The metal L thingy,
    t_17480.jpg
    is an L square.

    I see several measurement and construction errors that are easily made. Add in some boneheaded student errors and an error of 5% looks quite possible.

    Some of the sources:
    1. Drawing a 1.413 meter long straight line using a stick that is only one meter long. They might well have mis-measured or put a bend in this line.
    2. Drawing a line normal to the first line. Get the angle wrong and you have a good sized error. Watch a do-it-yourself construction project on TV and you will get the idea of how big an error people can make in this regard.
    3. Drawing a 0.468 meter long line along that normal, starting from the first line. What if they started from the edge of the first line rather than the centerline? They used chalk after all.
    4. Measuring the resultant diagonal. Here is where the errors can really stack up.

    An 8 cm error does seem a bit out-of-whack however.
     
  16. Sep 13, 2009 #15
    I dont like the phrase human error, as it basically means 'I didnt follow the instructions' which is a blunder rather then an error.

    In this case, I dont think the blunder was their fault as it is pretty hard to draw a straight line 1.4m long with a 1 m ruler on the ground.

    Peng if you want to know why they got answers so far off the mark get htem to answer it. Ask them to justify why they put their answers with regards to error. This will let you know if they have the concept of magnitude of error, and where its coming from.

    Also dont let them use human error, make then brake it down, becuase its a cop out answer.
     
  17. Sep 13, 2009 #16
    i think you looking at it wrong, your thinking of the error in absolute terms. because you think 8cm is alot, dont forget that its all relative. think in relative terms as in the 5%. is that alot? in my opinion no. not considering that those kids are on their hands and knees taking measurements greater than the measuring device, not once but twice. the first being the first leg and the second being the resultant vector which is as you know is about 1.5m.
    what were the error percentages of the other labs?

    on a side note, why do they call it an L square. isnt more appropriate to call it a squared L? eh...
     
  18. Sep 13, 2009 #17

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    ... with a fat piece of chalk, to boot.
     
  19. Sep 13, 2009 #18

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Definition of government work:

    Measure it with a micrometer, mark it with chalk, cut it with an axe.


    As already mentioned measuring a chalk line on concrete will have to be done carefully and errors will add up. Did you do a formal error analysis of the complete computation?
     
  20. Sep 13, 2009 #19

    nvn

    User Avatar
    Science Advisor
    Homework Helper

    Pengwuino: Assuming each side of your metal L square is 200 mm in length, and assuming the chalk line width is tc = 5 mm, I got a maximum possible equipment accuracy error, in the resultant vector length, of +/-2.9 %. Of this value, 0.5 % is meter stick equipment accuracy error; the remaining 2.4 % is chalk equipment error. If we instead assume tc = 6 mm, it increases the maximum possible equipment accuracy error to +/-3.4 %, in the resultant vector length.

    If either side of your metal L square is longer than assumed above, it would decrease the chalk equipment error.
     
    Last edited: Sep 13, 2009
  21. Sep 13, 2009 #20

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    nvn, did you account for the fact that two of the length measurements involved lengths longer than the measuring device? This creates multiple sources of error.

    Have any of you done home repairs? Use the wrong equipment, and you are bound to get right angles that aren't right, straight lines that bend, measurements that are off. A meter stick, a piece of chalk, a L square are what I would classify as the wrong equipment.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Accuracy of a meter stick
  1. Accuracy of sensors (Replies: 6)

  2. Compounding Accuracies (Replies: 4)

Loading...