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6.2: Activities

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    • carts & track
    • laptop
    • Pasco sensor devices
    • cart linking accessories
    • weights
    • electronic weight scale

    The General Idea

    We have seen in the textbook that the impulse-momentum theorem is a repackaging of Newton's 2nd law:

    \[\vec F = m\vec a = m\frac{d\vec v}{dt} = \frac{d\left(m\vec v\right)}{dt} = \frac{d\vec p}{dt}\;\;\;\Rightarrow\;\;\; \int\limits_a^b\vec F dt = \vec p_b-\vec p_a\]

    We will use fancy sensing equipment to confirm this (as well as the 3rd law) by directly measuring all the physical quantities involved in different collisions.  Specifically, you will make these impulse/momentum and 3rd law tests for three separate scenarios, all of them involving a stationary target cart:

    • magnetic repulsion collision with carts of equal masses
    • magnetic repulsion collision with carts of unequal masses
    • link-up collision with carts of whatever masses you choose

    In addition to your analysis of impulse and momentum, you should also say a few words (backed-up with data!) about the conservation or non-conservation of kinetic energy in each case.

    Some Things to Think About

    The Pasco equipment and laptop can be finicky.  If you think it isn't working properly, don't waste time trying to debug it – call your TA over to assist you! Here are some things that should help, most of them related to proper use of the fancy equipment...

    • Here's how you get started with the equipment:
      • Turn on the Pasco Box (you need to do this before running the software in the laptop).
      • Go to the "Student" login in the laptop (there is no password), and open the 9A folder.  Open the file "dpdt."
      • Run the application when you are ready to record data.
      • Repeat as necessary – not every run gives especially "clean" data.
    • Be sure to "tare" (zero-out) the force sensors before every run.  You do this by pressing the button on the side of the force sensor.
    • Arrange the wires so that they introduce as little external force to the system as possible.
    • During the magnetic repulsion runs, do not push the incoming cart so hard that it contacts the other cart – the magnets should repel without an audible "clack."  This will not only produce the best results, but will also avoid breaking the magnets, which are quite brittle.  You will need to practice before taking data, to get just the right amount of initial push (you don't want them moving too slowly, either).
    • It is a good idea to set up your track so that the cart doesn't slow down or speed up when rolling on its own. There is going to be some effect due to friction in the wheels or from the wire, but you may be able to tilt the track ever so slightly to counteract this.  This "fudging" is fraught with pitfalls, however, and may not be practical. First, you need to do runs with the motion sensor to test this, and there is uncertainty involved in this process that may keep it from being worthwhile.  Second, a tilt that counters the friction of the wire of the incoming cart may be too great for the target cart to remain stationary before the collision. That is, the compensation may effectively work for only one of the two carts. And finally, this compensation only works in one direction.  If you have set up the masses so that the incoming cart bounces-back, then both the friction and the gravity component from the tilt will be in the same direction after the collision, which makes the error of measurement even worse!  It's up to you whether you just want to live with the errors introduced by friction for a level track, or venture into the perilous waters of "re-calibrating" the apparatus.
    • The software has some useful tools for extracting data after a run, but it is also a little idiosyncratic.  Here is what you need to know:
      • clipboard_ef731c098e51e0f8453f4d4f574b47caa.png is the highlight tool.  It provides a box for you to select a portion of a graph for future examination (see below).
      • clipboard_e101a1451384d85790542b318a7069df0.png  is the coordinate tool.  When you click on it, you can move the cursor over a point on the graph, and it will display its exact coordinates.
      • clipboard_e563d907e6ebe06f21ac79ac8c4603b6f.pngis the area-under-the-curve tool. The value of this tool in a lab involved with computing impulse should be obvious.  To use this, first use the highlight tool to drag a box around the part of a curve that you want to integrate, then click on this icon to compute the area under that segment of curve.
      • Important! You will have 4 graphs on your computer screen, and you will want to use these tools on each one, but the software has a maddening "feature."  The graph into which the tool appears is the last one that was selected.  This is as it should be, but the software selects the graph by mouse-over, rather than by clicking.  So if you want a tool to appear in the bottom graph, you need to make sure that was the last graph that your cursor was over before clicking the tool, which requires you to navigate the cursor around the other graphs on its way to clicking the tool.
    • This lab doesn't include data tables, so you need some way to display your raw data. You should do this by taking screen captures of the graphs generated (after manipulating/magnifying them so they are easy to read).  You can do this with command-shift-4, which gives you a cursor that you can drag into a box around the portion of the screen you wish to capture (the file will appear on the desktop).  Getting this file from the desktop to where you can add it to your lab report is up to you, but if you use a web login (such gmail or google drive), be sure to use a private window (Safari–>File–>New Private Window), so that your password is not stored.  You can also print it in the printer in that room, and scan/photo that hardcopy, though it does lose its pretty colors.
    • We will not be doing rigorous uncertainty analysis here (the uncertainties inherent to our black-box-measuring-apparatus are not immediately apparent), but some reckoning of how far off the results are from what you predict (oh, btw, you should be hypothesizing results in each case!) is expected.  As with most experiments we do, if you are off by more than 10%, you should probably assume you made an error somewhere.  Either you made an incorrect hypothesis, or something went wrong in your analysis of the data.

    Lab Report 

    Craft a lab report for these activities and analysis, making sure to include every contributing group member's name on the front page.  You are strongly encouraged to refer back to the Read Me as you do this, to make sure that you are not leaving out anything important.  You should also feel free to get feedback from your lab TA whenever you find that your group requires clarification or is at an impasse.

    Every member of the group must upload a separate digital copy of the report to their lab assignment in Canvas prior to leaving the lab classroom.  These reports are not to be written outside the lab setting.

    6.2: Activities is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Tom Weideman directly on the LibreTexts platform.

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