Physics 131; Lab 3

Describing Random Motion (Weeks 5 and 6)

Introduction

So far in the laboratories, we have been exploring motion of objects along one particular direction. We were able to connect this motion to forces since, in the cases we analyzed, the net of forces applied to the objects did not change significantly from frame to frame. This allowed us to apply Newton’s laws and connect forces and motion. The objects we studied underwent what we call directed motion.

However, for small objects inside a fluid, the pushes and pulls from the surrounding fluid change very rapidly, changing magnitude and direction much faster than the fastest imaging frame rate. On average, when the object is pushed to the right in one frame it will be pushed to the left in another frame. So when looking at such small object with our camera we no longer see directed motion, we see random motion. Such random motion is experienced by all microscopic objects and is quintessential to life: Cells and the molecules, proteins, DNA and lipids within them are always in seemingly chaotic motion, so it is essential to understand and characterize this volatile behavior if we hope to make sense of the biological world.

Over the next six weeks, you will have the chance to explore random motion. During the first two weeks you will characterize some essential features of random motion generally, during the two weeks that follow you will explore the dependence of random motion on particular experimental parameters, and during the final two weeks you will investigate motion that is random and directed at the same time.

Investigation

Your overall task for the next two weeks is to characterize the random motion of 2-micron silica beads suspended in water. Since random motion is most easily measurable for microscopic systems, we will be exploring it by studying the motion of microscopic silica beads under a microscope. Since the motion looks different for each bead, it is crucial to measure the motion of many beads (say 30-50). It will be useful for you to measure averages over all beads, but also histograms to see the variability from bead to bead (just like you might be curious to know the average grade and histogram of grades in an exam).

1. To be sure you know how to use the microscope, and to get a sense for scale, start by taking a look at yeast under the microscope. The yeast cells are about 4 microns in diameter, so they are of similar size to the silica beads we will be investigating. Qualitatively describe the motion of yeast cells.

2. Measure the motion of 2 micron beads. Compare and contrast their motion to what you would expect for directed motion.

1. Are the x- and y- displacements of the silica beads, ∆x and ∆y, larger if you measure displacements with a time interval of 4 seconds than with an interval of 1 second? What if you measured displacements with a time interval of 8 seconds?

[HINT: If you have an 8 second video, you can measure changes in position in 1 second, 4 seconds, and 8 second time intervals from the same video. If you have many beads in the same video, you can measure motion of all of the beads.]

2. How does the root mean square displacement, r =(∆x)² + (∆y)² , change as a function of the measurement time interval ?

Equipment

Familiarize yourself with the Microscope Basics sheet before beginning any experimentation. If you do not know how a particular part of the microscope works, please ask a TA - the equipment is expensive! Please be especially careful handling liquid samples near the microscope objectives.

The CCD camera attached to the microscope will allow us to capture video of what we observe. Using the same VirtualDub software we utilized in previous weeks, we can capture AVI videos of the motion we are trying to analyze. In VirtualDub, the microscope camera can be found under ‘Device’ and is named “UCMOS03100KPA”.

The adjustment options for the microscope CCD camera are slightly less user friendly than the webcam options. However, they are still found in the same VirtualDub menus. The compression and output size options can still be found under ‘Video’ and ‘Capture Pin’. Be sure to take note of which resolution at which you record your videos; it will be important when determining the distance to pixel ratio. This can be done by taking a picture of the 1mm calibration slide at the same resolution and magnification level as your videos. If calibration slides are not available, pictures can be found on the lab computers.

Brightness, contrast, and other exposure settings can be found under ‘Video’ and ‘Capture Filter’. The most important difference from the webcam cameras is that the frame rate cannot be directly set before capturing videos. It is necessary to control the frame rate by controlling the exposure time of the CCD camera. By telling it to expose the CCD to light for 100 ms intervals, for instance, you are telling it to take a picture every 0.1 seconds. This also means that you have to carefully control the amount of light through your sample using the iris and bulb power control. If you are having trouble getting the light settings correct, you can use the Auto Exposure option, but this will often result in very low frame rates.

Dilute solutions of 2-micron silica beads suspended in water have been provided. ImageJ will allow you to track the motion of the beads as they move through the fluid on the microscope slide, and Excel will allow you to analyze this tracking data. The results should give an interesting perspective on random motion.