High-Speed Video Analysis of Two-Dimensional Movement of Objects onto Fine Beads

Transcription

1 High-Speed Video Analysis of Two-Dimensional Movement of Objects onto Fine Beads Minoru SATO School of Science, Tokai University, Kitakaname, Hiratsuka, Kanagawa, , Japan. Fine spherical polystyrene beads, which are industrial materials of styrene form, or fine spherical glass beads, which are grind media for industrial process, are useful for frictionless demonstrations of dynamics and kinematics. The fine polystyrene beads (the average of the diameter is 280 µm and the standard deviation of the diameter is 56 µm) and the fine glass beads (the average of the diameter is 491 µm and the standard deviation of the diameter is 38 µm) function as ball bearings to reduce the friction between a moving object, e.g. glass Petri dish, and the surface of the board. The polystyrene beads onto the glass board or the glass beads onto the acrylic acid resin board are electrified by static electricity. Therefore, the beads adhere to the board and arrange themselves in the aperture-triangular-lattice-like pattern. The movement characteristic of a Petri dish that moves on the fine beads that adhere to the board is shown by video analysis using a USB camera and a digital high-speed camera (CASIO, EX-F1). The movement of the Petri dish on the fine beads onto the board is good linearity, but the friction of the beads is not too small. The high-speed video showed that only a small number of beads behind the bottom of the Petri dish supported the Petri dish. The number of the beads that supported the Petri dish that caused the friction is about INTRODUCTION Two-dimensional kinematics demonstrations are difficult to apply in practice by friction. In case of horizontal motion, many teaching materials are developed and some of them, such as the dry ice pack, the ball bearings and the air table 1), have come into general use in classrooms or laboratories. These conventional apparatuses, however, are not easy to demonstrate in the classroom for the material or the noise. Sawamoto et al. have developed the method of demonstrations using the fine polystyrene beads onto a glass board 2). These polystyrene beads function as ball bearings to reduce the friction between the moving objects (glass Petri dishes or metal disks) and the surface of the glass board. Therefore, the polystyrene beads are suited to demonstrate some two-dimensional kinematics from quietness and easy handling. In this paper, each of the movement characteristic of a glass Petri dish that moves on the fine polystyrene beads that adhere to the glass board and the movement characteristic of a glass Petri dish that moves on the fine glass beads that adhere to the acrylic acid resin board are shown by video analysis using a USB camera and a high-speed digital camera. MATERIALS AND METHODS The apparatus of frictionless twodimensional kinematics demonstration consisted of a moving object and a flat table. The table was assembled into the combination of fine spherical polystyrene beads and a flat glass board (Plastic Beads Table, PBT) or the combination of fine spherical glass beads and a flat acrylic acid resin board (Glass Beads Table, GBT). The moving object utilized for a glass Petri dish. The fine beads function as solid lubricant between the board and the Petri dish. The PBT, shown schematically in FIG- URE 1, consisted of a glass board (583mm 478mm, 5mm in thickness), fine solid spheri-

2 cal polystyrene beads (NaRiKa, D ), and a glass Petri dish (51mm outside diameter, 11mm thick, weight 16.4g). The glass board supports the fine polystyrene beads and the Petri dish. The fine polystyrene beads are originally made for industrial materials of styrene form. FIGURE 1. Schematic of the PBT setup (the scale is incorrect). The apparatus of two-dimensional kinematics demonstration with a low friction consists of a glass board (583mm 478mm, 5mm in thickness), fine solid spherical polystyrene beads (NaRiKa, D ), and a glass Petri dish (51mm outside diameter, 11mm thick, weight 16.4g). The fine polystyrene beads function as solid lubricant between the glass board and the Petri dish. The typical size of the fine polystyrene beads is 300µm. As shown in FIGURE 2, it had been understood that the shape of the fine polystyrene bead was almost sphere from the observation with the microscope. FIGURE 3 shows the frequency distribution of the diameter of the polystyrene beads. The range of the diameter of the beads was from 200 to 600 µm. The average of the diameter of the beads was 280 µm, and the standard deviation of the diameter was 56 µm (n = 48). It is noted that a few beads have the extremely larger diameter, about twice the average size. FIGURE 2. Micrograph of the fine solid polystyrene beads. Scale bar, 300µm. FIGURE 3. The relative frequency distribution of the diameter of the fine polystyrene beads. The average of the diameter of the beads is 280µm, and the standard deviation of the diameter is 56µm (n = 48). The GBT, shown schematically in FIG- URE 4, consisted of a flat acrylic acid resin board (583mm 478mm, 5mm in thickness), fine solid spherical glass beads (Potters- Ballotini Co.,Ltd (PBJ), GB190M), and a glass Petri dish (the above-mentioned). The flat acrylic acid resin board supports the fine glass beads and the Petri dish. The fine glass beads are originally made for grinding media of industrial process. FIGURE 4. Schematic of the GBT setup (the scale is incorrect). The apparatus of two-dimensional kinematics demonstration with a low friction consists of a flat acrylic acid resin board (583mm 478mm, 5mm in thickness), fine solid spherical glass beads (Potters- Ballotini Co.,Ltd (PBJ), GB190M), and a glass Petri dish (51mm outside diameter, 11mm thick, weight 16.4g). The fine glass beads function as solid lubricant between the flat acrylic acid resin board and the Petri dish. The typical size of the fine glass beads is 450µm. As shown in FIGURE 5, it t had been understood that the shape of the fine glass bead

3 was almost sphere from the observation with the microscope. FIGURE 6 shows the frequency distribution of the diameter of the glass beads. The range of the diameter of the beads was from 430 to 570 µm. The average of the diameter of the beads was 491 µm, and the standard deviation of the diameter was 38 µm (n = 51). In the case of the PBT, the polystyrene beads are negatively electrified, and the glass board is positively electrified. As a result, the polystyrene beads adhere onto the glass board, and arrange themselves at intervals in the triangular-lattice-like pattern (FIGURE 7, left). It is noted that the beads arrange themselves in the aperture-triangular-lattice-like pattern. In contrast, the polystyrene beads scattered on aluminum foil are not electrified. The beads stick mutually on the aluminum foil, but don't stick to the aluminum foil (FIGURE 7, right). FIGURE 5. Micrograph of the fine solid glass beads. Scale bar, 400µm. FIGURE 7. Close-up of the fine polystyrene beads scattered on the glass board (left), and on aluminum foil (right). Because the position of the triboelectric series is different, the polystyrene beads adhere onto the glass board, and arrange themselves in the aperture-triangular-lattice-like pattern. In contrast, the beads stick mutually on the aluminum foil, but don't stick to the aluminum foil. FIGURE 6. The relative frequency distribution of the diameter of the fine glass beads. The average of the diameter of the beads is 491µm, and the standard deviation of the diameter is 38µm (n = 51). The fine polystyrene beads scattered on the plate glass and the fine glass beads scattered on the plate flat acrylic acid resin are electrified. The electrified reason is a difference of the position of the triboelectric series of polystyrene or acrylic acid resin and glass. In the case of the GBT, the grass beads are positively electrified, and the acrylic acid resin board is negatively electrified. Consequentially, it becomes a similar situation to the PBT though the charges are opposite. In order to low frictional properties of the apparatus for two-dimensional kinematics demonstration, the PBT and the GBT were compared with an air table by video analysis. The air table (SHIMADZU RIKA CORPO- RATION, GTV-100) is an ordinary apparatus for two-dimensional kinematics demonstration. The air that blows off through the fine perforations with the top-board allows the object to glide relatively friction-free. Since the property of friction-free, the air table was used standard to evaluate low frictional prop-

4 erties of the apparatus. The top-board of the air table was the same size as that the board of the PBT and the GBT (583mm 478mm). There was a USB camera (Logicool, Qcam- Pro3000) to take movies of the movement of the object (The same Petri dish as the case of the beads was used) for video analysis in each apparatus. The image size of the camera was adjusted to capture SD video ( pixels), and the frame rate of the movie was adjusted to 5fps. The installation position of the camera was set up in the height that became 1mm/pixel on the center of the boards. In addition, a digital clock (unit of minimum measurement was 0.01s) was put on the position that entered the capturing image. The digital clock was used to measure the accurate interval time of frames. In addition, to know what movement the fine polystyrene beads did under the Petri dish high-speed videos were taken. The digital high-speed camera (CASIO, EX-F1) was put on the position in which the Petri dish passed the right under. The frame rate of the high-speed video was adjusted to 600fps. (FIGURE 7, left). The reason for that the linearity might become bad in a few cases was not known. FIGURE 8. Trajectories of the Petri dish as a moving object obtained from the result of the video analysis. The same Petri dish was used in all the cases. The number of trials was 35 respectively. a, In case of the air table. b, In case of the PBT. c, In case of the GBT. RESULTS AND DISCUSSION FIGURE 8 shows the trajectories of the Petri dish as a moving object obtained from the result of the video analysis. The trajectories of the Petri dish on the air table (FIG- URE 8, a), on the PBT (FIGURE 8, b), and on the GBT (FIGURE 8, c) contain 35 trials respectively. The same Petri dish was used in all the cases. The results of the fine beads were similar to the air table except a few cases. As the evident from FIGURE 8, the linearity of the movement was in good agreement with the fine beads to the same extent as the case of the air table. There are two reasons for the goodness of linearity of the movement with the fine beads. The first reason is that the shape of most of the beads is almost perfectly spherical (FIGURE 2 and FIGURE 5). And the second reason is that the beads arrange themselves at intervals FIGURE 9. Distribution of accelerations of the Petri dish as a moving object obtained from the result of the video analysis (same trials as FIGURE 8). The mean acceleration of the Petri dish for the air table (blue) was -20mm/s 2 (s.d. 10mm/s 2 ), for the PBT (orange) was -50mm/s 2 (s.d. 23mm/s 2 ), and for the GBT (red) was -143mm/s 2 (s.d. 73mm/s 2 ). FIGURE 9 shows the distribution of accelerations of the Petri dish as a moving object obtained from the result of the video analysis (calculation from the same data as the trajectories seen in FIGURE 8). The mean accel-

5 eration of the Petri dish for the air table was -20mm/s 2 (s.d. 10mm/s 2 ), for the PBT was -50mm/s 2 (s.d. 23mm/s 2 ) and for the GBT was -143mm/s 2 (s.d. 73mm/s 2 ). This had been shown that the friction of the GBT is not too small, but the PBT was similar to the air table. The reason for that the friction was not too small was the moment of inertia and the rolling resistance of the beads. This suggests that if the number of the beads supporting the Petri dish reduces, the resistance becomes small. FIGURE 10. Composite photograph of movement of the fine polystyrene beads under the moving glass Petri dish was taken by the digital high-speed camera (CASIO, EX-F1). This reversal image was made from ten consecutive frames of the 600fps high-speed video. The movement of the fine polystyrene beads under the moving glass Petri dish was taken by the digital high-speed camera (CASIO, EX-F1). The beads under the glass Petri dish were visible through the bottom of the Petri dish. FIGURE 10 shows one piece of photographs composed from the highspeed video. This composite photograph was made from ten consecutive frames of the 600fps high-speed images. Additionally, to make easily to see, this composite photograph reversed black and white. Therefore, the black point in the white background in the photograph corresponds to the bead, the gray circle corresponds to the rims of the Petri dish each frame, and the black line in the gray circles corresponds to the bead that moved under the Petri dish. As shown in FIGURE 10, this composite photograph indicates that only a small number of beads support the Petri dish (it shows in yellow lines in the photograph). The ratio of the number of supported beads to the total number of behind the Petri dish is 0.14 (the number of trials was 8). This is due to the fact that a few beads have the larger diameter in its distribution. The results may be summarized as follows: the movement of the Petri dish on the PBT / GBT was good linearity, the friction of the beads, however, was not too small. The number of the beads that supported the Petri dish that caused the friction was about 14%. This suggests that if the number of the beads supporting the Petri dish reduces, the resistance becomes small. More detailed work is necessary to examine whether to have related to the friction of the Petri dish on the PBT / GBT and the ratio of the number of supported beads to the total number of behind the Petri dish. If the friction is reduced, it is possible to use the fine polystyrene beads and the glass beads as an apparatus for twodimensional kinematics demonstration. However, in that case, it is necessary to deal with the health hazard and the environmental hazard. The experimenter will have to wear the goggle and the mask, and to take care not going out of the fine polystyrene beads to the environment. The safe demonstration method will have to be researched in the future. ACKNOWLEDGMENTS I would like to thank Prof. Takashi Yagi, Mr. Hiroshi Kiyuna and Ms. Yuka Takagi for the micrographs and Potters-Ballotini Co.,Ltd (PBJ) for a generous gift of the glass beads. REFERENCES 1) E. M. Rogers, Nuffield Physics Pupils' text years 1 and 2, Longman Group Ltd, London, ) S. Sawamoto, K. Hosotani, N. Idris, K. H. Kurniawan, Y. I. Lee, B. J. Ahn, K. Ishii, and K. Kagawa, J. of Sci. Edu. in Japan 32, (2008).