Device for measuring Young's elastic modulus of object by single slit diffraction method

Abstract

The utility model relates to the technical field of physics teaching aids, in particular to a device for measuring Young's elastic modulus of an object by a single slit diffraction method. The device comprises a base, a lower knife edge is arranged on the base, an upper knife edge which moves up and down relative to the lower knife edge is arranged above the lower knife edge, a light source is arranged on one side of the lower knife edge, and a moving measurement microscope is arranged on the other side of the lower knife edge. The upper ends of the upper knife edges are connected through metal wires, and the upper ends of the metal wires are connected with the fixing frame. A tray is arranged on the metal wire; the lower end of the clamping groove body is provided with a connecting column, and the connecting column is connected with the tray; the middle of the corresponding weight is provided with a circular hole in which the connecting column is inserted and sleeved, and the circular hole is provided with a notch for the connecting column to pass through. On the basis of a stretching method, the length change of the metal wire is enlarged through the distance change of diffraction fringes, the elongation of the metal wire under the action of tensile force can be accurately measured, the structure is reasonable, and the tiny elongation of the metal wire under the action of the tensile force is accurately measured.

Description

Technical Field

[0001] The utility model relates to the technical field of physical teaching aids, in particular to a device for measuring the Young's modulus of an object by the single-slit diffraction method. Background Technique

[0002] In the prior art, in the physics experiment teaching of colleges and universities, the stretching method is often used to measure the Young's modulus. The Young's modulus (abbreviation: Young's modulus) is one of the inherent properties of solid materials and is also one of the commonly used parameters in the field of engineering technology design. From the perspective of experimental teaching, the experiment of measuring the Young's modulus is one of the required experiments offered in the college physics experiment courses of most domestic universities. At present, the 4 major measurement principles for measuring the Young's modulus measurement experiment include the static stretching method, the dynamic resonance method, the beam bending method, and the ultrasonic measurement method, etc. Regarding the static stretching method, currently, most colleges and universities mainly use the optical lever method for experiments, but this method has problems such as insufficient combination with optical knowledge and low experimental accuracy. Since the deformation of metal materials is very small, the error in measuring the elongation of metal wires is the main reason affecting the accuracy of the Young's modulus.

[0003] The Chinese utility model patent document disclosed on March 23, 2016, a device named "a device for measuring the Young's modulus of a metal rod by a diffraction method", the method belongs to the beam bending method, and the measurement object is a metal rod. The beam bending method has deficiencies in three aspects: First, the principle is slightly complicated, and students need to understand the detailed process of the elastic modulus calculation formula, making the connection between the Young's modulus and the single-slit diffraction method not intuitive enough. Second, there is no adjustment device for the orientation of the lower knife edge under the device, which may cause the upper and lower knife edges not to be coplanar, reducing the diffraction pattern effect. Third, due to the inaccurate scale on the single-slit diffraction light screen, the measurement result accuracy is insufficient and the relative error is relatively large. Content of the Utility Model

[0004] The purpose of the utility model is to provide a device for measuring the Young's modulus of an object by the single-slit diffraction method, which can accurately measure the tiny change in the elongation of a metal wire, has a reasonable structure, and a remarkable experimental effect, aiming at the above deficiencies.

[0005] The technical solution of the utility model is: a device for measuring the Young's modulus of an object by the single-slit diffraction method, including a base, there is a lower knife edge on the base, there is an upper knife edge that moves up and down relative to the lower knife edge above the lower knife edge, there is a light source on one side of the lower knife edge, and a traveling microscope on the other side of the lower knife edge. It is characterized in that the upper end of the upper knife edge is connected by a metal wire, the upper end of the metal wire is connected to a fixed frame; a tray is carried on the metal wire; a card slot body is carried on the upper part of the metal wire, a connecting column is carried at the lower end of the card slot body, and the connecting column is connected to the tray; there is a round hole for inserting and sleeving the connecting column in the middle of the corresponding weight, and the round hole has a notch for the connecting column to pass through.

[0006] In the above solution, it also includes:

[0007] There is an azimuth adjustment device under the lower cutting edge described above.

[0008] The light source described above is a sodium lamp.

[0009] The advantages of the present utility model are as follows: 1. Based on the stretching method, this device uses the diffraction method of light to measure the elastic modulus of an object. By magnifying the change in the length of the metal wire through the change in the spacing of the diffraction fringes, the elongation of the metal wire under the action of tension can be accurately measured. This can not only improve the accuracy of experimental measurement, but also has a relatively low cost. Moreover, the random error of measurement can be reduced through multiple measurements under the same experimental conditions. It has very good laboratory demonstration scenarios and application scenarios, and realizes the accurate measurement of the tiny elongation of the metal wire under the action of tension. 2. Through the single-slit diffraction experiment, the understanding of the wave nature of light and the diffraction phenomenon is deepened. Using the single-slit diffraction device combined with the mechanical principle, the Young's modulus of the metal wire is measured, and the relationship between the elastic deformation and stress of the material is understood. 3. The principle is simple and more suitable for students to carry out college physics experiments. Students can establish an intuitive connection between the core measurement problem of the elastic modulus, that is, the change in elongation, and the change in the slit width of the single-slit diffraction knowledge, improving the comprehensiveness of the experiment. 4. An azimuth adjustable device is set on the platform where the lower cutting edge is located below. Through laser calibration, the upper and lower cutting edges can be accurately adjusted to be coplanar, improving the clarity of the single-slit diffraction experimental phenomenon and being conducive to improving the experimental measurement accuracy. 5. Adopting a slot body, connecting column and tray connection structure to prevent the metal wire from swinging and the weights from falling off. The structure is reasonable and conducive to the experiment. 6. Using a micrometer eyepiece for quantitative measurement, the process is conducive to exercising the students' hands-on ability. By accurately measuring the position of the dark fringes of the single-slit diffraction, the change in the slit width is obtained, and the result is accurate. The experimental phenomenon is obvious, the error is small, and the students' ability to comprehensively apply knowledge is exercised.

[0010] The following will further describe the embodiments of the present utility model in detail with reference to the accompanying drawings. Description of the Drawings

[0011] Figure 1 is a schematic diagram of the structure of the present utility model.

[0012] Figure 2 is a schematic diagram of the single-slit diffraction principle of the present utility model. Specific Embodiments

[0013] See Figure 1 , the names of the components are as follows: wire clip 1, metal wire 2, slot body 3, connecting column 4, weight 5, tray 6, laser calibration plate 7, upper cutting edge 8, lower cutting edge 9, laser tube 10, base 11, light source 12, traveling microscope 13.

[0014] See Figure 1, An apparatus for measuring Young's modulus of elasticity of an object by single-slit diffraction method, which includes a base 11 that can be adhered to a platform. There is a lower knife-edge 9 on the base 11. Above the lower knife-edge 9, there is an upper knife-edge 8 that can move up and down relative to the lower knife-edge 9. A slit with adjustable width is formed between the lower knife-edge 9 and the upper knife-edge 8. On the left side of the lower knife-edge 9, there is a light source 12, and the light source 12 is a sodium lamp. On the right side of the lower knife-edge 9, there is a traveling microscope 13 for observing the change of the single-slit diffraction pattern. The position height of the traveling microscope 13 is adjustable and it is a commercially available product, and the figure is omitted. The upper end of the upper knife-edge 8 is connected by a metal wire 2 (steel wire), and the upper end of the metal wire 2 is connected to a fixing frame, such as connected to a wire clip 1. The fixing frame can be a bracket, such as a gantry. There is an azimuth adjustment device under the lower knife-edge 9. A tray 6 for placing weights is carried on the metal wire 2. When the mass of the weights on the tray 6 is changed, the elongation of the metal wire changes, and the width of the slit between the upper and lower knife-edges changes. The upper part of the metal wire 2 is provided with a card slot body 3. The lower end of the card slot body 3 is provided with a connecting column 4, and the connecting column 4 is connected to the tray 6. The metal wire 2 passes up and down through the middle of the card slot body 3 to prevent the metal wire from swinging. There is a round hole in the middle of the corresponding weight 5 for inserting and sleeving the connecting column 4, and the round hole is provided with a notch for the connecting column 4 to pass through.

[0015] When the weight placed on the tray 6 changes, the elongation of the metal wire 2 changes, and the position of the upper knife-edge 8 changes accordingly, thereby changing the width of the slit formed by the upper and lower knife-edges. Using the principle of light diffraction, by measuring the change of the diffraction fringe spacing, the slit width is measured, and thus the elongation of the metal wire 2 is determined.

[0016] The card slot body 3 reduces the time required for the slit to return to rest each time a weight is installed by limiting the shaking frequency of the slit. The card slot body 3 is fixed on a bracket (such as the middle cross beam of a gantry, and the fixing points in the figure are omitted). The card slot body 3 can be a cylinder with the metal wire 2 passing through the middle. The cylinder is fixed on the middle cross beam of the gantry, and the metal wire 2 can move freely up and down in the middle of the cylinder, and the metal wire 2 is positioned by a chuck. The lower end of the card slot body 3 is the connecting column 4, and one or more weights 5 can be placed on the connecting column 4 on the tray 6.

[0017] The azimuth adjustment device is a base with adjusting screws on four sides. By screwing in or out the adjusting screws, the base of the lower knife-edge 9 placed on the base of the adjusting screws can be moved forward, backward, left, and right (the figure is omitted). The upper and lower knife-edges are made coplanar by aligning the laser tube 10 with the reference point on the laser calibration plate 7.

[0018] The light source 12 can be placed on a platform with an up-and-down telescopic frame (the figure is omitted), and the height of the light source 12 is adjusted to be equal to the height of the knife-edge slit.

[0019] The connecting column 4 in the middle of the tray 6 is thinner at the top and thicker at the bottom. There is a round hole at the center of the weight 5, and its size corresponds to the thick diameter of the connecting column 4. There is a notch from the round hole to the edge (the size corresponds to the diameter of the connecting column 4). During use, the notch of the weight 5 is placed from the thin part of the connecting column 4 and placed on the tray 6 along the connecting column 4 from top to bottom to prevent the weight 5 from falling off during the experiment.

[0020] Working principle: The main problem in measuring the Young's modulus of a metal wire is how to accurately measure the tiny length change of the metal wire 2. In this device, an upper knife edge 8 is fixed at the lower end of the metal wire 2, and at the same time, a lower knife edge 9 with adjustable orientation is fixed below. A sodium lamp is placed on the left side, and a traveling microscope 13 is placed on the right side of the knife edge. When a weight 5 is placed on the metal wire 2, causing the metal wire 2 to elongate by ΔL, at this time, the slit width of the upper and lower knife edges changes by Δb, then ΔL = Δb. During this process, the change in the spacing of the single-slit diffraction fringes can be seen in the micrometer eyepiece. Using the principle of single-slit diffraction, the change in the slit width can be measured by measuring the change in the position of the dark fringes, thereby obtaining the elongation ΔL of the metal wire, and achieving the accurate measurement of the tiny elongation (about a few hundredths of a millimeter) of the metal wire under the action of tension.

[0021] The average value of the Young's modulus measured by this device is 2.02×10 11 N / m 2 ; the relative error is 3.69%; the uncertainty is 4.6%.

[0022] The average value of the Young's modulus by the traditional single-slit diffraction method is 1.91×10 11 N / m 2 ; the relative error is 7.5%; the uncertainty is 4.1%.

[0023] The average value of the Young's modulus by the optical lever method is 1.864×10 11 N / m 2 ; the relative error is 11.23%; the uncertainty is 4.68%.

[0024] Experimental principle:

[0025] By combining Hooke's law and the principle of single-slit diffraction, the measurement of the Young's modulus of the metal wire is indirectly realized by measuring the spacing of the single-slit diffraction dark fringes.

[0026] Formula derivation:

[0027] According to Hooke's law, within the elastic limit, the stress and strain of an elastic body are proportional, then there is

[0028]

[0029] Among them, E is the Young's modulus, S is the cross-sectional area of the metal wire, d is the diameter of the metal wire, L is the original length of the metal wire, and F is the external force applied to the metal wire to cause an elongation of ΔL.

[0030] From equation (1), we get

[0031]

[0032] According to the principle of single-slit diffraction, as Figure 2 shown, parallel light passes through the slit and forms an image on the screen, and we can observe diffraction fringes on the screen.

[0033] Condition for a bright fringe at point P:

[0034]

[0035] Condition for a dark fringe at point P:

[0036] b sinθ = ±kλ (k = 1, 2, 3...) (4)

[0037] where b is the width of the single slit, θ is the diffraction angle, and λ is the wavelength of the incident light.

[0038] Let the distance between the k-th dark fringe and the center of the central bright fringe be X k , then

[0039] X K = f·tanθ (5)

[0040] where f is the focal length. When θ is very small,[[]]

[0041]

[0042] Then the distance X m+n between the m-th dark fringe on the left and the n-th dark fringe on the right of the central bright fringe is

[0043]

[0044] We get

[0045] As Figure 1 shown, the elongation ΔL of the metal wire is equal to the change in the slit width, i.e.:

[0046] ΔL = b0 - b (8)

[0047] Substitute (7) into equation (8) to get

[0048]

[0049] Substitute (9) into (2) to obtain the Young's modulus of the metal wire as:

[0050]

[0051] Experimental apparatus

[0052] The measuring microscope 13 is placed at the position 13 in the figure and observes to the left. The crosshairs in the eyepiece of the measuring microscope 13 are moved to record the positions of the dark lines at each level, so as to achieve the precise measurement of the length change ΔL of the metal wire.

[0053] Sodium lamp, with a wavelength of 589.3nm, produces a more obvious diffraction phenomenon when light passes through a slit, and is safer than laser.

[0054] Laser tube, emits laser to calibrate the slit.

[0055] Tape measure to measure the length of the wire.

[0056] Micrometer, to measure wire diameter.

[0057] By learning the basic length measurement methods, you will master the use of ruler, outside micrometer and micrometer eyepiece.

[0058] Experimental procedures

[0059] 1. Fix the metal wire 2 to Figure 1 Location.

[0060] 2. Turn on the light source 12 and preheat for 3-6 minutes. Turn on the laser calibration device and adjust the azimuth adjustment device to make the lower blade 9 and the upper blade 8 coplanar.

[0061] 3. Adjust the heights of the slit, the sodium lamp, and the moving microscope 13, adjust the eyepiece of the moving microscope 13 so that the eyes can see a clear crosshair image, focus the moving microscope 13, and observe a clear single-slit diffraction pattern.

[0062] 4. When the tray 6 is not loaded with weights 5, record the positions of the diffraction fringes at each level, then add 50g weights to the tray 6 one by one. Then subtract the added weights 5 one by one. Place the weights 5 on the tray 6, and after the upper blade 8 is stable, use the moving microscope 13 to measure the position of the single slit diffraction dark fringes. Increase the mass of the weights 5 and measure multiple sets of data.

[0063] 5. Measure the focal length of the measuring microscope 13, and record the readings in the measuring state (reading value) and when the micrometer eyepiece lens is retracted to the innermost position (correction value), f = 125mm + reading value + correction value.

[0064] 6. Use a tape measure to measure the length of the wire (measure 10 times) and record.

[0065] 7. Use a screw micrometer to measure the diameter of the wire (measure 10 times) and record.

[0066] 8. Use the difference method to process the data and calculate the value of E.

[0067] 9. Result analysis. Compare the measurement results with the recognized values.

[0068] The above description is only the specific implementation manner of the present utility model, and various illustrative examples do not constitute a limitation to the substantial content of the present utility model.

Claims

1. An apparatus for measuring the Young's modulus of an object by single-slit diffraction method, comprising a base (11), on which there is a lower knife-edge (9), above the lower knife-edge (9) there is an upper knife-edge (8) that moves up and down relative to the lower knife-edge (9), on one side of the lower knife-edge (9) there is a light source (12), and on the other side of the lower knife-edge (9) there is a traveling microscope (13), characterized in that The upper end of the upper cutting edge (8) is connected by a wire (2), and the upper end of the wire (2) is connected to a fixing frame; a tray (6) is provided on the wire (2); a card slot body (3) is provided on the upper part of the wire (2), a connecting column (4) is provided at the lower end of the card slot body (3), and the connecting column (4) is connected to the tray (6); a round hole for inserting and sleeving the connecting column (4) is provided in the middle of the corresponding weight (5), and the round hole is provided with a notch for the connecting column (4) to pass through.

2. The device for measuring Young's elastic modulus of an object by the single-slit diffraction method according to claim 1, characterized in that A position adjusting device is provided below the lower cutting edge (9).

3. The device for measuring the Young's modulus of elasticity of an object by the single-slit diffraction method according to claim 1 or 2, characterized in that The light source (12) is a sodium lamp.

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