Tensile method to measure the elastic modulus of metal (2) Experimental principle It can be seen from equation (1) that as long as the F, S, L, and L quantities are measured, the Young's modulus of the object can be obtained. Where F can be directly written from the added weight; S can be calculated by measuring the diameter d of the wire with a spiral micrometer (micrometer); L can be measured by the meter ruler, only L is very small, and the general tool is not accurate. The experiment uses the optical lever to make an accurate indirect measurement of L.
The basic device for measuring the small elongation L of the optical lever is shown in Figure 2. The upper end of the wire L to be tested is fixed, and the lower end is clamped in the central slot of the small cylinder. The small cylinder is sleeved in a circular hole of a fixed small platform, and can be freely moved up and down, and a ring at the lower end can be hung. The weight is used to generate the force F. The front end of the optical lever stands on a fixed small platform, and the rear toe stands on the small cylinder. There is an observed scale and a reading telescope at the D distance in front of the optical lever.
It is assumed that the mirror of the small mirror M of the optical lever is vertical before the weight is added, and the image formed by the reflection of the scale N0 on the scale N0 can be seen from the horizontal wire in the telescope. After adding the weight, the wire is elongated by L, and the rear toe of the optical lever is also lowered by L with the small cylinder. At this time, the rear foot will drive the small mirror to rotate a small angle θ to M', so in the telescope The image formed by the scale of the scale Ni incident and reflected at the angle θ will be seen. The angle between the incoming ray and the reflected line is 2θ. According to the geometric relationship of Fig. 3, it can be obtained:
∵ Very small, the last two can be written as:
Can be obtained:
(5)
The above equation shows that if the value of D is much larger than , then n will be a multiple of L ("1), which is the magnification of the optical lever. (5) The right amount of each type can be directly measured by the general length measuring tool, which can be obtained by the difference in reading on the scale; D can be measured by the meter ruler; α is the light lever and the foot length is long, and the light lever can be removed and printed out three times. Toe, use the caliper to measure the distance from the toe to the midpoint of the first two feet. Therefore, L can be calculated by the formula (5), which is the principle of the optical lever L measurement.
Substituting equation (5) into equation (1), the final formula for obtaining Young's modulus E is:
E (6)
Experimental method (1) First set the level on a small platform, check and adjust the level of the small platform (should reach the horizontal indication in both directions orthogonal to each other), after reaching the level, remove the level.
(2) The lower end of the small cylinder is pre-mounted with a 2kg weight to straighten the wire, then adjust the height of the platform to make the upper surface of the small platform the same as the upper end of the small cylinder, and transcribe the length L of the wire (fixed end to The distance between the upper surfaces of the small cylinders).
(3) Stand the light lever on the small platform (the front foot is placed in the groove on the small platform, the rear foot is placed on the small cylinder), and the small mirror surface of the optical lever is adjusted to be vertical (it can be estimated).
(4) Adjusting the scale reading telescope:
Stand the distance reading mirror at about 1.10~1.30m in front of the light lever small mirror, adjust its height, make the telescope roughly equal to the light lever small mirror; use the ruler to read the telescope aiming line to the small mirror; use one eye first Close to the lens above the small mirror, you should see the image of the ruler in the mirror; if you can't see it, you can change the relative position of the telescope and the ruler, or move the ruler to read the telescope base, or adjust the optical lever mirror. Until the above phenomenon occurs.
Adjust the telescope in the above state, in two steps: 1 first adjust the telescope's eyepiece until you see the clearest crosshair, and rotate the telescope eyepiece tube to make the horizontal wire horizontal; 2 adjust the telescope's focusing handwheel (pass Turn the middle knob until you see the image of the ruler, and the scale image is on the same side as the crosshair, that is, when the eye moves up and down slightly, the horizontal wire and the scale image have no relative displacement (no parallax). After that, you can observe and record the scale reading n0 that the horizontal wire is aligned with.
(5) Add the weights seven times in sequence (1 kg each time), and record the scales n1, n2, ..., n7 appearing in the telescope successively. Then, subtract the weight seven times (1kg each time), and record the corresponding readings n7, n6, n5, n4, ..., n0, and find the average readings under the same tension, , ..., . The average reading is then divided into two groups, , , , , , , and , and the difference between the average readings for each additional 4 kg weight is calculated using the difference method. The calculation is: =[( - )+( - )+( - )+( - )]/4
(6) Use the ruler to read the telescope to measure the distance D from the front foot of the optical lever; the difference between the scale of the upper and lower forks of the telescope and the scale of the scale × 100 times is twice the value of D. Use a caliper to measure the length of the foot of the optical lever (as described in the last section of the optical lever measuring device); measure the diameter d of the wire with a spiral micrometer (should be five times at different positions, average).
(7) Record the length L of the wire, the tensile force F of the four weights, and D, a. Their uncertainty and L value are given by the laboratory. The Young's modulus E is calculated by the formula (6), the uncertainty of E is calculated, and E±UE is written. Http://news.chinawj.com.cn Submission:
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