Three thinking problems in college physics experiment. Urgent! ! !

Measurement of Young's modulus of elasticity by tensile method

Any object will deform under the action of external force. When the deformation does not exceed a certain limit, the deformation energy disappears after the external force is removed. This deformation is called elastic deformation. If the external force is large, when the action stops, the deformation caused by it does not completely disappear, but there is residual deformation, which is called plastic deformation. When elastic deformation occurs, the internal stress of the object returns to its original state. Elastic modulus is a physical quantity reflecting the relationship between material deformation and internal stress, and it is one of the commonly used parameters in engineering technology.

I. The purpose of the experiment

1. Learn to measure small changes in length by optical lever amplification.

2. Learn a method to measure Young's modulus of elasticity of metal wire.

3. Learn to process data by difference method.

Two. laboratory apparatus

Young's elastic modulus measuring instrument bracket, optical lever, weight, micrometer, steel tape measure, ruler, lamp source, etc.

Three. Experimental principle

In deformation, the simplest deformation is the elongation or shortening of a cylindrical object under the action of external force. Let the length of a cylindrical object be L, the cross-sectional area be S, the elongation (or shortening) under the action of external force F along the length direction be δ L, the vertical force F/S per unit cross-sectional area be called normal stress, and the relative elongation δ L/L of the object be called linear strain. The experimental results show that the normal stress is proportional to the straight line in the elastic range, that is,

(3- 1- 1)

This law is called Hooke's law. Where the proportional coefficient y is called Young's modulus of elasticity. In the international system of units, its unit is n/m2, and in the cm-g-s system, it is dyne /cm2. It is a fixed parameter to characterize the strain resistance of materials, which is completely determined by the properties of materials and has nothing to do with the geometric shape of materials.

This experiment is to measure the Young's modulus of elasticity of steel wire. The experimental method is to hang the steel wire on the bracket, fix the upper end, add a weight to the steel wire at the lower end, measure the elongation δ L corresponding to the steel wire to get Y, measure the length L of the steel wire with a steel tape, measure the cross-sectional area and diameter of the steel wire with a micrometer, and calculate the output F from the mass of the weight. In actual measurement, the value of steel wire elongation δ L is very small, about an order of magnitude. Therefore, the optical lever amplification method is used to measure δ L.

(a) (b)

1-mirror and lens; 2- Movable tray; 3- Fixed tray; 4 feet; 5— Light source

Figure 3- 1- 1 Optical Lever Device and Measuring Principle Diagram

Optical lever is a highly sensitive instrument designed according to the principle of geometric optics, which can measure tiny length or angle changes. As shown in Figure 3- 1- 1(a), the device consists of a rotatable plane mirror M fixed on a U-shaped frame.

Fig. 3- 1- 1(b) is an enlarged schematic diagram of the optical lever. Assuming that the normal of the mirror M is horizontal at first, the light emitted from the light source coincides with the normal of the mirror and is reflected by the mirror M to the scale n0. When the metal wire is extended by Δ l, the rear leg of the optical lever mirror frame descends by Δ l with the metal wire, which drives M to rotate by θ angle, and the mirror surface reaches M', and the normal also rotates by the same angle. According to the law of light reflectiOn, the included angle between light On0 and light on is 2θ.

If the distance from the mirror to the scale is d, and the distance from the rear sharp foot to the connecting line of the front two feet is b, there is

;

Because θ is very small, so;

Eliminate θ and get () (3- 1-2).

Because the elongation Δ l is a tiny length that is difficult to measure, when D is much larger than B, the conversion amount of the optical lever is larger, and 2D/b determines the magnification of the optical lever. This is the principle of optical amplification, which is applied in many precision measuring instruments. Such as: sensitive current, impact galvanometer, spectrometer, electrostatic voltmeter, etc.

Substituting (3- 1-2) into (3- 1- 1) gives:

(3- 1-3)

In this experiment, the force F of the elongated steel wire is the gravity mg of the weight acting on the steel wire, so the measurement formula of Young's modulus of elasticity is:

(3- 1-4)

Where Δ n corresponds to m, and if m is the mass of 1 weight, Δ n should be the cursor deviation caused by the increase (or decrease) of load 1 weight; If Δ n is the cursor deviation caused by the increase (or decrease) of four weights, m should be the mass of four weights.

Fig. 3- 1-2 schematic diagram of measuring device

Four. Experimental content

1. Instrument adjustment

(1) Install the instrument according to Figure 3- 1-2, and adjust the screws of the bracket base to make the base level (observe the level on the base).

(2) Adjust the reflector to make its mirror surface roughly perpendicular to the tray, and then adjust the height of the light source to make it equal to the mirror surface.

(3) Adjust the perpendicularity of the scale, and adjust the distance d between the light source lens and the scale and the mirror to make the lens image engraved on the scale clear. Then adjust the direction of the mirror and the height of the scale properly, so that the light is basically horizontal at the beginning of the measurement, and the imaging of the reticle is roughly in the middle of the scale. Write down that the reticle image falls on the ruler and the reading is n.

Note: at this time, the instrument has been adjusted, and it can't be adjusted again when measuring!

measure

(1) Add weights one by one, write down the corresponding scale reading of each weight, * * * 8 times, then remove the weights one by one, and record the corresponding reading' until it is measured.

When adding or subtracting weights, the movements should be light, so as to prevent the rear tip of the plane reflector from slightly vibrating and the readings from fluctuating greatly.

(2) Take the average reading of the scale under the same load, and calculate the average deviation δ n of the time scale when the steel wire load increases or decreases by four weights by differential method.

(3) Measure the length l of the steel wire between the upper chuck and the lower chuck and the distance d from the reflector to the scale with a steel tape measure.

(4) Put the three feet of the optical lever mirror frame on the paper, press it gently to get the accurate position of the three points, and then connect the front two toes on the paper, and the vertical distance from the rear toe to this connecting line is b..

(5) Measure the diameter d of the steel wire with a micrometer. Because the diameter of steel wire may be uneven, it should be measured in three parts according to the engineering requirements. Each position is measured once in mutually perpendicular directions.

Verb (abbreviation of verb) data processing

1. Measure the tiny elongation of steel wire and record the following table.

serial number

Weight quality

Meter (kg)

Optical label value ni (cm)

Cursor offset

Δ n = Ni+4-Ni (cm)

deviation

∣δ(δn)∣

When the load increases

Load shedding time

average value

three

four

five

six

seven

The amplification measurement result of tiny elongation of steel wire is δn =(+-)cm.

2. Steel wire diameter d0= mm measurement record

Measuring place

upside

middle

Lower part

average value

Measuring direction

longitudinal

shelving

longitudinal

crosswise

longitudinal

crosswise

Diameter (mm)

Uncertainty mm

Measurement result d = (+-) mm.

3. Single measurement of L, D and B values:

l =()m；

d =()m；

b=( )m

4. Bring the obtained quantity into the formula (3- 1-4), calculate the Young's modulus of elasticity of the metal wire, calculate the uncertainty according to the transfer formula, and express the measurement result as the standard formula (+-) n/m2.

Discussion of intransitive verbs on problems

1. Is the Young's modulus of two wires with the same material but different thickness and length the same?

2. What are the advantages of optical lever? How to improve the sensitivity of optical lever?

3. If the relative uncertainty of measurement in the experiment is not more than 5%, how to choose the length and diameter of steel wire? How far should the ruler be from the mirror of the optical lever?

4. Can you find Young's modulus of elasticity by graphic method? If the increased weight is taken as the horizontal axis and the corresponding change is taken as the vertical axis, what shape should the graph line be?

Attached table: Young's modulus of elasticity of common metals and alloys

Material name

Young's elastic modulus

(10 1 1 dyne/cm2)

Material name

Young's elastic modulus

(10 1 1 dyne/cm2)

aluminium (Al)

7.0

Cast copper (99.9%)

7.44

Cast iron (99.99%)