Abstract

The traditional teaching method for university physics experiments mainly involves the instructor explaining the principles, operational methods, and precautions in the laboratory, after which students operate the experimental instruments according to the instructor’s explanations, record experimental data, analyze the data, and finally write experimental reports^[1]. This teaching model ensures the standardization of student operations and the success of experiments, but it greatly reduces students’ autonomy in exploration, leading to a tedious and uninteresting experimental process, which is detrimental to cultivating students’ interest in exploratory research. Moreover, under this step-by-step “hands-on” teaching method based on lecture notes, the knowledge absorbed by students in class is limited, and they passively receive knowledge; students who study diligently may gain something, while those who do not prepare will acquire very little knowledge and skills. The result is that many students may still have a superficial understanding of the entire experimental process after the experiment is completed and have not thoroughly learned the knowledge points.

Arduino is a set of tools that can sense and control the physical world. It is based on open-source development boards and expansion boards, has its own specialized development environment, and is equipped with a large number of sensors that can detect various physical quantities and other electronic components for various purposes. In addition, Arduino is also characterized by its low cost and ease of use, making it very suitable for experimental exploration and research. Students can use Arduino and various electronic components to improve experiments^[2].

The measurement of Young’s modulus is a very important experiment in university physics experiments^[3]. Among them, measuring the small deformation of the sample is the focus of this experiment. Young’s modulus is an important physical quantity of materials used to describe the elastic properties of materials. It measures the ability of materials to resist deformation and is commonly used in the study of the mechanical properties of materials and engineering design. In the Young’s modulus measurement experiment, a long and thin material sample is suspended on a fixed support, with a weight hanging from it. By applying a force perpendicular to the sample, the sample bends. By measuring the elongation of the suspension line and the sample’s dimensions and geometric parameters, Young’s modulus can be calculated. This experiment helps students understand the elastic properties of materials, explore the mechanical behavior of materials, and provides important references for engineering design and material selection.

Currently, methods for measuring Young’s modulus in university physics experiments typically include static tensile methods^[4], dynamic resonance methods^[5], beam bending methods^[6], and interference fringe methods^[7]. Among them, static tensile methods can be further divided into optical measurement and electrical measurement. Dynamic resonance methods can be divided into ordinary resonance methods, load dynamic methods, and laser double grating methods. Beam bending methods can be divided into laser optical lever amplification measurement, single-slit diffraction methods, Hall sensor measurement methods, and fiber Bragg sensor methods^[8,9]. However, the experimental instruments for these methods are structurally complex, making it difficult for students to thoroughly understand their principles during experiments, and the process can be tedious and uninteresting, which may lead to a lack of exploratory interest among students.

To address this situation, this paper designs a metal Young’s modulus measurement experiment based on Arduino, aiming to enhance student interest, help students master various knowledge and skills in the experiment, and transform “passive” into “active,” allowing students to actively and consciously acquire knowledge through continuous exploration.

1 Experimental Principle

As shown in Figure 1, consider a uniform rectangular metal rod with a thickness of d and a width of a, freely placed on a pair of parallel knife edges, with a spacing of L, and a weight of m is suspended in the middle. Within the elastic limit, neglecting the weight of the metal rod itself, if the weight descends by Δz, when Δz is much smaller than L, the Young’s modulus E of the metal rod satisfies^[3]

Where Δz is a small quantity that is difficult to measure accurately, therefore, it is generally amplified using an optical lever for measurement.

Figure 2 shows the principle diagram of the optical lever. A laser beam is emitted from the laser source, reflected by a plane mirror, and incident on the photosensitive resistor. Let the optical lever constant be b, the horizontal distance from the photosensitive resistor to the plane mirror be B, and the vertical distance from the light source to the position where the photosensitive resistor receives the reflected light signal be ΔH. When the tested metal wire is stressed, the angle of deflection of the plane mirror is θ, then we have

Substituting equation (5) into equation (2) gives

Let the initial height of the light source be H₀, and the height detected by the photosensitive resistor of the reflected light signal is H. Then ΔH=H–H₀, substituting into equation (6) gives

From equation (7) we can derive

In equation (8), H₀ cannot be measured accurately, but can be solved using the following method. Suppose there are two sets of data: the effective length of the brass rod with a mass of m_i corresponding to the height detected by the photosensitive resistor H_i, and the mass m_i+1 corresponding to the height H_i+1, substituting into equation (8) gives

Equation (10) minus equation (9) gives

Where ΔH_i=H_i+1–H_i, Δm_i=m_i–m₁.

From equation (11) it can be seen that a specific mass m₁ can be selected as the initial mass, and the corresponding height of the light signal detected by the photosensitive resistor is the initial height H₁. Then measure a series of masses m_i corresponding to the heights H_i. Then obtain a series of mass differences Δm_i=m_i–m₁ corresponding to the height differences ΔH_i=H_i+1–H₁, and perform linear fitting on the obtained data to find the slope of the fitting equation, thereby obtaining the Young’s modulus E of brass. This method not only reduces the errors caused by the movement of the photosensitive resistor but also resolves the measurement problem of the initial height H₀ .

2 Experimental Hardware Design

2.1 Main Control Circuit

The main hardware of Arduino development includes development boards and expansion boards (development boards that can achieve special functions). Commonly used development boards include Arduino Uno, Arduino Nano, Arduino Mega 2560, etc. Among them, the Nano development board is the smallest; the Mega development board is the largest and most powerful; while the Uno development board is intermediate and is the most commonly used by developers during the development process. Compared to the Nano development board, the Uno development board has more complete functions. Compared to the Mega development board, the Uno development board is more affordable while its functions are sufficient for most programming applications. Therefore, this paper chooses the Uno development board for experimental design.

2.2 Photosensitive Resistor Module

This experiment uses a four-pin photosensitive resistor module, which has four ports: VCC, GND, DO, and AO. Before the experiment starts, connect the VCC port to the Arduino Uno 3.3V pin; connect the GND port to the Arduino GND pin; connect the DO port to the Arduino digital pin 5; and connect the AO port to the Arduino analog pin A0 (see Figure 3).

Write code to test whether the module is functioning properly, as shown below:

int DO=5;

int AO=A0;

void setup() {

pinMode( DO,INPUT ); //Configure digital pin 5 as input mode

pinMode( AO,INPUT ); //Configure analog pin A0 as input mode

Serial.begin( 9600 );

}

void loop() {

Serial.println( digitalRead( DO )); //Output the value of digital pin 5,

the output value is 0 or 1

Serial.println( analogRead( AO ));//Output the value of analog pin A0 ,

the output value is 0~1023

delay( 200 );

}

2.3 Stepper Motor

Figure 4 shows the connection diagram of the stepper motor. This experiment will use the DM42L driver to drive a 57-step stepper motor, using a common anode wiring method, as shown in Figure 4. Among them:

(1) The four wires of the stepper motor are connected to the driver ports A+, A-, B+, and B-;

(2) The driver VCC port is connected to the positive terminal of the external power supply, and the driver GND port is connected to the negative terminal of the external power supply, supplying 9V voltage;

(3) PUL- is connected to Arduino Uno digital pin 7, and DIR- is connected to digital pin 6;

(4) Use a breadboard to connect PUL+ and DIR+ to the Arduino Uno 5V pin.

(5) Write code to control the stepper motor, as shown below:

int PUL=7;

int DIR=6; //Define the corresponding pins for PUL and DIR

#define steps 1600 //For every 360° rotation of the stepper motor, the motor advances 1600 steps

void setup() {

pinMode( PUL,OUTPUT );

pinMode( DIR,OUTPUT ); //Configure digital pins 6 and 7 as output mode

Serial.begin( 9600 );

}

void loop() {

for(int i=0;i<steps;i++){

digitalWrite( DIR,HIGH ); //Control motor direction HIGH for forward,

LOW for reverse

digitalWrite( PUL,HIGH );

delayMicroseconds( 500 );

digitalWrite( PUL,LOW );

delayMicroseconds( 500 ); //The two delayMicroseconds()

functions control the speed of the stepper motor

}

}//After this program runs, the stepper motor will keep rotating forward until the program is manually stopped or the stepper motor loses power. To reverse, the level of the DIR connected pin needs to be changed to LOW

2.4 SGX Linear Module

The SGX linear module is driven by a 57-step stepper motor. By setting the stepper motor to move forward 1 step per millisecond through the program, it takes 1600ms or 1.6s to move forward 1600 steps. Therefore, the stepper motor rotates 360 degrees every 1.6s, and the sliding table moves x=3.5mm=3.5×10^-3m. Let the speed of the sliding table be v, then the running speed is v=x/t≈2.19×10^-3m/s.

The code to control the stepper motor using Arduino is as follows:

int PUL=7;

int DIR=6;

int DO=5;

int AO=A0; //Define pins

unsigned long time;

#define steps 1600

void setup() {

}

void loop() {

for( int i=0 ; i<steps ; i++){

digitalWrite( DIR,HIGH ); //HIGH for forward,

LOW for reverse

digitalWrite ( PUL,HIGH );

delayMicroseconds( 500 );

digitalWrite( PUL,LOW );

delayMicroseconds( 500 );

if(digitalRead(DO)==1){

Serial.println( analogRead( time ));

}//If light is detected, output the running time

}

}

3 Experimental Exploration

The experimental hardware includes a laser light source (λ=532nm), Arduino Uno development board, photosensitive resistor module (4 pins), DC stabilized power supply (0~24V), stepper motor driver (DM42L), SGX linear module (screw accuracy 0.03mm, repeat positioning accuracy 0.05mm), brass rod to be tested, breadboard, and several Dupont wires. The schematic diagram of the experimental device is shown in Figure 5.

3.1 Experimental Method

The experimental steps are as follows:

(1) Measure the optical lever constant b and the effective length of the brass rod L with a ruler; use a vernier caliper to measure the thickness d and width a of the brass rod;

(2) Use the brass rod as the experimental sample and assemble the experimental instruments according to the experimental device diagram in Figure 5;

(3) Measure the horizontal distance from the photosensitive resistor to the optical lever with a ruler, five times, to obtain B;

(4) Support the metal rod with a bracket and hang a knife edge with weights at the midpoint of the effective length (ensure the knife edge is hung at the center);

(5) Start Arduino, begin uploading the program, and control the SGX linear module slider to move up and down; each time it moves up, read the time t when the light signal is detected; each time it moves down to the initial position, press the reset button on the Arduino Uno development board;

(6) Scan up and down three times with the SGX linear module and change the weight each time;

(7) Read the time t when detecting the light signal with weights of 20.0g, 40.0g, 50.0g, 70.0g, 100.0g, and 150.0g, measuring each weight three times.

3.2 Experimental Result Analysis

Using a ruler to measure the effective length of the knife edge L=24.35cm, the optical lever constant b=11.36cm, and the horizontal distance from the photosensitive resistor to the optical lever B=112.76cm. Using a vernier caliper, the thickness of the brass rod is measured as d=1.50mm, and the width of the brass rod is a=1.50mm. The known gravitational acceleration is g=9.8m/s².

Under different weights, the time detected by the photosensitive resistor is shown in Table 1.

Furthermore, the time difference Δt can be calculated for different mass differences Δm, and using the speed of the SGX linear module, the height difference ΔH can be obtained, as shown in Figure 6. Performing linear fitting on the data results in the fitting equation ΔH=0.192Δm-0.034, where R²=0.999, indicating a high degree of fit.

From equations (11) and the fitting equation, we can derive . Therefore, the Young’s modulus of brass is calculated as E=10.25×10¹⁰N/m². The standard value of Young’s modulus for brass is known as E₀=10.55×10¹⁰N/m^2[10], allowing us to calculate the relative error of this experiment as .

4 Conclusion

This experiment combines the Arduino microcontroller for measuring large physical experiments. The experiment uses the beam bending method based on the optical lever principle, introducing a photosensitive resistor to measure the small deformation of the brass rod under different stress conditions and determine the Young’s modulus of brass as E=10.25×10¹⁰N/m². The relative error of the experiment is 2.8%, indicating relatively high measurement accuracy and that the experimental design is reasonable. This experimental design can effectively stimulate students’ interest in experiments, improve their hands-on skills, and cultivate their innovative abilities. Furthermore, the methods and experimental techniques provided in this paper are easy to implement and promote in undergraduate basic physics experiments.

References

Funding Project: Ministry of Education Higher Education College Physics Curriculum Teaching Guidance Committee Project (DJZW202310hb, WX202206); Ministry of Education Industry-University Cooperation Collaborative Education Project (220905259141912); Nankai University Undergraduate Teaching Reform Project (NKJG2023048, NKJG2023107, NKJG2022096, 22NKSYKF05).

Corresponding Author: Wang Xiaojie, Male, Assistant Researcher at Nankai University, mainly engaged in physics teaching and research, research direction is nonlinear optics, [email protected].