CN111312036A - Double-cone falling demonstration experiment system and method - Google Patents
Double-cone falling demonstration experiment system and method Download PDFInfo
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Abstract
The invention discloses a double-paper cone falling demonstration experiment system and an experiment method thereof, wherein the double-paper cone falling demonstration experiment system comprises a fixed plate, a paper cone, a wireless distance measurement system and a data processing platform; the left side and the right side of the top end of the demonstration frame are respectively provided with a fixing mechanism with the same structure, each fixing mechanism comprises a fixing plate and an electromagnet, and the electromagnets are fixed on the edges of the fixing plates; an iron sheet is arranged at the edge of the cone bottom of the paper cone; the wireless distance measuring system measures the distance data from the paper cone to the fixed plate at the cone angle and transmits the measuring time and the distance data to the data processing platform; and the data processing platform calculates and obtains the speed of the paper cone and the distance relative to the ground according to the measuring time and the distance data. The invention simplifies the experimental process and improves the perceptual knowledge of the experiment; the experiment demonstration frame introduces the contrast experiment of two paper cones, so that the experiment phenomenon is more vivid and clear, and the experiment demonstration frame has a good demonstration effect in actual teaching.
Description
Technical Field
The invention relates to the technical field of physical experiment teaching and demonstration, in particular to a double-cone falling demonstration experiment system.
Background
In the section of 8-grade registration 'speed' of junior middle school physics department edition, a research activity 'for comparing the falling speed of a paper cone' is arranged, the paper cone can better keep a linear motion state compared with the falling time of a paper sheet, and the falling time can be measured, so that the paper cone is selected as a research object for comparing the falling speed in a teaching material, in the traditional experiment teaching, the experiment depends on experimental equipment such as a ruler, the paper cone (copy paper), a stopwatch and the like, the paper cone is artificially released and the displacement of the paper cone in the falling process is measured, and the factors influencing the falling speed of the paper cone are researched by adopting the same path and the comparison time.
The error sources of the traditional paper cone falling experiment have a plurality of aspects: (1) errors in the manufacturing process; (2) error in measuring height; (3) the error in reaction time is measured.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a double-paper cone falling demonstration experiment system, and solves the technical problems of large error, complex process, poor repeatability and large workload of later data processing in the traditional paper cone falling experiment.
In order to solve the technical problem, the invention provides a double-paper cone falling demonstration experiment system which is characterized by comprising a fixing plate, a paper cone, a wireless distance measurement system and a data processing platform;
the left side and the right side of the top end of the demonstration frame are respectively provided with a fixing mechanism with the same structure, each fixing mechanism comprises a fixing plate and an electromagnet, and the electromagnets are fixed at the edges of the fixing plates;
an iron sheet is arranged at the edge of the cone bottom of the paper cone;
the wireless distance measuring system is fixed on the paper cone and close to the cone angle and used for measuring the distance data between the cone angle of the paper cone and the fixed plate and transmitting the measuring time and the distance data to the data processing platform;
and the data processing platform is used for obtaining the speed and the distance of the paper cone according to the measuring time and the distance data.
Further, fixed establishment still includes the hydraulic stem, and on the stiff end of hydraulic stem was fixed in the demonstration frame, the flexible end of hydraulic stem was fixed in on the fixed plate so that the fixed plate can inwards contract and be close to the demonstration frame or expand to the side and keep away from the demonstration frame.
Further, the demonstration frame comprises a base and a supporting frame vertically installed on the base.
Furthermore, the electromagnet sets up to at least two, and each electromagnet distributes along the fixed plate edge.
Furthermore, all electromagnets are connected in parallel and then connected with a power supply through a switch.
Furthermore, an iron wire is wound on the edge of the cone bottom of the paper cone.
Correspondingly, the invention provides an experimental method of the double-cone falling demonstration experimental system, which is characterized by comprising the following steps of:
when the experiment is started, the electromagnet is electrified to enable the electromagnet to have magnetism, the iron sheets of the two paper cones are respectively attracted with the electromagnet, so that the two paper cones are respectively fixed on the fixed plate, and the cone angles of the two paper cones are positioned at the same horizontal height;
when the experiment is started, the electromagnet is powered off at the same time, and the two paper cones respectively fall freely; meanwhile, the wireless distance measuring system measures the distance data from the paper cone to the fixed plate at the cone angle in a timing mode and transmits the measuring time and the distance data to the data processing platform; and the data processing platform calculates and obtains the speed and the distance of the paper cone according to the measuring time and the distance data.
Further, the process of calculating and obtaining the speed and the distance of the paper cone by the data processing platform according to the measuring time and the distance data is as follows:
1) calculating the speed of the paper cone in the falling process according to the following speed solving formula according to the sampling period of the wireless distance measuring system;
wherein v isnSpeed, x, at the nth measurement instantnDistance, x, at the nth measurement instantn-1The distance of the nth-1 measurement time is obtained, and △ t is the sampling period of the wireless distance measurement system;
2) calculating the theoretical speed of the paper cone when falling according to the following formula:
wherein k is a resistance coefficient, m is the mass of the paper cone, t is the falling time, g is the gravity acceleration, and v is the speed of the paper cone;
the theoretical speed error interval is established by the following formula:
wherein v (n)minAnd v (n)maxIs the maximum and minimum value of the theoretical velocity at the theoretical nth measurement instant, t0Is the theoretical time of a single measurement; the minimum value and the maximum value form a theoretical speed error interval;
3) and screening the falling speed of the paper cone obtained by solving the experimental data through the following inequality according to the established theoretical maximum value and the theoretical minimum value of the speed:
v(n)min≤vn≤v(n)max
wherein v (n)minAnd v (n)maxIs the maximum and minimum value, v, of the theoretical velocity at the theoretical nth measurement instantnThe speed at the nth measurement moment; replacing the experimental speed outside the error interval with the theoretical speed at the moment;
4) the distance data of the paper cone relative to the fixed plate from the moment of starting to fall to the ground is recalculated according to the following formula:
xn＝xn-1+vnΔt
wherein xnFor the nth measurement of the distance, x, from the fixed platen-1For the n-1 th measurement, the distance v from the fixed platenAnd delta t is the speed at the nth measurement moment, and is the time difference of two distance measurements obtained by the measurement of the single-chip timer.
Further, the method also comprises a step 5) of obtaining a distance curve of the paper cone relative to the ground in the falling process according to the distance between the upper fixing plate and the ground and the distance information of the paper cone relative to the upper fixing plate in the falling process by making a difference between the upper fixing plate and the lower fixing plate:
dn＝H-xn
wherein d isnThe distance between the paper cone and the ground at the nth measurement time is H, the distance between the tips of the two paper cones and the ground is xnThe distance of the paper cone relative to the fixed plate is measured for the nth time.
Compared with the prior art, the invention has the following beneficial effects: the invention solves the experimental error existing in the traditional paper cone falling experiment, further simplifies the experimental process and improves the perceptual knowledge of the experiment on the basis of ensuring the scientificity of the experimental process; the experiment demonstration frame introduces the contrast experiment of two paper cones, so that the experiment phenomenon is more vivid and clear, and the experiment demonstration frame has a good demonstration effect in actual teaching.
Drawings
FIG. 1 is a schematic diagram of a demonstration experiment system according to the present invention;
FIG. 2 is a schematic diagram of the principle of the present invention;
FIG. 3 is a schematic structural view of a paper cone according to the present invention;
fig. 4 is a graph showing the displacement curve and the speed curve of two paper cones in the example of the present invention.
Reference numerals: 1. a demonstration shelf; 11. a base; 12. a support frame; 2. a fixing plate; 3. an electromagnet; 4. a hydraulic lever; 5. a paper cone; 6. iron sheets; 7. a wireless distance measurement system.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The invention discloses a double-paper cone falling demonstration experiment system, which comprises a demonstration frame 1, a wireless distance measurement system 7 and a data processing platform, wherein the demonstration frame comprises a fixing plate 2, a paper cone 5 and the wireless distance measurement system;
the left side and the right side of the top end of the demonstration frame 1 are respectively provided with a fixing mechanism with the same structure, the fixing mechanism comprises a fixing plate 2 and an electromagnet 3, and the electromagnet 3 is fixed on the edge of the fixing plate 2; the fixing mechanism can also be a foldable mechanism, namely, the fixing mechanism also comprises a hydraulic rod 4, the fixed end of the hydraulic rod 4 is fixed on the demonstration frame 1, and the telescopic end of the hydraulic rod 4 is fixed on the fixing plate 2 so that the fixing plate 2 can be inwards contracted to be close to the demonstration frame 1 or be unfolded to the side edge to be far away from the demonstration frame 1;
an iron sheet 6 is arranged at the edge of the bottom of the paper cone 5; at the beginning of the experiment, the paper cone 5 is fixed on the fixed plate 2 by utilizing the attraction between the iron sheet 6 and the electromagnet 3;
the wireless distance measuring system 7 is fixed on the paper cone 5 and close to the cone angle, and is used for measuring the distance data between the cone angle of the paper cone and the fixed plate and transmitting the measuring time and the distance data to the data processing platform;
and the data processing platform is used for calculating and obtaining the speed and the distance of the paper cone according to the measuring time and the distance data.
Examples
The double-cone falling demonstration experiment system of the embodiment of the invention is shown in fig. 1 and specifically comprises the following components: demonstration frame 1, fixed plate 2, data processing platform, paper awl 5 and wireless distance measurement system 7.
The demonstration frame 1 comprises a base 11 and a support frame 12 vertically installed on the base 11, and is shown in fig. 1, wherein the base 11 is an I-shaped base formed by 4 aluminum profiles with the length of 0.4m and one aluminum profile with the length of 0.6m, the support frame 12 comprises two symmetrically arranged aluminum profiles, each support frame 12 is formed by two aluminum profiles with the length of 1m vertically installed on the base, two aluminum profiles with the length of 1m are connected by aluminum alloy groove strips along the inner groove type of the aluminum profiles to form a support frame with the length of 2m, the separation of the upper part and the lower part is realized through the aluminum alloy groove strips, and the detachability of the demonstration frame is realized. In order to improve the stability of the structure, an aluminum profile with the length of 0.5m is added between two vertical parallel aluminum profiles, so that the support frame is in an I-shaped stable structure. Foldable mechanisms with the same structure are respectively installed on the left side and the right side of the top ends of the two vertical parallel aluminum profiles (supporting frames).
Two foldable mechanisms are symmetrically arranged at two sides of the support frame, and are described in detail by using a specific one of the foldable mechanisms, as shown in fig. 1, each foldable mechanism comprises a fixed plate 2 (the fixed plate can be specifically an acrylic plate) with the length of 0.5m by 0.5m, and two 2020 aluminum profiles with the length of 0.5m are fixed at the front side and the rear side of the fixed plate 2 through T-shaped corner pieces; the aluminum profile is fixed at one end of the support frame through a movable hinge; the telescopic end of a hydraulic rod 4 with the pressure of 30N is arranged at the outer side of the aluminum profile at the side edge of the fixed plate 2, and the fixed end (the other end) is arranged on the aluminum profile of the fixed movable hinge to form a triangular foldable supporting structure; the hydraulic rods 4 are arranged so that the fixing plates 2 can be retracted inwardly close to the demonstration frame 1 or extended sideways away from the demonstration frame 1. An electromagnet 3 is fixed on the edge of the fixed plate 2; in order to make the paper cone fixing more stable, the number of the electromagnets 3 can be at least two, and each electromagnet is distributed along the edge of the fixing plate. All electromagnets are connected in parallel and then connected with a power supply through a switch.
In order to carry out a multi-cone contrast experiment and increase the intuitiveness of an experiment result, two cones are adopted to carry out a falling experiment in the experiment process, the cones 5 specifically comprise two circular surfaces with the diameter of 0.6m made of a PET high-transmittance polyester film material which is not easy to damage and has good deformation recovery capacity, and because the falling speed and the received resistance of the cones formed after the circles with the same size are cut out of the circular surfaces with different angles are different in the paper cone falling experiment, the two circular surfaces which are made are respectively cut out of the circular surfaces with the larger angle difference in order to visually observe the experiment phenomenon in the actual experiment, so that the speed of the two cones which are different from each other is different by human eyes in the actual falling process.
In the experiment, 130-degree fan-shaped and 70-degree fan-shaped are cut off on two circular surfaces with the diameter of 0.6m respectively and abandoned, the rest parts form two fan-shaped with central angles of 230 degrees and 290 degrees, the structure of the paper cone is shown in figure 3, the two manufactured fan-shaped parts are curled along the generatrix direction, the connecting parts are adhered by hot melt adhesive to form a closed paper cone, in order to match with an electromagnet to enable the paper cone to be better fixed, two iron sheets 6 are symmetrically installed at two ends along the diameter direction of the cone bottom circle of the paper cone 5 by using iron wires, in order to solve the problem that the paper cone is too large and the material is lighter and easy to deform, and the edge of the paper cone is annularly fixed by using fine iron wires.
In order to realize the simultaneous falling of the two paper cones, the paper cones 5 with the iron sheets 6 are simultaneously fixed or simultaneously released by adopting the electromagnets 3, and the electromagnets are connected in parallel and then connected with a power supply through a switch. The electromagnet 3 for fixing the paper cone is a 2kg miniature 12V direct current electromagnet with the diameter of 10mm, holes are formed in the fixing plate according to the diameter of the selected electromagnet and the size of the cone bottom of the manufactured paper cone, the hole size is slightly larger than the diameter of the electromagnet, the distance between the hole position and the center of the fixing plate is larger than the radius of a circle of the cone bottom of the paper cone, and after the principle is met, the manufactured paper cone can fix the paper cone on the fixing plate through attraction between an iron sheet at the edge of the cone bottom of the paper cone and the electromagnet on the fixing plate.
In order to compensate for the difference in height of the two paper cones caused by the difference in central angles of the two paper cones, the difference in height of the left side and the right side is compensated when the paper cone fixing plate is installed, so that the cone angles of the two paper cones are at the same height after the two paper cones are fixed, and the demonstration frame meets the condition that the falling of the paper cones in the experiment teaching material needs to be at the same height.
The specific implementation scheme is as follows: the calculation formula of the known paper cone height is as follows:
wherein h is the height of the paper cone, L is the length of a fan-shaped bus 30cm, r is the radius of the bottom surface of the paper cone, the radius of the bottom surface of the paper cone with 290 degrees is 24cm, the radius of the bottom surface of the paper cone with 230 degrees is 19cm, and the data are obtained through actual measurement.
Then, as can be seen from the above formula, the height of the paper cone made of 230 degree sector is approximately 23cm, the fixing plate for fixing it is installed at the uppermost end of the demonstration frame of 2m and kept horizontal, the height of the paper cone made of 290 degree sector is approximately 18cm, the paper cone fixing plate for fixing it is installed at the position of 1.95m of the paper cone demonstration frame, and the height thereof is 5cm lower than that of the 230 degree paper cone fixing plate, and by the above scheme, the height of both paper cones relative to the ground is 1.77 m.
The wireless distance measuring system 7 is fixed on the paper cone 5 and close to the cone angle, and is used for measuring the distance data of the cone angle of the paper cone from the fixed plate and transmitting the measuring time and the distance data to the data processing platform. The wireless distance measuring system is a distance measuring device which is used for measuring the distance of a paper cone in the falling process by a low-cost distance sensor meeting the precision requirement, is built by utilizing the existing single chip microcomputer minimum system board, a wireless serial port device and a 200mAh miniature lithium battery, has light weight and high precision and has a wireless transmission function. The device not only replaces the artificial complex process of measuring by using the ruler in the falling process of the paper cone, but also improves the distance measuring precision in the process; the distance sensor comprises an ultrasonic sensor or a laser ranging sensor with a serial port communication function, the ultrasonic sensor or the laser ranging sensor is connected with the single chip microcomputer in a serial port mode, the single chip microcomputer sends a serial port command to measure in a 50ms period, the distance sensor returns a distance value between the distance sensor and an upper fixing plate at the current moment, and the single chip microcomputer stores distance data received from the serial port into the single chip microcomputer; the single chip microcomputer is externally connected with a wireless serial port device to be in serial port communication with the single chip microcomputer of the data processing platform on the demonstration frame, and the measuring time and the corresponding distance data are sent to the data processing platform through the established serial port communication protocol.
The wireless distance measurement system is arranged at the cone angle inside the paper cone, and the damping sponge with the surface area larger than the bottom area of the wireless distance sensor is filled at the bottom when the wireless distance measurement system is arranged, so that the horizontal installation of the distance sensor is ensured, and meanwhile, the damage of falling impact of the paper cone on the internal distance sensor is also avoided.
The principle structure of the data processing platform is shown in figure 2, and concretely comprises a single chip microcomputer (STM32F series single chip microcomputer), two wireless serial ports, a data transmission radio station and an experiment trigger switch, wherein the power supply of the data processing platform is driven by 5v voltage obtained by reducing voltage of a 12v lithium battery, the wireless serial ports and the data transmission radio station are both connected with the single chip microcomputer in a serial port mode, two wireless serial port devices receive distance data of a paper cone relative to a fixed plate, which is sent by a wireless distance measuring system, through a fixed serial port protocol, the experiment trigger switch is divided into two paths, one path is connected with a power supply of an electromagnet, the other path is connected with a GND (ground) port and an I/O (input/output) port of the single chip microcomputer, the on-off state of the electromagnet is controlled through a ship-shaped switch, the on-off state of the electromagnet can, one way of I/O port connected with GND and the single chip microcomputer is used as a trigger switch of an experiment, the grounding of the IO port of the single chip microcomputer corresponds to the ground level when the single chip microcomputer is in an open state, so when the electromagnet is switched from power-on to power-off, the IO port is switched from the grounding state to the suspension state, the single chip microcomputer reads a rising edge at the moment, the rising edge serves as an experiment starting signal to trigger data receiving and data processing of the single chip microcomputer, and a data transmission radio station sends processed experiment result data to a computer according to a communication protocol of an anonymous ground station (existing software) for curve drawing.
The theoretical derivation process of the falling speed of the paper cone is as follows:
step 1) establishing an air resistance equation in the falling process of the paper cone, wherein the equation is as follows:
wherein C is an air resistance coefficient; ρ is the air density; s, the windward area of an object; v is the relative movement velocity of the object and the air; f represents the air resistance, and since the sum of the air resistance and the square of the speed are in direct proportion, and the proportionality coefficient is defined as k, the resistance in the falling process of the paper cone can be represented as:
f＝kv2
step 2) the paper cone only receives gravity and air resistance in the falling process, the direction is positive, the gravity is positive, the air resistance is negative, and Newton's second law can obtain
mg-kv2＝ma
Wherein m is the mass of the paper cone, g is the gravity acceleration, a is the acceleration of the paper cone, and the differential can be obtained:
in step 3), since the initial time speed of the paper cone is 0 and the initial time falling distance is 0, the functional relation between the falling distance x (t) and the time can be obtained after differentiation according to the two initial conditions:
wherein ln is a logarithmic function, cosh is a hyperbolic cosine function, and the change relation of the falling speed along with time is obtained by derivation of x (t):
where tanh is a hyperbolic tangent function, the expression from the function v (t) is found when t approaches infinity, v (t) and
for limitation, after considering the air resistance, the speed does not increase without limitation as much as the speed without the air resistance, the speed finally reaches a stable value, and the subsequent motion can be regarded as uniform linear motion.
The invention discloses a double-cone falling demonstration experiment system, which comprises the following specific experiment steps:
step 1) opening the fixed plates on the left side and the right side of the demonstration frame, then connecting the wireless serial port equipment to a USB port of a computer, opening an anonymous ground station at the computer end, selecting a port corresponding to the wireless serial port equipment, and performing serial port connection with a data processing platform.
And 2) checking whether the voltage of a lithium battery for supplying power to the demonstration frame is greater than or equal to 12V, if so, connecting the lithium battery to a power supply port of the demonstration frame through an XT60 interface, and opening a ship traveling switch on the demonstration frame to enable the electromagnet on the fixing plate to be in an electrified state.
And 3) checking whether the voltage of lithium batteries of the wireless distance measuring systems in the two paper cones is greater than 3.7V or not, and if so, switching on the power supply of the wireless distance measuring systems so that the wireless distance measuring systems in the paper cones are in a working state.
And 4) fixing the two paper cones on the electromagnets in the power-on state on the fixing plates on the two sides of the demonstration frame respectively by utilizing the iron sheets on the edges of the paper cones, and after the step is completed, the two paper cones falling experiment demonstration process can be realized only by shifting the ship-shaped switch on the side surface of the demonstration frame to the closing state.
And 5) toggling a ship-shaped switch on the side surface of the demonstration frame, enabling the two paper cones to move in a free falling mode after the electromagnets are powered off simultaneously, and enabling a wireless distance measurement system in each paper cone to start to measure the distance between the paper cone and the upper fixing plate in real time in a period of 50ms and send the result to the data processing platform.
The specific processing procedure of the data processing platform is as follows:
1) and the data processing platform receives and stores the distance data of the paper cones relative to the fixed plate, which is obtained by measuring the wireless distance measuring system in the paper cones in the falling process of the two paper cones, in an unsigned integer array with the length of 50 in a serial port communication mode.
Because the falling process time of the two paper cones is less than 2 seconds, the single chip microcomputer can collect 40 points at most according to the sampling period of 50ms, and therefore the serial port receiving array is set to be unsigned integer with the length of 50 so as to meet the requirement of data length.
2) And calculating the speed of the paper cone in the falling process according to the following speed solving formula according to the sampling period of the wireless distance measuring system of 50 ms.
Wherein v isnSpeed, x, at the nth measurement instantnDistance, x, at the nth measurement instantn-1The distance of the n-1 measurement time is △ t, which is the sampling period 50ms of the wireless distance measurement system.
Since the paper cone is in a static state before being released, the theoretical speed of the paper cone is 0cm/s, but the measured value of the sensor fluctuates in a small range in the actual experimental process, so that the theoretical speed of the paper cone is not 0 cm/s. In the experimental process, the moment when the paper cone speed is greater than 10cm/s is selected as the moment when the paper cone falls, in order to avoid the distance data before the paper cone falls to participate in the following data calculation, the data processing time is increased, the distance data before the falling moment is completely deleted, and only the distance data after the paper cone falling moment is reserved for the following data processing.
3) According to the theoretical derivation process result of the falling speed of the paper cone, the theoretical speed of the paper cone when falling meets the following formula:
wherein k is a resistance coefficient, m is the mass of the paper cone, t is the falling time, g is the gravity acceleration, v is the speed of the paper cone, and the theoretical speed of the falling of the paper cone at any moment can be obtained according to the formula as the measurement period of the wireless distance measurement system is 50 ms.
Considering that a measurement error of a sensor exists in the falling process of an actual paper cone, wherein the measurement error specifically comprises time required by serial communication and the paper cone still in a motion state during the period that the sensor sends ultrasonic waves to receive echoes in the measurement process, in order to make up for the influence of the measurement error of the sensor on an experiment, after the actual speed of the paper cone is obtained through the speed formula in the step 2, a theoretical speed error interval is established for subsequent data screening through the following formula, wherein 1/3 is an experience value set manually, and since the total error of the serial communication and the measurement time of the sensor is less than 10ms, 1/3 of a sampling period is selected as the error interval to remove data;
wherein v (n)minAnd v (n)maxIs the maximum and minimum value of the theoretical velocity at the theoretical nth measurement instant, t0Theoretical time for a single measurement of 50 ms. The minimum and maximum values constitute the theoretical speed error interval.
4) Screening the falling speed of the paper cone obtained by solving the experimental data through the following inequality according to the established theoretical maximum value and the theoretical minimum value of the speed,
v(n)min≤vn≤v(n)max
wherein v (n)minAnd v (n)maxIs the maximum and minimum value, v, of the theoretical velocity at the theoretical nth measurement instantnThe velocity at the nth measurement time obtained in step 2.
That is, the actual falling speed of the paper cone obtained in step 2 needs to be within the theoretical error interval established in step 3 to be considered as an effective experimental speed, and the experimental speed outside the error interval is replaced by the theoretical speed at the moment obtained in step 3 through theoretical derivation.
5) Because the distance data of the paper cone in the falling stage measured by the distance sensor in the experimental process has errors relative to the fixed plate, and the errors cause that the speed obtained by the distance has larger errors with the theory, after the speed substitution is carried out in the step 4, the distance data of the paper cone relative to the fixed plate from the beginning of falling to the landing time (the speed is 0cm/s) is recalculated according to the following formula, so as to obtain the distance data of the falling stage which accords with the theoretical free falling body movement;
xn＝xn-1+vnΔt
wherein xnFor the nth measurement of the distance, x, from the fixed platen-1For the n-1 th measurement, the distance v from the fixed platenThe speed at the nth measurement moment is obtained, and delta t is the time difference of two distance measurements obtained by the measurement of the single-chip timer;
6) and 4, obtaining the speed of the falling process of the paper cone and the distance of the paper cone relative to the upper fixing plate through the step 4 and the step 5, measuring the distance of the paper cone relative to the ground in order to meet the requirements in the experimental teaching materials, and obtaining a distance curve of the paper cone relative to the ground in the falling process according to the distance between the upper fixing plate and the ground and the distance information between the falling process of the paper cone and the upper fixing plate through the difference between the upper fixing plate and the ground.
The distance conversion is specifically realized by the following formula:
dn＝H-xn
wherein d isnThe distance between the paper cone and the ground at the nth measurement time is H, the distance between the tips of the two paper cones and the ground is 1.77m (detailed above), and xnThe distance of the paper cone relative to the fixed plate is measured for the nth time.
And 6) after the paper cones fall to the ground, the data processing platform sends the corresponding distance (relative to the ground) and speed of each 50ms in the falling process of the paper cones to the computer end for displaying, and the computer end can see the distance curve and speed curve of the falling process of the two paper cones through anonymous ground station software.
The distance curve and the speed curve of the two paper cones are mainly displayed to an experimenter on a data curve display platform at the computer end, as shown in fig. 4, after one experiment, the experimenter can observe through the speed curve that the paper cones are in a motion state of first accelerating and then uniform speed in the falling process, and when the paper cones are close to the ground, the resistance borne by the paper cones is greater than the self gravity due to the near-top effect, and the paper cones are in a deceleration motion state; meanwhile, the two paper cones have different resistance surfaces due to different central angles, the paper cones have different air resistance in the falling process, and the time for the two paper cones to move at a constant speed and the speed of the two paper cones are obviously different.
The experimental system can release the two paper cones simultaneously, and can measure and display the distance and the speed of the paper cones relative to the ground in real time in the falling process of the paper cones.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (9)
1. A double-paper cone falling demonstration experiment system is characterized by comprising a fixing plate, a paper cone, a wireless distance measurement system and a data processing platform;
the left side and the right side of the top end of the demonstration frame are respectively provided with a fixing mechanism with the same structure, each fixing mechanism comprises a fixing plate and an electromagnet, and the electromagnets are fixed at the edges of the fixing plates;
an iron sheet is arranged at the edge of the cone bottom of the paper cone;
the wireless distance measuring system is fixed on the paper cone and close to the cone angle and used for measuring the distance data between the cone angle of the paper cone and the fixed plate and transmitting the measuring time and the distance data to the data processing platform;
and the data processing platform is used for obtaining the speed and the distance of the paper cone according to the measuring time and the distance data.
2. The double-cone falling demonstration experiment system of claim 1, wherein the fixing mechanism further comprises a hydraulic rod, a fixed end of the hydraulic rod is fixed on the demonstration frame, and a telescopic end of the hydraulic rod is fixed on the fixing plate so that the fixing plate can be retracted inwards to be close to the demonstration frame or extended sideways to be away from the demonstration frame.
3. The dual cone drop demonstration experiment system according to claim 1, wherein the demonstration rack comprises a base and a support vertically mounted on the base.
4. The dual awl fall demonstration experiment system of claim 1, wherein at least two electromagnets are provided, each electromagnet being distributed along an edge of the stationary plate.
5. The system according to claim 1, wherein the electromagnets are connected in parallel and then connected to a power supply through a switch.
6. The system of claim 1, wherein the paper cone has a wire wrapped around the bottom edge of the cone.
7. The experimental method of the double-cone falling demonstration experimental system according to any one of claims 1 to 6, characterized by comprising the following steps:
when the experiment is started, the electromagnet is electrified to enable the electromagnet to have magnetism, the iron sheets of the two paper cones are respectively attracted with the electromagnet, so that the two paper cones are respectively fixed on the fixed plate, and the cone angles of the two paper cones are positioned at the same horizontal height;
when the experiment is started, the electromagnet is powered off at the same time, and the two paper cones respectively fall freely; simultaneously measuring the distance data from the conical angle of the paper cone to the fixed plate at regular time; and calculating to obtain the speed and the distance of the paper cone according to the measuring time and the distance data.
8. An experimental method as claimed in claim 7, wherein the process of calculating the speed and distance of the paper cone from the measured time and distance data comprises:
1) calculating the speed of the paper cone in the falling process according to the following speed solving formula according to the sampling period of the wireless distance measuring system;
wherein v isnSpeed, x, at the nth measurement instantnDistance, x, at the nth measurement instantn-1The distance of the nth-1 measurement time is obtained, and △ t is the sampling period of the wireless distance measurement system;
2) calculating the theoretical speed of the paper cone when falling according to the following formula:
wherein k is a resistance coefficient, m is the mass of the paper cone, t is the falling time, g is the gravity acceleration, and v is the speed of the paper cone;
the theoretical speed error interval is established by the following formula:
wherein v (n)minAnd v (n)maxIs the maximum and minimum value of the theoretical velocity at the theoretical nth measurement instant, t0Is the theoretical time of a single measurement; the minimum value and the maximum value form a theoretical speed error interval;
3) and screening the falling speed of the paper cone obtained by solving the experimental data through the following inequality according to the established theoretical maximum value and the theoretical minimum value of the speed:
v(n)min≤vn≤v(n)max
wherein v (n)minAnd v (n)maxIs the maximum and minimum value, v, of the theoretical velocity at the theoretical nth measurement instantnThe speed at the nth measurement moment; replacing the experimental speed outside the error interval with the theoretical speed at the moment;
4) the distance data of the paper cone relative to the fixed plate from the moment of starting to fall to the ground is recalculated according to the following formula:
xn＝xn-1+vnΔt
wherein xnFor the nth measurement of the distance, x, from the fixed platen-1For the n-1 th measurement, the distance v from the fixed platenΔ t is the time difference between two distance measurements, which is the speed at the nth measurement instant.
9. The experimental method as claimed in claim 8, further comprising step 5) of obtaining a distance curve of the paper cone relative to the ground during the falling process by subtracting the distance information of the upper fixing plate from the ground and the distance information of the paper cone relative to the upper fixing plate during the falling process:
dn＝H-xn
wherein d isnThe distance between the paper cone and the ground at the nth measurement time is H, the distance between the tips of the two paper cones and the ground is xnIs as followsThe distance of the paper cone relative to the fixed plate at the moment is measured n times.
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| CN113405608A (en) * | 2021-07-07 | 2021-09-17 | 淮南泰隆机械制造有限公司 | Iron wire galvanizing film monitoring system and working method thereof |
| CN113405608B (en) * | 2021-07-07 | 2022-11-18 | 淮南泰隆机械制造有限公司 | Iron wire galvanizing film monitoring system and working method thereof |
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