CN107452258A - The measurement apparatus and method of acceleration of gravity - Google Patents
The measurement apparatus and method of acceleration of gravity Download PDFInfo
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- CN107452258A CN107452258A CN201710872198.6A CN201710872198A CN107452258A CN 107452258 A CN107452258 A CN 107452258A CN 201710872198 A CN201710872198 A CN 201710872198A CN 107452258 A CN107452258 A CN 107452258A
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- 230000005484 gravity Effects 0.000 title claims abstract description 46
- 238000005259 measurement Methods 0.000 title claims abstract description 44
- 230000001133 acceleration Effects 0.000 title claims abstract description 42
- 238000000034 method Methods 0.000 title claims abstract description 23
- 230000003287 optical effect Effects 0.000 claims abstract description 30
- 238000012545 processing Methods 0.000 claims abstract description 12
- 230000001105 regulatory effect Effects 0.000 claims description 7
- 230000000149 penetrating effect Effects 0.000 claims description 3
- 230000000737 periodic effect Effects 0.000 claims description 3
- 238000002474 experimental method Methods 0.000 abstract description 4
- 238000007796 conventional method Methods 0.000 description 3
- 239000000203 mixture Substances 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000005236 sound signal Effects 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/06—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics
- G09B23/08—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics
- G09B23/10—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics of solid bodies
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
- G01V7/12—Measuring gravitational fields or waves; Gravimetric prospecting or detecting using pendulums
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- Life Sciences & Earth Sciences (AREA)
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- Length Measuring Devices By Optical Means (AREA)
Abstract
The present invention provides a kind of measurement apparatus and method of acceleration of gravity, the device includes base, support, cycloid, swing ball, laser, optical receiver and processing terminal, branch is set up on base, one end connection swing ball of cycloid, the other end of cycloid is on support, laser is oppositely arranged with optical receiver, and swing ball is located between laser and optical receiver；This method by changing the pendulum length of single pendulum, record multigroup pendulum length variation length Δ L and pendulum length change after cycle T, and then respectively obtain multigroup π Δs L of variable 4 and variable T2Value, then to the π Δs L of variable 4 and variable T2Value carry out linear fit, the value of acceleration of gravity is tried to achieve by the slope of fitting a straight line；The present invention can be improved in senior middle school or college physical experiment teaching, and the measurement accuracy of acceleration of gravity is measured using single pendulum, can make measurement error control within the scope of very little, and typically about 0.05%.
Description
Technical field
The present invention relates to a kind of measurement apparatus of acceleration of gravity and method.
Background technology
In senior middle school and college physics teaching, measure the method for acceleration of gravity have electromagnetic shooting point timer method, single pendulum method,
Freely falling body method etc..Need to measure pendulum length and cycle using common practices during Measurement of Gravity Acceleration by Simple Pendulum.In the measurement of pendulum length, by
Swing ball barycenter is difficult to the influence determined, and the direct measurement of pendulum length is more difficult, it is also difficult to accurately measures the length of cycloid change；
When surveying the cycle, due to being that manual operation stopwatch starts or stopped timing, situation that is advanced or lagging timing unavoidably occurs,
Larger timing error be present.
Above mentioned problem is should to pay attention to and solve the problems, such as in the measurement process of acceleration of gravity.
The content of the invention
It is an object of the invention to provide a kind of measurement apparatus of acceleration of gravity and method to solve present in prior art
When surveying the cycle, due to being that manual operation stopwatch starts or stopped timing, situation that is advanced or lagging timing unavoidably occurs,
Larger timing error be present, also accurately measure cycloid change length the problem of.
The present invention technical solution be：
A kind of measurement apparatus of acceleration of gravity, including base, support, cycloid, swing ball, laser, optical receiver and place
Terminal is managed, branch is set up on base, and one end connection swing ball of cycloid, on support, laser connects the other end of cycloid with light
Receive device to be oppositely arranged, swing ball is located between laser and optical receiver, and the output end of optical receiver connects processing eventually by connecting line
The input interface at end.
Further, support uses adjustable jack post, and support includes montant, cross bar, adjusting knob one, one end of montant
Connect base, the other end connection cross bar of montant, cross bar are provided with adjusting knob one, and cross bar is additionally provided with through hole, and cycloid passes through through hole
And connect adjusting knob one.
Further, montant uses height-adjustable montant, and montant includes regulation upper boom and regulation lower beam, and regulation lower beam is provided with
Regulating tank, regulation upper boom are penetrated in regulating tank, and regulation lower beam is vertically provided with adjusting knob two, and adjusting knob two penetrates regulating tank
It is interior.
Further, cross bar is provided with groove.
A kind of measuring method of acceleration of gravity, during measurement, by changing the pendulum length of single pendulum, record the change of multigroup pendulum length
Cycle T after length Δ L and pendulum length change, and then respectively obtains multigroup π Δs L of variable 4 and variable T2Value, then to the π of variable 4
Δ L and variable T2Value carry out linear fit, the value of acceleration of gravity is tried to achieve by the slope of fitting a straight line.
Further, measured, specifically included following using the measurement apparatus of acceleration of gravity described in any of the above-described
Step：
Step 1, laser and optical receiver face placed, laser is injected optical receiver, and by optical receiver
Output end access computer audio input interface, open computer on audio edited software；
Step 2, with pencil mark is done every setpoint distance on cycloid, and then obtain multigroup 4 π Δs L data；
Step 3, the through hole for penetrating cycloid on experimental provision cross bar, and be connected with the adjusting knob of crossbeam left end；
Step 4, by adjusting knob first mark point on cycloid is set to fall on the groove on cross bar；
Step 5, the length for adjusting montant, enable swing ball to fall between laser and optical receiver, and ensure swing ball energy
Successfully it is in the light；
Step 6, the recording function for opening audio edited software, caused waveform during record swing ball is swung；
Step 7, in software window, select the region shared by a cycle, read by " time span " of beneath window
Go out concrete numerical value, by the multiple measurement period in other regions, obtain average value；
Step 8, the length by adjusting knob change cycloid, make second on cycloid mark point fall the quarter on crossbeam
On line；And above step 5-7 is repeated, the periodic quantity under different length is obtained, and then obtain multigroup T2Data；
Step 9, multigroup 4 π Δs L and T obtained by by above step 2 and step 82Data inputting Excel forms, and be fitted straight
Line, the value of acceleration of gravity is tried to achieve by the slope of straight line.
The beneficial effects of the invention are as follows：The measurement apparatus and method of this kind of acceleration of gravity, it is possible to increase senior middle school is big
Learn in physics experiment teaching, the measurement accuracy of acceleration of gravity is measured using single pendulum, measurement error control can be made in the model of very little
Within enclosing, typically about 0.05%.The measuring method of this kind of acceleration of gravity, solve existing for conventional method and ask in terms of two
Topic：Without the concrete numerical value of single pendulum pendulum length, the uncertain caused error due to swing ball center of gravity is avoided；Using processing eventually
End, audio edited software, photodiode and laser pen composition, being capable of performance periods similar to the experimental provision of " photoelectric door "
Accurate measurement.
Brief description of the drawings
Fig. 1 is the structural representation of the measurement apparatus of acceleration of gravity of the embodiment of the present invention；
Fig. 2 is that the current signal signal being in the light occurs in the single pendulum that processing terminal records in embodiment in swing process
Figure；
Fig. 3 is to utilize the straight line schematic diagram that the data of table 1 are fitted in embodiment；
Wherein：1- bases, 2- cycloids, 3- swing balls, 4- lasers, 5- optical receivers, 6- processing terminals, 7- cross bars, 8- are adjusted
Save knob one, 9- through holes, 10- regulation upper booms, 11- regulation lower beams, 12- adjusting knobs two, 13- grooves.
Embodiment
The preferred embodiment that the invention will now be described in detail with reference to the accompanying drawings.
Embodiment
A kind of gravity is provided and accelerated using deficiency existing for Measurement of Gravity Acceleration by Simple Pendulum, such as Fig. 1, embodiment for traditional
The measurement apparatus of degree, including base 1, support, cycloid 2, swing ball 3, laser 4, optical receiver 5 and processing terminal 6, branch is set up in
On base 1, one end connection swing ball 3 of cycloid 2, on support, laser 4 is relative with optical receiver 5 to be set the other end of cycloid 2
Put, swing ball 3 is located between laser 4 and optical receiver 5, and the output end of optical receiver 5 connects the defeated of processing terminal 6 by connecting line
Incoming interface.Cross bar 7 is provided with groove 13.
The measurement apparatus of this kind of acceleration of gravity, cost is low, easy to use, it is possible to increase senior middle school or Experiment of College Physics
In teaching, the measurement accuracy of acceleration of gravity is measured using single pendulum, measurement error control can be made within the scope of very little, typically
About 0.05%.
Support uses adjustable jack post, and support includes montant, cross bar 7, adjusting knob 1, one end connection bottom of montant
Seat 1, the other end connection cross bar 7 of montant, cross bar 7 are provided with adjusting knob 1, and cross bar 7 is additionally provided with through hole 9, and cycloid 2 passes through through hole
9 and connect adjusting knob 1.
Montant uses height-adjustable montant, and montant includes regulation upper boom 10 and regulation lower beam 11, and regulation lower beam 11, which is provided with, to be adjusted
Groove is saved, regulation upper boom 10 is penetrated in regulating tank, and regulation lower beam 11 is vertically provided with adjusting knob 2 12, and adjusting knob 2 12 penetrates tune
Save in groove.
The measurement apparatus of this kind of acceleration of gravity, by using adjustable jack post, can realize to the height of cycloid 2 with
The easy regulation of length, is easy to measurement to use.
Embodiment also provides a kind of measuring method of acceleration of gravity, and during measurement, by changing the pendulum length of single pendulum, record is more
Cycle T after the variation length Δ L of group pendulum length and pendulum length change, and then respectively obtains multigroup π Δs L of variable 4 and variable T2Value,
Then to the π Δs L of variable 4 and variable T2Value carry out linear fit, the value of acceleration of gravity is tried to achieve by the slope of fitting a straight line.
The measuring method of this kind of acceleration of gravity, solve the problems, such as that conventional method is present in terms of two：Put without single pendulum
Long concrete numerical value, avoid the uncertain caused error due to the center of gravity of swing ball 3；Utilize processing terminal 6 such as computer, audio
Software for editing, photodiode and laser pen composition similar to " photoelectric door " experimental provision, can performance period more
Accurately measurement.
The measuring principle of the acceleration of gravity of embodiment is as follows：
In experiment with simple pendulum, there is following relation in period of single pendulum with acceleration of gravity, pendulum length：
In formula, T0、L0The respectively initial period of single pendulum and pendulum length.
Formula (1) both sides square：
If the pendulum length changes delta L of single pendulum, then the cycle of single pendulum necessarily changes, and the cycle now is designated as T, (2) formula
It is rewritten as：
(3) formula of arrangement obtains：4π2Δ L=gT2-4π2L0 (4)
From (4) formula, the π Δs L of variable 4 and variable T2Linear relationship be present, the slope of linear equation is that gravity accelerates
The value g of degree.Therefore, the length of cycloid 2 is varied multiple times, records multigroup 4 π Δs L and T2Value, be then fitted the straight line sides of two variables
Journey, you can obtain the value of acceleration of gravity.
Such a method is easier to obtain accurate data compared with conventional method in terms of linear measure longimetry.Next to solve
Be exactly period measurement the problem of.The measurement in cycle is as follows：To be provided with audio edited software (such as：Audacity processing)
Terminal 6 such as computer, photodiode, the composition of laser 4 are similar to the device of " photoelectric door ", as shown in Figure 1.
In embodiment, audio edited software serves key effect.The main function of such a software is processing audio letter
Number, but can be changed into current signal first before audio signal input computer, accordingly, it can be said that software processing is actually
Current signal.
When surveying the cycle, single pendulum is placed between laser 4 and optical receiving set, the audio of the output termination computer of optical receiver 5
Input interface.Single pendulum occurs in swing process to be in the light, and change of the photodiode in optical receiver 5 to light is very quick
Sense, can convert optical signal into current signal, current signal is delivered to by audio input interface can be by audio editing after computer
Software records are got off, as shown in Figure 2.
In single pendulum swing process, a set of pulses can be produced each time by being in the light.Single pendulum is in the light twice in a cycle, occurs two
Group pulse, therefore, the time interval of adjacent " two groups " pulse is the period of motion of single pendulum.Selected in the graphical window of software
Time zone shared by middle a cycle, beneath window can show the time " length " automatically, and the levels of precision of numerical value is better than general
Digital stopwatch, it can read 0.001s.
Measure as stated above, to change the pendulum length of single pendulum, also to ensure that swing ball 3 is in laser 4 and light all the time
Position between receiver 5, in addition, also to guarantee to accurately measure the length of the change of cycloid 2.Therefore, embodiment
A kind of measurement apparatus of acceleration of gravity is also provided.
As shown in figure 1, the montant of device can be with adjustment length, montant top connecting cross beam, aperture, cycloid are drilled with crossbeam
2 are penetrated from aperture, and are connected to the knob of crossbeam left end, and the length of cycloid 2 can be adjusted by the knob.Small on crossbeam
A groove 13 is carved between hole and adjusting knob, it is identical to facilitate cycloid 2 to change every time for the mark point alignd on cycloid 2
Length.
(1) laser 4 and the face of optical receiver 5 are placed, laser is injected optical receiver 5, and by optical receiver 5
Output end access computer audio input interface.Open the audio edited software on computer.
(2) with pencil, (such as 10cm or 5cm) does a mark at a certain distance on cycloid 2.
(3) through hole for penetrating cycloid 2 on experimental provision cross bar, and be connected with the adjusting knob of cross bar left end.
(4) first mark point on cycloid 2 is made to fall on the groove 13 on cross bar by adjusting knob.
(5) length of montant is adjusted, swing ball 3 is fallen between laser 4 and optical receiver 5, and ensure the energy of swing ball 3
Successfully it is in the light.
(6) recording function of audio edited software, caused waveform during record swing ball 3 is swung are opened.
(7) in software window, the region shared by a cycle is selected, tool is read by " time span " of beneath window
Body numerical value, by the multiple measurement period in other regions, obtain average value.
(8) change the length of cycloid 2 by adjusting knob, second on cycloid 2 mark point is fallen the quarter on cross bar
On line 13.And operated more than repeating, obtain the periodic quantity under different length.
(9) by multigroup 4 π Δs L and T2Data inputting Excel forms, and fitting a straight line, gravity is tried to achieve by the slope of straight line
The value of acceleration.
Embodiment device and method substantially increase the measurement accuracy accelerated using single pendulum measurement gravity, by repeatedly testing
Card, measurement result and recognised standard are all very close.It is one group of data of examples measure below, and utilizes this group of data
The straight line of fitting.
The measurement data of the embodiment of table 1
From the figure 3, it may be seen that the coefficient R of straight line2=1, the linearity for illustrating straight line is extraordinary.Straight line in Fig. 3
Equation is：Y=9.8014x-48.443.The slope for the linear equation being fitted according to data is 9.8014, i.e. acceleration of gravity
Measured value is 9.8014m/s2.Taizhou Region is located at 32.5 degree or so of north latitude, and the acceleration magnitude of this area is about 9.7964m/s2,
It is very close between the two.
Claims (6)
- A kind of 1. measurement apparatus of acceleration of gravity, it is characterised in that：Connect including base, support, cycloid, swing ball, laser, light Device and processing terminal are received, branch is set up on base, and one end connection swing ball of cycloid, the other end of cycloid is on support, laser Device is oppositely arranged with optical receiver, and swing ball is located between laser and optical receiver, and the output end of optical receiver is connected by connecting line Connect the input interface of processing terminal.
- 2. the measurement apparatus of acceleration of gravity as claimed in claim 1, it is characterised in that：Support uses adjustable jack post, Support includes montant, cross bar, adjusting knob one, one end connect base of montant, and the other end of montant connects cross bar, and cross bar is provided with Adjusting knob one, cross bar are additionally provided with through hole, and cycloid is through through hole and connects adjusting knob one.
- 3. the measurement apparatus of acceleration of gravity as claimed in claim 1, it is characterised in that：Montant uses height-adjustable montant, Montant includes regulation upper boom and regulation lower beam, and regulation lower beam is provided with regulating tank, and regulation upper boom is penetrated in regulating tank, and regulation lower beam hangs down Adjusting knob two directly is provided with, adjusting knob two is penetrated in regulating tank.
- 4. the measurement apparatus of acceleration of gravity as claimed in claim 1, it is characterised in that：Cross bar is provided with groove.
- A kind of 5. measuring method of acceleration of gravity, it is characterised in that：During measurement, by changing the pendulum length of single pendulum, record multigroup Cycle T after variation length Δ L and the pendulum length change of pendulum length, and then respectively obtain multigroup π Δs L of variable 4 and variable T2Value, so Afterwards to the π Δs L of variable 4 and variable T2Value carry out linear fit, the value of acceleration of gravity is tried to achieve by the slope of fitting a straight line.
- 6. the measuring method of acceleration of gravity as claimed in claim 5, it is characterised in that：Using any one of claim 1-4 The measurement apparatus of the acceleration of gravity measures, and specifically includes following steps：Step 1, laser and optical receiver face placed, laser is injected optical receiver, and by the defeated of optical receiver Go out the audio input interface terminated into computer, open the audio edited software on computer；Step 2, with pencil mark is done every setpoint distance on cycloid, and then obtain multigroup 4 π Δs L data；Step 3, the through hole for penetrating cycloid on experimental provision cross bar, and be connected with the adjusting knob of cross bar left end；Step 4, by adjusting knob first mark point on cycloid is set to fall on the groove on cross bar；Step 5, the length for adjusting montant, enable swing ball to fall between laser and optical receiver, and ensure that swing ball can succeed It is in the light；Step 6, the recording function for opening audio edited software, caused waveform during record swing ball is swung；Step 7, in software window, select the region shared by a cycle, tool read by " time span " of beneath window Body numerical value, by the multiple measurement period in other regions, obtain average value；Step 8, the length by adjusting knob change cycloid, make second on cycloid mark point fall the groove on cross bar On；And above step 5-7 is repeated, the periodic quantity under different length is obtained, and then obtain multigroup T2Data；Step 9, multigroup 4 π Δs L and T obtained by by above step 2 and step 82Data inputting Excel forms, and fitting a straight line, lead to The slope for crossing straight line tries to achieve the value of acceleration of gravity.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201710872198.6A CN107452258A (en) | 2017-09-22 | 2017-09-22 | The measurement apparatus and method of acceleration of gravity |
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| CN201710872198.6A CN107452258A (en) | 2017-09-22 | 2017-09-22 | The measurement apparatus and method of acceleration of gravity |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108693563A (en) * | 2018-07-12 | 2018-10-23 | 湖南科众兄弟科技有限公司 | Resonant mode absolute gravity measurement device |
| CN110675708A (en) * | 2019-11-12 | 2020-01-10 | 苏红 | Experiment demonstration instrument and experiment method for measuring gravity acceleration by using simple pendulum |
| CN112700698A (en) * | 2021-01-27 | 2021-04-23 | 武汉理工大学 | Gravitational acceleration measurement experimental device based on magnetic induction |
| CN113484922A (en) * | 2021-06-23 | 2021-10-08 | 武汉轻工大学 | Gravitational acceleration measuring method, device, storage medium and apparatus |
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| CN207651045U (en) * | 2017-09-22 | 2018-07-24 | 南京师范大学泰州学院 | The measuring device of acceleration of gravity |
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| CN2622794Y (en) * | 2003-03-25 | 2004-06-30 | 王喜云 | Microcomputerized pendulum experimental instrument |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108693563A (en) * | 2018-07-12 | 2018-10-23 | 湖南科众兄弟科技有限公司 | Resonant mode absolute gravity measurement device |
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| CN113484922A (en) * | 2021-06-23 | 2021-10-08 | 武汉轻工大学 | Gravitational acceleration measuring method, device, storage medium and apparatus |
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