CN103971570A - Method for measuring gravitational acceleration by increasing pendulum length of compound pendulum through water injection - Google Patents
Method for measuring gravitational acceleration by increasing pendulum length of compound pendulum through water injection Download PDFInfo
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- CN103971570A CN103971570A CN201410182942.6A CN201410182942A CN103971570A CN 103971570 A CN103971570 A CN 103971570A CN 201410182942 A CN201410182942 A CN 201410182942A CN 103971570 A CN103971570 A CN 103971570A
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Abstract
A method for measuring gravitational acceleration by increasing the pendulum length of a compound pendulum through water injection relates to the field of physical test instruments and test methods. The method is designed for overcoming the shortcomings that the data measurement process and the data processing process are cumbersome and time-consuming and reducing deviation caused by calculation. According to the technical scheme, a pendulum rod is composed of the pendulum rod lower portion, a cup cover and a forming cap, the distance from the mass center to the central axis of a hanging rod is 0.30-0.32 times of the overall length of the pendulum rod, the pendulum lower portion is in a hollow cylindrical shape, the bottom is sealed, the upper end is open, the opening is called a cup rim, the cup rim is provided with the cup cover, the cup cover is in threaded connected with the cup rim, and a seal gasket is arranged on a platform at the lower end of the cup rim and between the cup cover and the cup rim. The outer side of a rubber bag is covered with the forming cap, a locating rod fixed to the outer side face of the forming cap penetrates through two rows of locating rings, the locating cap is a hollow cylinder, the material, the inner diameter and the outer diameter of the forming cap are the same as the pendulum lower portion, a water injection pipe is arranged at the lower portion of the pendulum rod and at the position of the hanging rod, and a check valve is arranged in the water injection pipe. The method for measuring gravitational acceleration by increasing the pendulum length of the compound pendulum through water injection has the advantages that a measurement device and the measurement process are simple and clear, and data processing is simple and fast.
Description
Technical field
The physical pendulum that the present invention relates to experiment equipment and experimental technique field, particularly Physical Experiment is measured acceleration of gravity experiment.
Background technology
Physical pendulum in Experiment of College Physics is measured acceleration of gravity experiment, one of general employing has the strip fork of equidistant circular hole, there is scale on fork surface, the about 1cm of diameter, the spacing 2cm of circular hole, one of them circular hole of fork is suspended on to peg (peg is fixed on support) to be swung, measure hunting period, (this circular hole is to the distance at fork center for position coordinates while recording each circular hole suspension, also can be other true origin) and this circular hole hunting period while hanging, then on coordinate paper, map, utilize graphical method to calculate acceleration of gravity.
" Experiment of College Physics ", what former Zhu Jun chief editor of Wang Zhiheng, Dec in 2008 the 1st edition, Higher Education Publishing House, the 41st page, the moment of inertia of the uniform thin bar of mass distribution is I=(1/12) mL
2, the length that wherein L is thin bar, the quality that m is thin bar; The Period Formula (9) of " Experiment of College Physics " the 106th page of physical pendulum, T=2*p*[(a
2+ h
2)/(gh)]
0.5, wherein, definition I=ma
2, for the uniform thin bar of mass distribution, I=(1/12) mL
2=ma
2, h is the distance of hitch point to barycenter, so T=2*p*{[(1/12) and L
2+ h
2]/(gh) }
0.5, differentiate to h and make derivative equal 0 in both sides, h
tmin=L/ (12
0.5)=0.288675L 0.289L, be an extreme value (minimum) hunting period that hitch point is positioned at herein, this formula prompting: the first, there is the minimum wobble cycle; The second, in a side of the symcenter of physical pendulum, the cycle that may have two position h1 and h2 on the both sides of this minimum wobble periodic point apart from fork barycenter 0.289L equates; The 3rd, because the uniform elongated fork of mass distribution is about Central Symmetry, therefore, on physical pendulum, likely find 4 hitch points to there is same hunting period.
The data processing of physical pendulum generally adopts graphing method, as shown in Figure 1, on coordinate paper, retouch out measurement point, then retouch out a level and smooth curve and connect each measurement point or make measurement point be evenly distributed on the both sides of curve, form h-T graph of a relation, because graph of a relation is curve, describe one accurately curve be more difficult, then draw a straight line that is parallel to horizontal ordinate, this straight line and curve intersection are in 4 points, by the coordinate figure h of 4 corresponding horizontal ordinates
1, h
2, h
3, h
4calculate equivalent pendulum length L', thereby by formula gT
2/ (4p
2)=L' calculates gravity acceleration g.
Because measurement point is discrete data, the horizontal ordinate interval of discrete data is generally 2cm, interval is long, generally cannot find the cycle of 4 measurement points identical, cyclic curve is the curve of depicting, there is deviation with true curve, so make four points of a horizontal line and h-T curve intersection devious, also there is deviation in the coordinate figure of the horizontal ordinate reading from four points, therefore except the error of experiment itself, the relatively large deviation that its graphic computation method is also brought, and DATA REASONING process and processing procedure loaded down with trivial details consuming time.
Summary of the invention
Measure in acceleration of gravity experiment at physical pendulum, loaded down with trivial details consuming time and reduce and calculate the deviation of introducing for overcoming DATA REASONING process, data handling procedure, the present invention designs a water filling and extends physical pendulum pendulum length and measure the device of acceleration of gravity.
The technical scheme that the present invention realizes goal of the invention employing is: a kind of water filling extends the device of physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: fork is made up of fork bottom, bowl cover and shaping cap; Peg is cylindrical, peg is fixed on the outside surface of fork bottom, be separated into two sections by fork lower external face, peg is positioned at two sections of fork lower external face and has common axis, the axis of fork bottom of physical pendulum and the axis of peg are vertical and crossing, and the two ends of peg are placed in a pair of groove, and peg is placed after groove, peg axis is in horizontality, and fork can be around the axis reciprocally swinging of peg; Barycenter is 0.30-0.32 times of fork overall length to the distance of peg axis; Fork lower shape is hollow cylindrical, base seal, upper end open, its openend has external thread, for ease of describing, its opening is called rim of a cup, has a bowl cover, bowl cover external diameter is identical with fork bottom, bowl cover has internal thread, and bowl cover is fixed an elastic capsule, and bowl cover is connected with rim of a cup external thread by internal thread, between bowl cover and rim of a cup, on the platform of rim of a cup lower end, there is a packing washer; A shaping cap covers on the outside of rubber bag tank, the fixing backstay of shaping cap lateral surface passes the centring ring of bowl cover and fork bottom, or centring ring is all distributed in fork lower external face, centring ring is two rows, every row 3-5, the centring ring of two rows aligns mutually at vertical direction, and the line of the centring ring of the correspondence position of two rows is parallel to the axis of fork bottom; Shaping cap is hollow circular cylinder, and its material, internal diameter, external diameter are identical with fork bottom; A water injection pipe is arranged in peg position at fork bottom, has one-way cock in water injection pipe.
A Draw off valve is arranged at fork bottom.
Use a kind of water filling to extend the method for the measurement device acceleration of gravity of physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: swing by fork, utilize the apparatus measures such as photoelectricity door hunting period, water injection pipe by fork bottom is to water filling in fork, elastic capsule expands, be full of whole shaping cap, continue water filling, the elastic of elastic capsule elongates, shaping cap moves up, the barycenter C of fork also moves up, distance h between barycenter C and peg axis will diminish, T hunting period recording will diminish, record hunting period T and shaping cap upper end to the length L of lower end, fork bottom, be the length of whole fork, repeat water filling, the length L of measuring oscillating bar and hunting period T, until changing into from diminishing gradually, the discovery cycle becomes gradually large, now stop measuring, from data logger, inquire the oscillating bar length Lmin that minimum wobble cycle T min is corresponding, fork is now I=(1/12 around the moment of inertia of barycenter) mL
2min, h=0.289Lmin, Tmin=2*p*{ [(1/12) * L
2min+h
2]/g/h}
0.5, can calculate gravity acceleration g=22.78 * Lmin/ T by this formula
2min.
For the device that has water drain valve, the method of measuring acceleration of gravity is: swing by fork, utilize the apparatus measures such as photoelectricity door hunting period, water injection pipe by fork bottom is to water filling in fork, elastic capsule expands, be full of whole shaping cap, continue water filling, the elastic of elastic capsule elongates, shaping cap moves up, the barycenter C of fork also moves up, distance h between barycenter C and peg axis will diminish, T hunting period recording will diminish gradually, after reaching minimum, will increase gradually, the discovery cycle is changed into from diminishing gradually when becoming gradually large, emit a small amount of water, then measure hunting period, by constantly a small amount of water filling or discharge water, changed hunting period to the direction diminishing, find gradually minimum wobble cycle T min, the now length L min of measuring oscillating bar, fork is now I=(1/12 around the moment of inertia of barycenter) mL
2min, h=0.289Lmin, Tmin=2*p*{ [(1/12) * L
2min+h
2]/g/h}
0.5, can calculate gravity acceleration g=22.78 * Lmin/ T by this formula
2min.
The invention has the beneficial effects as follows: have the minimum period because physical pendulum swings, a uniform elongated fork of mass distribution, the hitch point that minimum period is corresponding and the distance of barycenter are overall length 0.289 times, water filling forces air bag to extend, thereby extend the length of physical pendulum fork, the length prolongation of physical pendulum fork causes change hunting period, the position that peg is rationally set makes the length of h>0.289 times of fork, preferably at 0.30-0.32 doubly, can reduce the asymmetric impact of mass distribution on the one hand, can also find that on the other hand hunting period is from diminishing greatly, then from the large process of little change, record the corresponding relation in pendulum length and cycle, find oscillating bar length corresponding to minimum wobble cycle, thereby calculating acceleration of gravity, for the device that has water drain valve, in near in minimum wobble cycle, can and discharge water by slow water filling, changed hunting period to the direction reducing, directly measure the minimum period, and then measure its length, thereby directly calculate acceleration of gravity, like this can simplified measurement and data recording, and improve the precision of measuring, two registration circles are conducive to avoid shaping cap to tilt, measurement mechanism of the present invention and measuring process are simple and clear, data processing is simple and quick.
Brief description of the drawings
Fig. 1 is that existing physical pendulum is measured acceleration of gravity data processing schematic diagram; Fig. 2 is physical pendulum fork bottom schematic diagram; Fig. 3 is bowl cover schematic diagram; Fig. 4 is shaping cap schematic diagram.
Wherein, 1, fork bottom, 2, peg, 3, water injection pipe, 4, centring ring, 5, rim of a cup, 6, bowl cover, 7, elastic capsule, 8, shaping cap, 9, backstay; C is the barycenter of fork bottom, and h is the distance of barycenter to peg axis.
Embodiment
Fork is made up of fork bottom 1, bowl cover 6 and shaping cap 8.
Peg 2 is cylindrical, peg 2 is fixed on the outside surface (being separated into two sections by fork lower external face) of fork bottom 1, peg 2 is positioned at two sections of fork bottom 1 outside surface and has common axis, the axis (center line) of the fork bottom 1 of physical pendulum is vertical with the axis (center line) of peg 2 and crossing, the two ends of peg 2 are placed in a pair of groove, peg 2 is placed after groove, and peg 2 axis are in horizontality, and fork can be around the axis reciprocally swinging of peg 2.
Fork bottom 1 is shaped as hollow cylindrical, base seal, upper end open, its openend has external thread, the similar water tumbler in fork bottom 1, for ease of describing, its opening is called rim of a cup 5, there is a bowl cover 6, bowl cover has internal thread, bowl cover 6 is fixed an elastic capsule 7, bowl cover 6 is connected with rim of a cup 5 external threads by internal thread, between bowl cover 6 and rim of a cup 5, on the platform of rim of a cup 5 lower ends, there is a packing washer, a shaping cap 8 covers on the outside of rubber bag tank 7, the fixing backstay 9 of shaping cap 8 lateral surfaces passes the centring ring 4 of bowl cover 6 and fork bottom 1, centring ring 4 also can only design at fork bottom 1 outside surface, centring ring 4 is two rows, every row 3-5, the centring ring of two rows aligns mutually at vertical direction, it is the axis (center line) that the line of the centring ring 4 of the correspondence position of two rows is parallel to fork.A water injection pipe 3 is arranged in peg position at fork bottom 1, in water injection pipe 3, has one-way cock.Shaping cap 8 is hollow circular cylinder, and its material, internal diameter, external diameter are identical with fork bottom 1.
By the swing of fork bottom 1, utilize the apparatus measures such as photoelectricity door hunting period, water injection pipe 3 by fork bottom 1 is to water filling in fork, elastic capsule 7 expands, be full of whole shaping cap, then continue water filling, the elastic of elastic capsule 7 elongates, shaping cap 8 moves up, the barycenter C of fork also moves up, distance h between barycenter C and peg axis (center line) will diminish, T hunting period recording will diminish, record hunting period T and shaping cap upper end to the length L of fork lower end, it is the length L of whole fork, repeat water filling, the length L of measuring oscillating bar and hunting period T, until changing into from diminishing gradually, the discovery cycle becomes gradually large, now stop measuring.From data logger, inquire the oscillating bar length Lmin that minimum wobble cycle T min is corresponding, fork is now I=(1/12 around the moment of inertia of barycenter) mL
2min, h=0.289Lmin, now the formula (9) of " Experiment of College Physics " teaching material becomes Tmin=2*p*{ [(1/12) * L
2min+h
2]/g/h}
0.5, can calculate gravity acceleration g=22.78 * Lmin/ T by this formula
2min.
In order to shorten the length of fork, design a Draw off valve in fork bottom 1, like this in finding that increase hunting period gradually, emit a small amount of water, then measure hunting period, by constantly a small amount of water filling or discharge water, find gradually minimum wobble cycle T min.Owing to there being Draw off valve, can be in finding the minimum wobble cycle, the just length of measuring oscillating bar.
After shaping cap 8 moves up, can bring the asymmetry of mass distribution, can adopt thinner and low weight aluminum alloy materials, or reduce the moving range of shaping cap; Bowl cover itself can bring asymmetry, by the spacing between thickness and the minimizing internal and external screw thread of appropriate design bowl cover, rim of a cup, can reduce and even eliminate its impact on mass distribution; The junction of shaping cap is positioned at bowl cover place, is moment of inertia to what exert an influence hunting period, and moment of inertia is the product of quality and square distance, reduce the impact that asymmetry is brought, and peg is close to rim of a cup; Want can observe hunting period from diminishing greatly, then from the large process of little change, in comprehensive symmetry factor above, the numerical optimization of original state h is 0.30-0.32 times of fork overall length L.
Claims (4)
1. water filling extends a device for physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: fork is made up of fork bottom (1), bowl cover (6) and shaping cap (8); Peg (2) is cylindrical, peg (2) is fixed on the outside surface of fork bottom (1), be separated into two sections by fork bottom (1) outside surface, peg (2) is positioned at two sections of fork bottom (1) outside surface and has common axis, the axis of the fork bottom (1) of physical pendulum is vertical with the axis of peg (2) and crossing, the two ends of peg (2) are placed in a pair of groove, peg (2) is placed after groove, peg (2) axis is in horizontality, and fork can be around the axis reciprocally swinging of peg (2); Barycenter is 0.30-0.32 times of fork overall length to the distance of peg axis; Fork bottom (1) is shaped as hollow cylindrical, base seal, upper end open, its openend has external thread, for ease of describing, its opening is called rim of a cup (5), has a bowl cover (6), bowl cover (6) external diameter is identical with fork bottom (1), bowl cover has internal thread, and bowl cover (6) is fixed an elastic capsule (7), and bowl cover (6) is connected with rim of a cup (5) external thread by internal thread, between bowl cover (6) and rim of a cup (5), on the platform of rim of a cup (5) lower end, there is a packing washer; A shaping cap (8) covers on the outside of rubber bag tank (7), the fixing backstay (9) of shaping cap (8) lateral surface passes the centring ring (4) of bowl cover (6) and fork bottom (1), or centring ring is all distributed in fork bottom (1) outside surface, centring ring (4) is two rows, every row 3-5, the centring ring of two rows aligns mutually at vertical direction, and the line of the centring ring of the correspondence position of two rows (4) is parallel to the axis of fork bottom (1); Shaping cap (8) is hollow circular cylinder, and its material, internal diameter, external diameter are identical with fork bottom (1); A water injection pipe (3) is arranged in peg position at fork bottom (1), and water injection pipe has one-way cock in (3).
2. a kind of water filling according to claim 1 extends the device of physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: fork bottom (1) has a Draw off valve.
3. right to use requires the method that a kind of water filling described in 1 extends the measurement device acceleration of gravity of physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: by the swing of fork, utilize the apparatus measures such as photoelectricity door hunting period, water injection pipe (3) by fork bottom (1) is to water filling in fork, elastic capsule (7) expands, be full of whole shaping cap, continue water filling, the elastic of elastic capsule (7) elongates, shaping cap (8) moves up, the barycenter C of fork also moves up, distance h between barycenter C and peg (2) axis will diminish, T hunting period recording will diminish, record hunting period T and shaping cap upper end (8) to the length L of lower end, fork bottom (1), be the length of whole fork, repeat water filling, the length L of measuring oscillating bar and hunting period T, until changing into from diminishing gradually, the discovery cycle becomes gradually large, now stop measuring, from data logger, inquire the oscillating bar length Lmin that minimum wobble cycle T min is corresponding, fork is now I=(1/12 around the moment of inertia of barycenter) mL
2min, h=0.289Lmin, Tmin=2*p*{ [(1/12) * L
2min+h
2]/g/h}
0.5, can calculate gravity acceleration g=22.78 * Lmin/ T by this formula
2min.
4. right to use requires the method that a kind of water filling described in 2 extends the measurement device acceleration of gravity of physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: by the swing of fork, utilize the apparatus measures such as photoelectricity door hunting period, water injection pipe (3) by fork bottom (1) is to water filling in fork, elastic capsule (7) expands, be full of whole shaping cap, continue water filling, the elastic of elastic capsule (7) elongates, shaping cap (8) moves up, the barycenter C of fork also moves up, distance h between barycenter C and peg (2) axis will diminish, T hunting period recording will diminish gradually, after reaching minimum, will increase gradually, the discovery cycle is changed into from diminishing gradually when becoming gradually large, emit a small amount of water, then measure hunting period, by constantly a small amount of water filling or discharge water, changed hunting period to the direction diminishing, find gradually minimum wobble cycle T min, the now length L min of measuring oscillating bar, fork is now I=(1/12 around the moment of inertia of barycenter) mL
2min, h=0.289Lmin, Tmin=2*p*{ [(1/12) * L
2min+h
2]/g/h}
0.5, can calculate gravity acceleration g=22.78 * Lmin/ T by this formula
2min.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410182942.6A CN103971570B (en) | 2014-05-04 | 2014-05-04 | Water filling extends physical pendulum pendulum length and measures acceleration of gravity |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410182942.6A CN103971570B (en) | 2014-05-04 | 2014-05-04 | Water filling extends physical pendulum pendulum length and measures acceleration of gravity |
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| CN103971570A true CN103971570A (en) | 2014-08-06 |
| CN103971570B CN103971570B (en) | 2016-05-18 |
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|---|---|---|---|
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1945659A (en) * | 2006-11-01 | 2007-04-11 | 四川大学 | Combined twistless compound pendulum |
| CN201000681Y (en) * | 2007-01-29 | 2008-01-02 | 代伟 | Compound pendulum instrument |
| CN102637377A (en) * | 2012-04-13 | 2012-08-15 | 四川大学 | Rotational inertia tester capable of measuring gravity acceleration |
| JP2013061158A (en) * | 2011-09-12 | 2013-04-04 | Yoichi Takagi | Apparatus and method for measuring gravity of earth |
-
2014
- 2014-05-04 CN CN201410182942.6A patent/CN103971570B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1945659A (en) * | 2006-11-01 | 2007-04-11 | 四川大学 | Combined twistless compound pendulum |
| CN201000681Y (en) * | 2007-01-29 | 2008-01-02 | 代伟 | Compound pendulum instrument |
| JP2013061158A (en) * | 2011-09-12 | 2013-04-04 | Yoichi Takagi | Apparatus and method for measuring gravity of earth |
| CN102637377A (en) * | 2012-04-13 | 2012-08-15 | 四川大学 | Rotational inertia tester capable of measuring gravity acceleration |
Non-Patent Citations (1)
| Title |
|---|
| 李建全 等: "复摆实验组合仪的设计", 《枣庄学院学报》 * |
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