CN103985290A - Method for measuring gravity acceleration by sleeving cylinder to increase compound pendulum length - Google Patents
Method for measuring gravity acceleration by sleeving cylinder to increase compound pendulum length Download PDFInfo
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- CN103985290A CN103985290A CN201410183422.7A CN201410183422A CN103985290A CN 103985290 A CN103985290 A CN 103985290A CN 201410183422 A CN201410183422 A CN 201410183422A CN 103985290 A CN103985290 A CN 103985290A
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Abstract
The invention provides a method for measuring the gravity acceleration by sleeving a cylinder to increase the compound pendulum length, and relates to the field of physical experiment devices and experimental methods. The method is designed to overcome the defect that the measurement process and the data processing process are complex and high in time consumption and to reduce deviation introduced by calculation. According to the technical scheme, a cylindrical hanging rod is fixed to a thin rod, the central axis of the thin rod and the central axis of the hanging rod are perpendicular and intersect, the two ends of the hanging rod are placed in a pair of grooves, the central axis of the hanging rod is horizontal after the two ends of the hanging rod are placed in the grooves, and the thin rod can swing around the central axis of the hanging rod in a reciprocating mode; the distance h between the mass center C of the thin rod and the central axis of the hanging rod is larger than 0.30 time of the length L of the thin rod and smaller than 0.35 time of the length L of the thin rod; a sleeve rod is fixed to the upper end of the thin rod and shares the same central axis with the thin rod, the cylinder, the sleeve rod and the thin rod are made of the same material, the periphery of the cross section of the cylinder and the periphery of the cross section of the thin rod are the same in shape and equal in size, and the gap between the cylinder and the sleeve rod is too small and can be omitted. The method has the advantages that a measurement device and the measurement process are simple and clear, and data processing is easy and rapid.
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, a strip fork that has equidistant circular hole of general employing, 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 quality that the length that wherein L is thin bar, m are thin bar; The Period Formula (9) of the 106th page of physical pendulum of < < Experiment of College Physics > >, 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 that hitch point is to the distance of 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 barycenter 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
At physical pendulum, measure in acceleration of gravity experiment, 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 kind of device that extends physical pendulum pendulum length measurement acceleration of gravity by being inserted in cylinder, and introduces its using method.
The technical scheme that the present invention realizes goal of the invention employing is: a kind of device that extends physical pendulum pendulum length measurement acceleration of gravity by being inserted in cylinder, is characterized in that: the fork of physical pendulum is comprised of thin bar and the cylinder that is inserted in loop bar; Original state, the loop bar of thin bar is not inserted in cylinder, and fork is now exactly thin bar; Fixing peg in thin bar, peg is cylindrical, and the axis of thin bar is vertical with the axis of peg and intersect, and the two ends of peg are placed in a pair of groove, put into after groove, the axis level of peg, thin bar can be around the axis reciprocally swinging of peg; The barycenter C of thin bar and the distance h of peg axis be greater than 0.30 times of thin bar length L, be less than 0.35 times of thin bar length L, and h is 0.30L-0.35L; Loop bar is fixed on the upper end of thin bar, and loop bar and thin bar have common axis, and cylinder, loop bar, thin bar are material of the same race, and cylinder is identical with the peripheral shape of thin bar xsect, equal and opposite in direction, and the gap between cylinder and loop bar is little of ignoring.
The cross-sectional area of loop bar be thin bar cross-sectional area 0.01-0.2 doubly.Loop bar is axisymmetric shape, and cylinder has a through hole, and the shape of through hole and the shape of loop bar are consistent.The height specification of cylinder is, highly for 1cm have 10, highly for 5mm have 4-8, highly be 2mm have 5-20 individual, highly for 1mm has 5-20 individual.
Employing extends by being inserted in cylinder the measuring method that physical pendulum pendulum length is measured the device of acceleration of gravity, it is characterized in that: by the swing of thin bar, utilize the time keeping instruments such as photoelectricity door to measure hunting period, the cylinder of placing height 1cm on the loop bar of thin bar upper end gradually, cylinder of every increase, measure T hunting period of a fork, along with the barycenter of fork moves on gradually, cycle diminished before this gradually, then become gradually large, when the cycle, just from diminishing, change to when becoming large, remove the cylinder of the 1cm of front twice placement, change the cylinder that placing height is 5mm or 2mm into, the cycle that again measures just changes to from diminishing when becoming large, again remove the cylinder of two height 5mm above or the cylinder of two height 2mm, change the cylinder of placing height 1mm into, until the cycle that again measures just changes to from diminishing when becoming large, now in the linear measure longimetry that is accurate to mm, arrived minimum Tmin hunting period, now the height of all cylinders is designated as h
ny, fork length=L+h
ny, fork is I=(1/12 around the moment of inertia of barycenter) and m (L+ h
ny)
2, h=0.289 (L+ h
ny), Tmin=2*p*{[(1/12) * (L+ h
ny)
2+ h
2]/g/h}
0.5=4.773*{ (L+ h
ny)/g}
0.5, by this formula, can calculate gravity acceleration g=22.78 (L+ h
ny)/T
2min.
The invention has the beneficial effects as follows: because physical pendulum swings, have the minimum period, 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, dwindle the diameter of loop bar and suitable length is set, make the impact of loop bar little in negligible situation, in loop bar, be inserted in cylinder, the cylinder being inserted in and loop bar are combined the line density of formation, the line density that is equivalent to physical pendulum fork, thereby extend equably the length of physical pendulum fork, by continuous increase and decrease, or replacing cylinder, directly find the minimum period, and then measure its length, or calculate its length (length of thin bar and the height of cylinder can be known quantity), thereby directly calculate acceleration of gravity, measurement mechanism of the present invention and measuring process are simple and clear, data processing is simple and quick.
Accompanying drawing explanation
Fig. 1 is that existing physical pendulum is measured acceleration of gravity data processing schematic diagram; Fig. 2 is physical pendulum fork schematic diagram; Fig. 3 is cylinder schematic diagram.
Wherein, 1, thin bar, 2, peg, 3, loop bar, 4, cylinder, 5, through hole; C is the barycenter of thin bar, the overall length that L is thin bar, and h is that fork barycenter is to the distance of peg axis, h
yheight for cylinder.
Embodiment
The fork of physical pendulum is comprised of thin bar 1 and the cylinder 4 that is inserted in loop bar 3; Original state, thin bar 1 is not inserted in cylinder 4, and fork is now exactly thin bar 1.
Fixing peg 2 in thin bar 1, the axis of thin bar 1 (center line) is vertical and crossing with the axis (center line) of peg 2, the two ends of peg 2 are placed in a pair of groove, put into after groove, the axis level of peg 2, peg is cylindrical, and thin bar 1 can be around the axis reciprocally swinging of peg 2.
The distance of the barycenter C of peg 2 axis and thin bar 1 is h, h>0.289L, preferably h is 0.30L-0.35L, loop bar 3 is fixed on the upper end of thin bar 1, loop bar 3 has common axis (center line) with thin bar 1, cylinder 4, loop bar 3, thin bar 1 are material of the same race, and the cross-sectional area of loop bar 3 is 0.01-0.2 times of thin bar 1 cross-sectional area.The physical dimension of cylinder 4 (shape of cross section is identical, equal and opposite in direction) in full accord with thin bar 1 physical dimension, the gap between cylinder 4 and loop bar 3 is little of ignoring (close contact, can freely be inserted in and take out again substantially, relevant with manufacturing accuracy).
Loop bar 3 is preferably axisymmetric shape, such as right cylinder, square, rectangular parallelepiped, triangular prism, the axis of loop bar 3 overlaps with the axis of thin bar 1, cylinder 4 has a through hole 5, the shape of the shape of through hole 5 and loop bar 3 is consistent, and the height of cylinder 4 is 1cm(10), 5mm (4), 2mm(10), 1mm(10).
By the swing of thin bar 1, utilize the time keeping instruments such as photoelectricity door to measure hunting period, the cylinder 4 of placing height 1cm on the loop bar 3 of thin bar 1 upper end gradually, cylinder 4 of every increase, measure T hunting period of a fork, along with the barycenter C of fork moves (because being inserted in cylinder) on gradually, h diminishes, cycle diminished before this gradually, reach minimum wobble after the cycle cycle become gradually large, when the cycle just (for the first time occur) from diminishing, change to when becoming large, remove the cylinder of the 1cm of front twice placement, change the cylinder that placing height is 5mm or 2mm into, the cycle that again just measures changes to from diminishing when becoming large, remove the cylinder of two height 5mm above or the cylinder of two height 2mm, change the cylinder of placing height 1mm into, until the cycle that again just measures changes to from diminishing when becoming large, now in the linear measure longimetry that is accurate to mm, arrived minimum Tmin hunting period, now the height of all cylinders is designated as h
ny, the length=L+h of fork
ny, fork is I=(1/12 around the moment of inertia of barycenter) and m (L+ h
ny)
2, h=0.289 (L+ h
ny), now the formula (9) of < < Experiment of College Physics > > teaching material becomes Tmin=2*p*{[(1/12) * (L+ h
ny)
2+ h
2]/g/h}
0.5=4.773*{ (L+ h
ny)/g}
0.5, by this formula, can calculate gravity acceleration g=22.78 (L+ h
ny)/T
2min.
The design that is 0.30L-0.35L according to h, the variable quantity of h is 0.05L, half of the variable quantity that the variable quantity of barycenter is length so, so the variable quantity of length is 0.1L, length variations amount is mainly to be caused by the high cylinder of 1cm, so want to reach this requirement, be 0.1L<10cm, the length of thin bar is less than 10cm/0.1=100cm, is being less than under the prerequisite of 100cm, user can select other size, such as 50cm, 60cm etc.
Claims (4)
1. by being inserted in cylinder, extend the device that physical pendulum pendulum length is measured acceleration of gravity, it is characterized in that: the fork of physical pendulum is comprised of thin bar (1) and the cylinder (4) that is inserted in loop bar (3); Original state, the loop bar (3) of thin bar (1) is not inserted in cylinder (4), and fork is now exactly thin bar (1); The upper fixedly peg (2) of thin bar (1), peg is cylindrical, the axis of thin bar (1) is vertical and crossing with the axis of peg (2), the two ends of peg (2) are placed in a pair of groove, put into after groove, the axis level of peg (2), thin bar (1) can be around the axis reciprocally swinging of peg (2); The distance h of the barycenter C of thin bar (1) and peg (2) axis is greater than 0.30 times of thin bar length L, be less than 0.35 times of thin bar length L, and h is 0.30L-0.35L; Loop bar (3) is fixed on the upper end of thin bar (1), loop bar (3) has common axis with thin bar (1), cylinder (4), loop bar (3), thin bar (1) are material of the same race, cylinder (4) is identical with the peripheral shape of thin bar (1) xsect, equal and opposite in direction, and the gap between cylinder (4) and loop bar (3) is little of ignoring.
2. according to claim 1ly a kind ofly by being inserted in cylinder, extend the device that physical pendulum pendulum length is measured acceleration of gravity, it is characterized in that: the cross-sectional area of loop bar (3) be thin bar (1) cross-sectional area 0.01-0.2 doubly.
3. according to claim 1 a kind of by being inserted in the device of cylinder prolongation physical pendulum pendulum length measurement acceleration of gravity, it is characterized in that: loop bar (3) is axisymmetric shape, cylinder (4) has a through hole (5), and the shape of the shape of through hole (5) and loop bar (3) is consistent.
A kind of device that extends physical pendulum pendulum length measurement acceleration of gravity by being inserted in cylinder according to claim 1, it is characterized in that: the height specification of cylinder (4) is, highly for 1cm have 10, highly for 5mm have 4-8, highly be 2mm have 5-20 individual, highly for 1mm has 5-20 individual.
4. adopt the method that extends the measurement device acceleration of gravity of physical pendulum pendulum length measurement acceleration of gravity by being inserted in cylinder claimed in claim 4, it is characterized in that: by the swing of thin bar (1), utilize the time keeping instruments such as photoelectricity door to measure hunting period, at the loop bar (3) of thin bar (1) upper end, go up gradually the cylinder (4) of placing height 1cm, a cylinder of every increase (4), measure T hunting period of a fork, along with the barycenter of fork moves on gradually, cycle diminished before this gradually, then become gradually large, when the cycle, just from diminishing, change to when becoming large, remove the cylinder of the 1cm of front twice placement, change the cylinder that placing height is 5mm or 2mm into, the cycle that again measures just changes to from diminishing when becoming large, again remove the cylinder of two height 5mm above or the cylinder of two height 2mm, change the cylinder of placing height 1mm into, until the cycle that again measures just changes to from diminishing when becoming large, now in the linear measure longimetry that is accurate to mm, arrived minimum Tmin hunting period, now the height of all cylinders is designated as h
ny, fork length=L+h
ny, fork is I=(1/12 around the moment of inertia of barycenter) and m (L+ h
ny)
2, h=0.289 (L+ h
ny), Tmin=2*p*{[(1/12) * (L+ h
ny)
2+ h
2]/g/h}
0.5=4.773*{ (L+ h
ny)/g}
0.5, by this formula, can calculate gravity acceleration g=22.78 (L+ h
ny)/T
2min.
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|---|---|---|---|
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107490806A (en) * | 2017-10-13 | 2017-12-19 | 齐齐哈尔大学 | It is a kind of to utilize the method for increasing pendulum radius measurement acceleration of gravity |
| CN107545812A (en) * | 2017-10-13 | 2018-01-05 | 齐齐哈尔大学 | A kind of hollow swinging cylinder experimental provision for measuring acceleration of gravity |
| CN109785726A (en) * | 2019-03-28 | 2019-05-21 | 上海图菱新能源科技有限公司 | The double inverted pendulum remote experimental system of artificial intelligence |
Citations (5)
| 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 |
| CN203503213U (en) * | 2013-09-03 | 2014-03-26 | 浙江海洋学院 | Experiment device for intelligent compound pendulum detection |
-
2014
- 2014-05-04 CN CN201410183422.7A patent/CN103985290A/en active Pending
Patent Citations (5)
| 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 |
| CN203503213U (en) * | 2013-09-03 | 2014-03-26 | 浙江海洋学院 | Experiment device for intelligent compound pendulum detection |
Non-Patent Citations (1)
| Title |
|---|
| 龚镇雄等: "复摆实验", 《教学仪器与实验》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107490806A (en) * | 2017-10-13 | 2017-12-19 | 齐齐哈尔大学 | It is a kind of to utilize the method for increasing pendulum radius measurement acceleration of gravity |
| CN107545812A (en) * | 2017-10-13 | 2018-01-05 | 齐齐哈尔大学 | A kind of hollow swinging cylinder experimental provision for measuring acceleration of gravity |
| CN107545812B (en) * | 2017-10-13 | 2019-08-16 | 齐齐哈尔大学 | A kind of hollow swinging cylinder experimental provision measuring acceleration of gravity |
| CN109785726A (en) * | 2019-03-28 | 2019-05-21 | 上海图菱新能源科技有限公司 | The double inverted pendulum remote experimental system of artificial intelligence |
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Application publication date: 20140813 |