CN104020501B - Many balls and slide more nest coordinate leading bead slip measuring gravity acceleration method - Google Patents
Many balls and slide more nest coordinate leading bead slip measuring gravity acceleration method Download PDFInfo
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- CN104020501B CN104020501B CN201410264323.1A CN201410264323A CN104020501B CN 104020501 B CN104020501 B CN 104020501B CN 201410264323 A CN201410264323 A CN 201410264323A CN 104020501 B CN104020501 B CN 104020501B
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Abstract
Many balls and slide nest more and coordinate leading bead to slide to measure the method for acceleration of gravity and relate to the mensuration field of physical parameter.The present invention proposes a kind of method substituting single pendulum measurement acceleration of gravity.Technical scheme is: one plate shaped becomes circular arc, its radius of curvature is R, 23 circular arc leading grooves are had in circular arc region, bead slides along leading groove from eminence, in the mutual conversion process of potential energy and kinetic energy, making reciprocally swinging, measure its hunting period of T, calculating acceleration of gravity is g=(2 π/T) 2R.Provide the benefit that: bead is positioned by multiple balls, it is ensured that bead can not roll, translation can only occur；The material of the present invention can use hard material, can be less relative to its deformation quantity of the single of single pendulum.
Description
Technical field
The present invention relates to the mensuration field of physical parameter, the particularly measurement of acceleration of gravity.
Background technology
In Experiment of College Physics room, single pendulum and physical pendulum are commonly used in the measurement of acceleration of gravity.The swing ball of single pendulum is only controlled by hitch point and cycloid, and cycloid is soft, when doing experiment with simple pendulum, without carrying out, the most just having made conical pendu0, conical pendu0 is equivalent to the single pendulum that pendulum length shortens, cause the cycle measured to diminish, thus cause the acceleration of gravity measured bigger than normal；Certainly, the most also it is unlikely to reach conical pendu0 the most extreme, it is common that one taper swinging momvement of superposition in simple harmonic motion.
Summary of the invention
For overcoming single pendulum cycloid that swing ball can not easily be occurred operative constraint superposition conical pendu0 or the problem even developing into conical pendu0, the present invention proposes many balls and slides the method that nest coordinates the slip of leading bead to measure acceleration of gravity more, is a kind of method substituting single pendulum measurement acceleration of gravity.
nullThe present invention realizes goal of the invention and the technical scheme is that many balls and slide nest cooperation leading bead slip measuring gravity acceleration method more，It is characterized in that: a bead，Its radius is r，Excise a part of spherical crown and form a circular tangent plane，Be parallel to the direction of circular tangent plane cutting out a height at residue spheroid is the pancake of h1，Between pancake and residue spheroid，Make 3-6 the elliposoidal cavity about the tangent plane center of circle symmetry of residue spheroid，Each elliposoidal cavity by just to the same bulb-shaped recess of two shapes and sizes form，One on residue spheroid、Another is on pancake，Elliposoidal cavity penetrates pancake，That is，Elliposoidal cavity forms through hole in pancake position，A spherical ball is placed in each elliposoidal cavity，It is h2 that spherical ball protrudes the height of pancake outer circular tangent plane，Residue spherome surface and pancake inner circular tangent plane are close to and are fixed by screw；One plate shaped becomes circular arc, its radius of curvature is R, has 2-3 bar circular arc leading groove in circular arc region, and its radius of curvature is r3, the degree of depth is h3, h2 > h3, radius of curvature r3 are more than the radius of spherical ball, the spacing of leading groove and the pitch match of spherical ball；Bead slides along leading groove from eminence, in the mutual conversion process of potential energy and kinetic energy, makees reciprocally swinging, measures its hunting period of T, and calculating acceleration of gravity is g=(2 π/T) 2R。
The invention has the beneficial effects as follows: bead is positioned by multiple spherical ball, it is ensured that bead can not roll, translation can only occur, thus be equivalent to single pendulum, it is proposed that a kind of mentality of designing deforming single pendulum；For single pendulum, owing to receiving the restriction of 2-3 bar leading groove, do not have the situation of conical pendu0；Owing to the cycloid of single pendulum is soft single, single pendulum is different due to the speed of each residing position, its suffered centripetal force is the most different, centripetal force is that the pulling force of cycloid produces, and therefore the power suffered by cycloid is different in each position, and its tensile deformation is also the most different, the cycloid length causing each position slightly has some difference, for fiber cycloid, the material of the present invention can use hard material, and its deformation quantity can be less.
Accompanying drawing explanation
Fig. 1 is conical pendu0 schematic diagram；Fig. 2 circular arc plate schematic diagram；Fig. 3 bead spherical crown, pancake and spherical ball relation schematic diagram；Fig. 4 is bead spherical crown, pancake and spherical ball position relationship elevational schematic；Fig. 5 has the circular arc plate schematic diagram of leading groove；The circular arc plate elevational schematic of Fig. 6 band leading groove.
Detailed description of the invention
Conical pendu0:
FDraw*cosθ=mg
FDraw*sinθ= FTo=mω2r= mω2* Lsinθ
Two formulas are divided by, and obtain
g=ω2Lcosθ=(2pi/T) 2Lcos θ wherein, pi=3.1415926
And the formula that single pendulum measures acceleration of gravity is g=(2pi/T) 2L, is equivalent to pendulum length for conical pendu0 and shortens to the single pendulum of L*cos θ, wherein；For the experiment with simple pendulum of superposition circumference pendulum, owing to the numerical value of acceleration of gravity is constant, the pendulum length being in molecule shortens, and the cycle T being in denominator also can shorten, if calculated according further to the pendulum length of single pendulum, acceleration of gravity measured value can be caused to become big.Experiment with simple pendulum typically will not be made a conical pendu0 purely, because the most obvious；One taper swinging momvement of superposition in simple harmonic motion often, the measured value causing the acceleration of gravity measured has a certain degree of change big, and, the most unfortunately, do not know that this conical pendu0 has great radius of curvature on earth, to such an extent as to be unable to estimate its impact brought.
Many balls and slide more nest coordinate leading bead slip measuring gravity acceleration method:
nullOne bead，Its radius is r，Excise a part of spherical crown and form a circular tangent plane，From the angle of mathematics: the vertical line (tangent plane normal) of the tangent plane at circular tangent plane center necessarily crosses the centre of sphere，Be parallel to the direction of circular tangent plane cutting out a height at residue spheroid is the pancake of h1，Between pancake and remaining spheroid，Make 3-6 the elliposoidal cavity about tangent plane center of circle symmetry，Each elliposoidal cavity by just to the same bulb-shaped recess of two shapes and sizes form，One on residue spheroid、Another is on pancake，Elliposoidal cavity penetrates pancake，That is，Elliposoidal cavity forms through hole in pancake position，A spherical ball is placed in each spherical hollow space，It is h2 that spherical ball protrudes from the height of the circular tangent plane outside pancake，Residue spherome surface and pancake inner surface are close to and are fixed by screw；One plate shaped becomes circular arc, and its radius of curvature is R, has 2-3 bar circular arc leading groove in circular arc region, and its radius of curvature is r3, the degree of depth is h3, h2 > h3, radius of curvature r3 is more than the radius of spherical ball.
The spacing of leading groove and the pitch match of spherical ball, from the angle supported, the spherical ball of three not conllinear just can support residue spheroid, four spherical ball are relative to three spherical ball, more for symmetry and ruggedness, when one of them spherical ball is removed, do not affect normal use；5-6 spherical ball mainly considers from stability, and owing to track presents circular arc, more spherical ball will be not suitable for (needing in cooperation that tangent plane is deformed into sphere more suitable).
Suggestion a: mathematically bead can move in the radius of curvature arc-shaped groove more than or equal to its radius, but due to frictional force and the precision of manufacture, suggestion rolls the radius radius of curvature less than its arc-shaped groove track of bead, and suitably makes with lubricator.
Leading groove with the matching relationship of spherical ball is, three spherical ball in a triangle, are mated with three leading grooves, and a spherical ball occupies a leading groove；Four spherical ball become foursquare four summits, mate with two or three leading grooves, article two, leading groove, then each two spherical ball occupies a leading groove, or foursquare one cornerwise two spherical ball occupy a leading groove of centre, another cornerwise two spherical ball occupy two leading grooves in outside respectively；For 5-6 spherical ball, using three leading grooves relatively more reasonable, the leading groove in outside is respectively arranged with two spherical ball.
Bead slides along leading groove from eminence, in the mutual conversion process of potential energy and kinetic energy, makees reciprocally swinging, measures its hunting period of T, thus calculating acceleration of gravity is g=(2 π/T) 2R。
Claims (1)
- null1. ball more than and slide more nest coordinate leading bead slip measuring gravity acceleration method，It is characterized in that: a bead，Its radius is r，Excise a part of spherical crown and form a circular tangent plane，Be parallel to the direction of circular tangent plane cutting out a height at residue spheroid is the pancake of h1，Between pancake and residue spheroid，Make 3-6 the elliposoidal cavity about the tangent plane center of circle symmetry of residue spheroid，Each elliposoidal cavity by just to the same bulb-shaped recess of two shapes and sizes form，One on residue spheroid、Another is on pancake，Elliposoidal cavity penetrates pancake，That is，Elliposoidal cavity forms through hole in pancake position，A spherical ball is placed in each elliposoidal cavity，It is h2 that spherical ball protrudes the height of pancake outer circular tangent plane，Residue spherome surface and pancake inner circular tangent plane are close to and are fixed by screw；One plate shaped becomes circular arc, its radius of curvature is R, has 2-3 bar circular arc leading groove in circular arc region, and its radius of curvature is r3, the degree of depth is h3, h2 > h3, radius of curvature r3 are more than the radius of spherical ball, the spacing of leading groove and the pitch match of spherical ball；Bead slides along leading groove from eminence, in the mutual conversion process of potential energy and kinetic energy, makees reciprocally swinging, measures its hunting period of T, and calculating acceleration of gravity is g=(2 π/T) 2R。
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| Application Number | Priority Date | Filing Date | Title |
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| CN201410264323.1A CN104020501B (en) | 2014-06-16 | 2014-06-16 | Many balls and slide more nest coordinate leading bead slip measuring gravity acceleration method |
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| CN201410264323.1A CN104020501B (en) | 2014-06-16 | 2014-06-16 | Many balls and slide more nest coordinate leading bead slip measuring gravity acceleration method |
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| CN104020501A CN104020501A (en) | 2014-09-03 |
| CN104020501B true CN104020501B (en) | 2016-08-24 |
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| DE3208811A1 (en) * | 1982-03-11 | 1983-09-29 | Konrad 6831 Brühl Möbus | Angle-of-inclination measuring instrument with an electronically controlled digital numeric display of angles of inclination referred to the horizontal, by means of continuous scanning of one or more electrical resistances of pendulums, spheres, mercury pearls or rollers, the movement of which is controlled by gravity |
| SU1250850A2 (en) * | 1984-08-10 | 1986-08-15 | Gurevich Leonid M | Device for determining slope of mobile object |
| CN2826420Y (en) * | 2005-08-25 | 2006-10-11 | 清华同方威视技术股份有限公司 | Single pendulum type apparatus for imaging experiment for detecting high-speed motion object |
| CN101303810A (en) * | 2008-07-07 | 2008-11-12 | 南京化工职业技术学院 | Instrument for real time demonstrating simple pendulum oscillation |
| CN201638426U (en) * | 2010-04-13 | 2010-11-17 | 浙江师范大学 | Closed controllable simple pendulum experimental instrument |
| CN102236989A (en) * | 2010-05-07 | 2011-11-09 | 上海市格致中学 | Portable gravity acceleration tester |
| RU2461027C1 (en) * | 2011-04-11 | 2012-09-10 | Федеральное государственное бюджетное учреждение науки Тихоокеанский океанологический институт им. В.И. Ильичева Дальневосточного отделения Российской академии наук (ТОИ ДВО РАН) | Method and apparatus for measuring gravitational acceleration |
| CN203242220U (en) * | 2013-05-24 | 2013-10-16 | 孙嘉男 | Experimental device for measuring gravitational acceleration by using single pendulum |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2013061158A (en) * | 2011-09-12 | 2013-04-04 | Yoichi Takagi | Apparatus and method for measuring gravity of earth |
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2014
- 2014-06-16 CN CN201410264323.1A patent/CN104020501B/en not_active Expired - Fee Related
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|---|---|---|---|---|
| DE3208811A1 (en) * | 1982-03-11 | 1983-09-29 | Konrad 6831 Brühl Möbus | Angle-of-inclination measuring instrument with an electronically controlled digital numeric display of angles of inclination referred to the horizontal, by means of continuous scanning of one or more electrical resistances of pendulums, spheres, mercury pearls or rollers, the movement of which is controlled by gravity |
| SU1250850A2 (en) * | 1984-08-10 | 1986-08-15 | Gurevich Leonid M | Device for determining slope of mobile object |
| CN2826420Y (en) * | 2005-08-25 | 2006-10-11 | 清华同方威视技术股份有限公司 | Single pendulum type apparatus for imaging experiment for detecting high-speed motion object |
| CN101303810A (en) * | 2008-07-07 | 2008-11-12 | 南京化工职业技术学院 | Instrument for real time demonstrating simple pendulum oscillation |
| CN201638426U (en) * | 2010-04-13 | 2010-11-17 | 浙江师范大学 | Closed controllable simple pendulum experimental instrument |
| CN102236989A (en) * | 2010-05-07 | 2011-11-09 | 上海市格致中学 | Portable gravity acceleration tester |
| RU2461027C1 (en) * | 2011-04-11 | 2012-09-10 | Федеральное государственное бюджетное учреждение науки Тихоокеанский океанологический институт им. В.И. Ильичева Дальневосточного отделения Российской академии наук (ТОИ ДВО РАН) | Method and apparatus for measuring gravitational acceleration |
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