CN104020502B - Three balls and three slide nest and coordinate leading bead slip measuring gravity acceleration method - Google Patents

Abstract

Three balls and three slide nest and coordinate the method that acceleration of gravity is measured in the slip of leading bead to relate to the mensuration field of physical parameter.The present invention proposes the replacement experimental technique of a kind of single pendulum.Technical scheme is: three balls and three slide the method that nest coordinates the slip of leading bead to measure acceleration of gravity, it is characterized in that: discharge bead from the eminence on the left side of circular groove or the right, bead under gravity, do reciprocally swinging in the conversion mutually of kinetic energy and potential energy, bead drives spherical ball to roll, bead is do the circular arc translation that radius of curvature is R, the motion of bead is equivalent to single pendulum, measures its hunting period of T, gravity acceleration g=(2 π/T) ²R.Provide the benefit that: bead is positioned by three spherical ball, it is ensured that bead can not roll, and translation can only occur；Receive the restriction of three leading grooves, do not have the situation of conical pendu0；For fiber cycloid, the material of the present invention can adopt hard material, and its deformation quantity can be less.

Description

Three balls and three slide nest and coordinate leading bead slip measuring gravity acceleration method

Technical field

The present invention relates to the measurement in the mensuration field, particularly acceleration of gravity of physical parameter.

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 limited only by the control of hitch point and cycloid, and cycloid is soft, when doing experiment with simple pendulum, without carrying out, often just having made conical pendu0, conical pendu0 is equivalent to the single pendulum that pendulum length shortens, cause that the cycle measured shortens, thus causing that the acceleration of gravity measured is bigger than normal；Certainly, also it is unlikely to reach conical pendu0 most of the time so 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 three balls and three and slides the method that nest coordinates the slip of leading bead to measure acceleration of gravity, is a kind of method substituting single pendulum measurement acceleration of gravity.

The present invention realizes goal of the invention and the technical scheme is that three balls and three slide nest and coordinate leading bead slip measuring gravity acceleration method, it is characterized in that: a bead, its radius is r, bead has 3 bulb-shaped recess, bulb-shaped recess radius of curvature is r1, the line wherein having the centre of sphere of two bulb-shaped recess crosses the centre of sphere of bead, and the line of the centre of sphere of another bulb-shaped recess and the bead centre of sphere is perpendicular to the line of two other bulb-shaped recess centre of sphere；Having three balls, its radius of curvature is r2, r2 < r1；One flat plate deformation forms circular arc, and its radius of curvature is R, and the both sides of circular arc are respectively arranged with one piece of baffle plate, forms a circular groove, and its vertical section is " door " font, and the height h of baffle plate is more than little radius of a ball r；The bottom center of circular groove and each piece of baffle plate of side have a spherical evagination, and its radius of curvature is r1；The spherical evagination one_to_one corresponding of the bulb-shaped recess of bead and circular groove, form 3 elliposoidal cavitys, holding a ball in each elliposoidal cavity, the equatorial radius of elliposoidal cavity is equal with the radius r2 of ball, the polar radius of elliposoidal cavity is more than the radius r2 of ball；Bead is discharged from the eminence on the left side of circular groove or the right, the bulb-shaped recess of ball contact bead and the spherical evagination of circular groove, bead under gravity, do reciprocally swinging in the conversion mutually of kinetic energy and potential energy, bead drives ball to roll, bead is do the circular arc translation that radius of curvature is R, measure its hunting period of T, gravity acceleration g=(2 π/T)²R。

The invention has the beneficial effects as follows: bead is positioned by three balls, it is ensured that bead can not roll, and translation can only occur, thus being equivalent to single pendulum, it is proposed that a kind of mentality of designing deforming single pendulum；Bulb-shaped recess and spherical evagination form leading groove, for single pendulum, owing to receiving the restriction of three leading grooves, do not have the situation of conical pendu0；Due to the single that the cycloid of single pendulum is soft, single pendulum is different due to the speed of each residing position, its suffered centripetal force is also different, the pulling force that centripetal force is cycloid produces, and therefore the power suffered by cycloid is different in each position, and its tensile deformation is also just different, the cycloid length causing each position slightly has some difference, for fiber cycloid, the material of the present invention can adopt hard material, and its deformation quantity can be less.

Accompanying drawing explanation

Fig. 1 is conical pendu0 schematic diagram；Fig. 2 is circular groove schematic diagram；Fig. 3 is bead and ball schematic diagram；Fig. 4 is circular groove elevational schematic；Fig. 5 be on circular groove three slide nest schematic diagram；Fig. 6 circular groove elevational schematic (processing has three to slide nest)；Fig. 7 be bead, ball and slide nest coordinate schematic diagram.

Detailed description of the invention

Conical pendu0:

F_Draw*cosθ=mg

F_Draw*sinθ=F_To=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=ω²L=(2pi/T)²L, is equivalent to pendulum length for conical pendu0 and is shortened to the single pendulum of Lcos θ by L, wherein；For the experiment with simple pendulum of superposition circumference pendulum, owing to the numerical value of acceleration of gravity is constant, the equivalent pendulum length being in molecule shortens, and the cycle T being in denominator also can shorten, if calculated according further to the original pendulum length of single pendulum, can cause that acceleration of gravity measured value becomes big.Experiment with simple pendulum generally will not be made a pure conical pendu0, because so too obvious；One taper swinging momvement of superposition in simple harmonic motion often, the measured value causing the acceleration of gravity measured has a degree of change big, and, very 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.

Three balls and three slide the method that nest coordinates the slip of leading bead to measure acceleration of gravity:

One bead, its radius is r, and bead has 3 bulb-shaped recess, and bulb-shaped recess radius of curvature is r1, the line wherein having the centre of sphere of two bulb-shaped recess crosses the centre of sphere of bead, and the line of the centre of sphere of another bulb-shaped recess and the bead centre of sphere is perpendicular to the line of two other bulb-shaped recess centre of sphere；Having three balls, its radius of curvature is r2, r2 < r1；One flat plate deformation forms circular arc, its radius of curvature is R, one piece of baffle plate it is respectively arranged with in the both sides of circular arc, form a circular groove, its vertical section is " door " font, the height h of baffle plate is more than little radius of a ball r, and circular groove can by various method molding: as by die casting, milling machine milling cutter etc.；A spherical evagination is had in the bottom center (symmetrical centre) of circular groove and each piece of baffle plate of side, its radius of curvature is r1, the bulb-shaped recess (less than hemisphere spherical crown) of bead and spherical evagination (spherical crown less than the hemisphere) one_to_one corresponding of circular groove, form 3 elliposoidal cavitys, each elliposoidal cavity holds a ball, the height (equatorial diameter of elliposoidal cavity) of cavity is equal with the diameter 2*r2 of ball, the polar radius of elliposoidal cavity is more than the radius r2 of ball, bulb-shaped recess can be the same size with spherical evagination, namely symmetrical, this is best coupling, form an elliposoidal cavity, can also be slightly asymmetric, but should not differ too big；Bead is discharged from the eminence on the left side of circular groove or the right, the bulb-shaped recess of ball contact bead and the spherical evagination of circular groove, bead under gravity, do reciprocally swinging in the conversion mutually of kinetic energy and potential energy, bead drives ball to roll, bead is do the circular arc translation that radius of curvature is R, the motion of bead is equivalent to single pendulum, measures its hunting period of T, gravity acceleration g=(2 π/T)²R.For promoting the smooth motion of ball and reducing friction, ball can smear lubricant.

As r2 < 0.2r, ball rotates the error brought less than 1%, and its evaluation method is: ball was about reciprocatingly sliding at circular groove 1.2 times of cycle in the cycle of circular groove reciprocating rolling, and the volume ratio that r2 < 0.2r brings is less than for 1/5³=/125, so the error that three balls bring is (1.2-1) * 3*1/125=0.5%；Owing to acceleration of gravity and cycle are quadratic relationship, therefore, its Enlarging-Errors one times, 2*0.5%=1%；Working as r2=0.1r, error is close to 0.1%.

Claims (1)

1. three balls and three slide nest cooperation leading bead slip measuring gravity acceleration method, it is characterized in that: a bead, its radius is r, bead has 3 bulb-shaped recess, bulb-shaped recess radius of curvature is r1, the line wherein having the centre of sphere of two bulb-shaped recess crosses the centre of sphere of bead, and the line of the centre of sphere of another bulb-shaped recess and the bead centre of sphere is perpendicular to the line of two other bulb-shaped recess centre of sphere；Having three balls, its radius of curvature is r2, r2 < r1；One flat plate deformation forms circular arc, and its radius of curvature is R, and the both sides of circular arc are respectively arranged with one piece of baffle plate, forms a circular groove, and its vertical section is " door " font, and the height h of baffle plate is more than little radius of a ball r；The bottom center of circular groove and each piece of baffle plate of side have a spherical evagination, and its radius of curvature is r1；The spherical evagination one_to_one corresponding of the bulb-shaped recess of bead and circular groove, form 3 elliposoidal cavitys, holding a ball in each elliposoidal cavity, the equatorial radius of elliposoidal cavity is equal with the radius r2 of ball, the polar radius of elliposoidal cavity is more than the radius r2 of ball；Bead is discharged from the eminence on the left side of circular groove or the right, the bulb-shaped recess of ball contact bead and the spherical evagination of circular groove, bead under gravity, do reciprocally swinging in the conversion mutually of kinetic energy and potential energy, bead drives ball to roll, bead is do the circular arc translation that radius of curvature is R, measure its hunting period of T, gravity acceleration g=(2 π/T)²R。