CN107657874A - A kind of experimental method using cylinder weight measurement acceleration of gravity - Google Patents
A kind of experimental method using cylinder weight measurement acceleration of gravity Download PDFInfo
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- CN107657874A CN107657874A CN201710949904.2A CN201710949904A CN107657874A CN 107657874 A CN107657874 A CN 107657874A CN 201710949904 A CN201710949904 A CN 201710949904A CN 107657874 A CN107657874 A CN 107657874A
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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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- 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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Abstract
The invention provides a kind of experimental method using cylinder weight measurement acceleration of gravity, this method obtains the hunting period for the swing rod that different number cylinder counterweights connect into first, again by the difference for the swing rod hunting period for contrasting that the mutually level cylinder counterweight of different radii formed, obtain the relational expression between swing rod difference of two squares hunting period and acceleration of gravity of the cylinder counterweight formation of identical each several lower different radiis, the slope of the relational expression is obtained by being fitted experimental data point, and then tries to achieve the numerical value of acceleration of gravity.This method obtains acceleration of gravity by the oblique line slope of fitting, has the characteristics of data processing is simple and convenient, the shortcomings that cumbersome data discrete of existing experimental method curve tracing complexity is big is avoided, suitable for college physical experiment teaching.
Description
Technical field
The present invention relates to a kind of experimental method, in particular to a kind of experiment side using cylinder weight measurement acceleration of gravity
Method.
Background technology
Physical pendulum measurement acceleration of gravity experiment in Experiment of College Physics is general to have the elongated of equidistant circular hole using one
Swing rod, swing rod surface indicate vertical scale, one of circular hole of swing rod are suspended on support swung in an experiment, note
The circular hole is recorded to the hunting period when distance at swing rod center and circular hole suspension, is then mapped on graph paper, utilizes diagram
Method carries out data processing and calculates acceleration of gravity.
The method of physical pendulum measurement acceleration of gravity Data Processing in Experiment is using the distance h of hitch point to swing rod barycenter as horizontal seat
Mark, using measured during the hitch point hunting period T as ordinate, measurement point is described on graph paper, then describe one it is smooth
Curve connect each measurement point or measurement point is evenly distributed on the both sides of curve, form h-T graphs of a relation, then draw one
Bar parallel to axis of abscissas straight line, the straight line and curve intersection at 4 points, that is, obtain four hunting period identical hitch point.
Pass through the coordinate value h of 4 points of corresponding abscissas1、h2、h3、h4Equivalent pendulum length L` is calculated, so as to by formula gT2/(4p2)=
L` calculates gravity acceleration g.
Above-mentioned widely used physical pendulum measurement acceleration of gravity experiment is present following difficult in actual mechanical process, when
Cyclic curve is the curve depicted, unlike fitting a straight line, describe one accurately curve for beginner very
It is difficult；Second, there is deviation in the cyclic curve and real curve depicted, so straight line and cyclic curve parallel to axis of abscissas
Intersecting 4 points, its coordinate value also certainly exists deviation；Three be due to that measurement point is discrete data, and abscissa interval is generally
2cm, 4 cycle identical measurement points are difficult to find that during such interval is real.To sum up, existing measurement acceleration test
Relatively large deviation be present, and DATA REASONING and processing procedure are also relatively complicated time-consuming.
The content of the invention
The invention provides a kind of experimental method for measuring acceleration of gravity, this method data processing is simple and convenient, can be with
Accurately obtain acceleration of gravity numerical value.To achieve the above object, one kind provided by the invention utilizes cylinder weight measurement gravity
The experimental method of acceleration comprises the steps of：
1st, it is r to take n radius1A height of h cylinder counterweight I, one cylinder counterweight I of measurement do small around its top surface horizontal middle spindle
Hunting period during angle swinging, then it is fixedly connected with another cylinder counterweight I one by one in its lower surface, forms multiple cylinders
Counterweight I joins end to end the swing rod of composition, often connects a swing week when swing rod small angle oscillation is measured after a cylinder counterweight I
Phase, if when swing rod is made up of x cylinder counterweight I, the hunting period of swing rod is；
2nd, it is r to take n radius2A height of h cylinder counterweight II, it is known that r2More than r1, repeat step 1, if when by x cylinder counterweight
Cycle during the swing rod small angle oscillation of composition is；
3rd, set, calculating Correspondent cy linder counterweight quantity x yxValue, obtain n data point：（1,）、
（2,）……（N,）；
4th, using counterweight quantity x as transverse axis, coordinate system is established by the longitudinal axis of y, by data point（X, y）Draw in a coordinate system, fitting n
Individual data point obtains oblique line, and the slope for calculating oblique line is k；
5th, utilize, you can calculate gravity acceleration g.
Cylinder counterweight I described in this method and cylinder counterweight II is n a height of h cylindrical weight, wherein n be not less than
10 are not more than 15 integer, and head and the tail can be fixedly connected each cylinder counterweight I or cylinder counterweight II each other.
The experimental principle of the present invention is as follows：
According to Newton's second law, when the cylinder counterweight that x quality is m joins end to end composition swing rod, it is around top cylinder
The top surface horizontal middle spindle of counterweight does low-angleSystem vibration equation during swing is：
In formula, J is the rotary inertia around barycenter trunnion axis of cylinder counterweight, and g is local acceleration of gravity.
The free vibration natural period that the swing rod that x cylinder counterweight forms can be obtained according to above formula is：
（1）
If the radius of cylinder counterweight is r, a height of h, quality m, its rotary inertia is calculated, formula 1 is substituted into, can
：
（2）
As radius r=r of cylinder counterweight1When, i.e., it is by the free vibration natural period of the x cylinder counterweight I swing rods formed：
（3）
Similarly, as r=r2When, i.e., it is by the free vibration natural period of the x cylinder counterweight II swing rods formed：
（4）
If, formula 3 and formula 4 are substituted into, can be obtained：
（5）
Using x as transverse axis, coordinate system is established by the longitudinal axis of y, by point（X, y）It is drawn in coordinate system, is fitted oblique line, it is oblique obtains oblique line
Rate is k, you can is tried to achieve。
Experimental method of the present invention using cylinder weight measurement acceleration of gravity, multiple cylinder counterweights are formed and put
Bar, the hunting period of the swing rod of the cylinder counterweight composition of varying number is obtained, recycles and contrasts different radii phase under identical quantity
The difference of the swing rod hunting period of level cylinder counterweight I and II composition, obtain the calculation formula of acceleration of gravity.
Compared to existing common method, the data point that the present invention obtains can be fitted to an oblique line, and which reduce depict
The complicated cumbersome mapping work that curve belt comes, while data processing speed is improved, reduces the human error of data processing,
Improve experimental precision and efficiency；Acceleration of gravity is calculated using oblique line slope, it also avoid causing to retouch because experimental data is discrete
The curve imitated can not accurately find cycle identical data point problem；In addition, experimental method of the present invention is by change cylinder
Counterweight quantity, the effect for changing swing rod pendulum length is reached, principle is simply clear and definite, readily appreciates, easily operated, is adapted to College Physics
Teaching.
Brief description of the drawings
Fig. 1 is cylinder counterweight I and cylinder counterweight II of the present invention schematic diagram；
Fig. 2 is the schematic diagram of the present invention tested using cylinder counterweight I；
Fig. 3 is the schematic diagram of Data Processing in Experiment of the present invention；
In figure：1st, cylinder counterweight I；2nd, cylinder counterweight II；3rd, suspension member.
Embodiment
The present invention is further illustrated with a specific embodiment below in conjunction with the accompanying drawings.
As shown in figure 1, it is r that cylinder counterweight I 1, which is radius,1A height of h cylindrical metal body, its upper and lower surface have magnetic
Property, can be closely coupled with the head and the tail of other cylinder counterweights I 1；Cylinder counterweight II 2 is that radius is r2A height of h cylindrical metal
Body, its upper and lower surface equally have magnetic, can be closely coupled with the head and the tail of other cylinder counterweights II 2.The present embodiment chooses n
10, i.e. cylinder counterweight I 1 and cylinder counterweight II 2 form by 10 counterweights, and r2More than r1。
Tested as shown in Fig. 2 forming swing rod using 10 cylinder counterweight I 1, first led to a cylinder counterweight I 1
Cross suspension member 3 to hang up, it is carried out small angle oscillation around the upper surface trunnion axis of itself, measure its hunting period,
Its lower surface connects another cylinder counterweight I 1, is connected by the magnetic stable of upper and lower surface between the two, measures by the two circles
The hunting period for the swing rod that post counterweight I 1 is formed；It is sequentially completed 10 cylinder counterweight I 1 and connects one by one and is formed in the case of swing rod
Hunting period measurement, obtain。
The experimental procedure shown in 10 repetitions of cylinder counterweight II 2 Fig. 2 is chosen, 1 ~ 10 cylinder counterweight II 2 is obtained and forms
Hunting period during swing rod is。
If, corresponding counterweight quantity x y values are calculated, obtain 10 data points：（1,）、
（2,）……（10,）.
As shown in figure 3, using counterweight quantity x as transverse axis, coordinate system is established by the longitudinal axis of y, by data point（X, y）It is plotted in seat
In mark system, it is fitted 10 data points and obtains oblique line, the slope for calculating oblique line is k, is utilized, you can calculate weight
Power acceleration g.
Above example is only a kind of application of experimental provision of the present invention, is not limitation ot it.
The invention provides a kind of experimental method measured using cylinder weight measurement acceleration of gravity, this method passes through survey
The hunting period of the physical pendulum system of the counterweight composition of varying number is measured, and contrasts two groups of radius different height identical cylinder counterweights
The difference of the swing rod hunting period of formation, obtains acceleration of gravity by the slope of fitting data oblique line, has experimental method
Simply, the advantages of data processing is convenient, complicated cumbersome Data Processing in Experiment is avoided, improves the precision of experimental data, easily
In operation, the characteristics of readily appreciating, it is suitable for student's complete independently.
Claims (1)
1. a kind of experimental method using cylinder weight measurement acceleration of gravity, it is characterised in that this method comprises the following steps：
（1）It is r to take n radius1A height of h cylinder counterweight I, one cylinder counterweight I of measurement do small around its top surface horizontal middle spindle
Hunting period during angle swinging, then it is fixedly connected with another cylinder counterweight I one by one in its lower surface, forms multiple cylinders
Counterweight I joins end to end the swing rod of composition, often connects a swing week when swing rod small angle oscillation is measured after a cylinder counterweight I
Phase, if when swing rod is made up of x cylinder counterweight I, the hunting period of swing rod is；
（2）It is r to take n radius2A height of h cylinder counterweight II, it is known that r2More than r1, repeat step 1, if when by x cylinder counterweight
Cycle during the swing rod small angle oscillation of composition is；
（3）If, calculating Correspondent cy linder counterweight quantity x yxValue, obtain n data point：（1,）、
（2,）……（N,）；
（4）Using counterweight quantity x as transverse axis, coordinate system is established by the longitudinal axis of y, by data point（X, y）Draw in a coordinate system, fitting
N data point obtains oblique line, and the slope for calculating oblique line is k；
（5）Utilize, you can calculate gravity acceleration g.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201710949904.2A CN107657874A (en) | 2017-10-13 | 2017-10-13 | A kind of experimental method using cylinder weight measurement acceleration of gravity |
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| CN201710949904.2A CN107657874A (en) | 2017-10-13 | 2017-10-13 | A kind of experimental method using cylinder weight measurement acceleration of gravity |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110930834A (en) * | 2019-11-25 | 2020-03-27 | 齐齐哈尔大学 | Experimental device and method for obtaining liquid level height difference of uniform accelerated motion |
| CN113916359A (en) * | 2021-09-16 | 2022-01-11 | 许昌许继风电科技有限公司 | Vibration switch debugging method and device |
-
2017
- 2017-10-13 CN CN201710949904.2A patent/CN107657874A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110930834A (en) * | 2019-11-25 | 2020-03-27 | 齐齐哈尔大学 | Experimental device and method for obtaining liquid level height difference of uniform accelerated motion |
| CN110930834B (en) * | 2019-11-25 | 2021-10-12 | 齐齐哈尔大学 | Experimental device and method for obtaining liquid level height difference of uniform accelerated motion |
| CN113916359A (en) * | 2021-09-16 | 2022-01-11 | 许昌许继风电科技有限公司 | Vibration switch debugging method and device |
| CN113916359B (en) * | 2021-09-16 | 2023-08-08 | 许昌许继风电科技有限公司 | Vibration switch debugging method and device |
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Application publication date: 20180202 |