Gravity acceleration measuring device

Abstract

To provide a gravity acceleration measuring device that can measure gravitational acceleration simply and accurately with a simple configuration. [Solution] The gravitational acceleration measuring device comprises a ring pendulum having a constant width and thickness, a knife edge having a straight tip, and a stand for fixing the knife edge with the tip pointing upward and horizontal. By hanging the inner surface of the ring pendulum on the tip of the knife edge and suspending the ring pendulum, and observing the pendulum motion of the ring pendulum with the tip as the fulcrum, the gravitational acceleration can be measured simply and accurately.

Description

[Technical Field]

[0001] This invention relates to a device for measuring gravitational acceleration using a pendulum. [Background technology]

[0002] The gravity (gravitational acceleration) observed on Earth varies slightly depending on the latitude of the observation point. For example, at the North Pole, it is approximately 9.83 m / s². 2 Near the equator, the velocity is approximately 9.76 m / s. 2 Gravitational acceleration is observed. This difference in gravitational acceleration is due to the influence of centrifugal force caused by the Earth's rotation. In addition to centrifugal force caused by the Earth's rotation, gravitational acceleration is also known to be affected by the altitude of the observation site, the density structure of the subsurface, and even the gravitational pull of celestial bodies such as the Moon and the Sun.

[0003] One common theme in physics experiments at universities and other institutions is "measuring gravitational acceleration using a pendulum." A Borda pendulum, as shown in Figure 1, is one such device for measuring gravitational acceleration. Because such a Borda pendulum allows for the simple measurement of gravitational acceleration from the pendulum's period, it is widely used in physics experiments at universities and other institutions. In experiments using this Borda pendulum, the pendulum's weight is treated as a rigid body, and gravitational acceleration can be measured based on short-amplitude free pendulum motion, taking its moment of inertia into account. Through such experiments, students can deepen their understanding of rigid body motion. [Overview of the project] [Problems that the invention aims to solve]

[0004] In the aforementioned model of the equation of motion for the Borda pendulum, only the pendulum weight is treated as a rigid body, and its moment of inertia is defined accordingly. However, the suspension wires that suspend the weight and the knife-edge that swings with the weight are not taken into account in the calculation of the pendulum's moment of inertia. Therefore, the effects of these components become a source of error in accurately measuring gravitational acceleration. Furthermore, conventional Borda pendulums have suspension wires that are typically 1 meter or longer, which presents challenges such as limitations on the transport and installation locations of the device.

[0005] Therefore, the present invention aims to provide a gravitational acceleration measuring device that can measure gravitational acceleration simply and accurately with a simple configuration, or to provide a method for measuring gravitational acceleration simply and accurately using such a device. [Means for solving the problem]

[0006] To solve the above-mentioned problems, the present invention provides a gravity acceleration measuring device comprising: an annular pendulum having a certain width and thickness; a knife edge having a straight tip; and a stand for fixing the knife edge with the tip pointing upward and horizontal. The device is configured to measure gravity acceleration by suspending the annular pendulum by placing the inner surface of the annular pendulum on the tip of the knife edge and observing the pendulum motion of the annular pendulum with the tip as the fulcrum.

[0007] In the gravity acceleration device, it is preferable that the knife edge is cantilevered and fixed to the stand.

[0008] Furthermore, it is preferable that the gravity acceleration device is further equipped with an adjustment mechanism on the stand for fine-tuning the posture of the knife edge. [Effects of the Invention]

[0009] According to the present invention, it is possible to provide a gravity acceleration measuring device that can measure gravitational acceleration simply and accurately with a simple configuration. [Brief explanation of the drawing]

[0010] [Figure 1] These are front and side views of a conventional Borda pendulum. [Figure 2] This is a front view of a gravity acceleration measuring device according to an embodiment of the present invention. [Figure 3] Figure 2 is a side view of the gravity acceleration measuring device. [Figure 4] This figure shows a magnified view of the observation method in Figure 2. [Figure 5] This diagram illustrates the equations of motion model for a typical rigid body undergoing pendulum motion. [Figure 6] This diagram illustrates the equation of motion model for a rigid cylindrical body (annular pendulum) undergoing pendulum motion. [Modes for carrying out the invention]

[0011] <Configuration of a gravity acceleration measuring device> Figure 2 is a front view of a gravity acceleration measuring device 1 according to a preferred embodiment of the present invention. Figure 3 is a side view of the gravity acceleration measuring device 1. The gravity acceleration measuring device 1 basically comprises an annular pendulum 2, a knife edge 3 that supports the inner circumferential surface 2A of the annular pendulum 2 at an arbitrary position, and a stand 4 that fixes the knife edge 3.

[0012] The annular pendulum 2 is an annular pendulum (weight) having a constant width and thickness. The annular pendulum 2 can be formed by cutting a metal plate, such as an aluminum alloy, into a disc shape on a lathe, and then rotating and cutting the inner circumferential surface 2A without changing the position of the main spindle, so that the center of the circle of the outer circumferential surface 2B and the center of the circle of the inner circumferential surface 2A coincide, i.e., forming an annular shape with a constant width. The concentricity between the outer circumferential surface 2B and the inner circumferential surface 2A of the annular pendulum 2 is preferably 0.05 mm or less.

[0013] The knife edge 3 is a triangular prism-shaped metal member extending with a straight tip 31. The knife edge 3 can be manufactured from, for example, an aluminum alloy. The knife edge 3 is cantilevered and horizontally fixed to the support column 41 of the stand 4, with its tip 31 facing upwards. The direction in which the tip 31 of the knife edge 3 extends is precisely perpendicular to the longitudinal direction of the support column 41.

[0014] The stand 4 is composed of a support column 41 and a tabletop 42 that vertically fixes the support column 41. The longitudinal direction of the support column 41 and the flat upper surface 42A of the tabletop 42 are precisely perpendicular to each other.

[0015] As described above, the horizontal direction in which the tip 31 of the knife edge 3 extends and the longitudinal direction (vertical direction) of the support column 41 are precisely perpendicular, and the vertical direction in which the support column 41 extends and the upper surface 42A of the tabletop 42 are precisely perpendicular, so that the tip 31 of the knife edge 3 and the upper surface 42A of the tabletop 42 are highly parallel. Preferably, the degree of parallelism between the tip 31 of the knife edge 3 and the upper surface 42A of the tabletop 42 is 0.1 mm or less.

[0016] The stand 4 preferably has an adjustment mechanism 5 for fine-tuning the horizontal position of the knife edge 3. The adjustment mechanism 5 can be configured as a plurality of adjustment screws 51, 51 that are screwed into multiple positions on the tabletop 42, as shown in Figures 2 and 3. In the illustrated embodiment, the adjustment screws 51, 51 also function as variable length legs of the stand 4 (tabletop 42). For example, by installing a spirit level on the tabletop 42 and appropriately turning the adjustment screws 51, 51 to adjust the upper surface 42A of the tabletop 42 to be horizontal, the knife edge 3 parallel to the tabletop 42 can be precisely adjusted to be horizontal. In this embodiment, it is sufficient that such adjustment screws 51 are provided in at least three or more locations on the tabletop 42, and it is more preferable that four screws be provided at each of the four corners of the tabletop 42.

[0017] The gravitational acceleration measuring device 1 according to this embodiment includes an observation means 6 for observing the period of the annular pendulum 2 that performs a free pendulum motion with the tip 31 of the knife edge 3 as a fulcrum. For example, the observation means 6 of the embodiment shown in FIG. 4 can include a scale line 61 scratched on the front surface of the annular pendulum 2 and a scale (graduation) 62 provided on the support portion 41.

[0018] The inner peripheral surface 2A of the annular pendulum 2 is hung on the tip 31 of the knife edge 3 and suspended. As a result, the annular pendulum 2 can perform a free pendulum motion with the tip 31 of the knife edge 3 as a fulcrum. At the bottom dead center when the annular pendulum 2 performs a pendulum motion, the annular pendulum 2 is hung on the knife edge 3 so that the scale line 61 points to exactly the center (scale "0" in FIG. 4) of the scale 62 directly below it.

[0019] As an example of the observation means 6, for example, a stopwatch can be used to visually measure the period of the annular pendulum 2. When visually measuring the period of the annular pendulum 2, it is preferable to calculate the period from the average value of the time required for a plurality of pendulum vibrations.

[0020] Also, as another example, the observation means 6 may include a video camera (imaging device) 63. Even in this case, the state of the pendulum vibration can be photographed and recorded with the video camera 63, and the period can be measured from the time of a plurality of pendulum vibrations.

[0021] <Principle of Measuring Gravitational Acceleration> Next, the principle of measuring gravitational acceleration using the gravitational acceleration measuring device 1 will be described. First, consider the pendulum motion of a general rigid body. As shown in FIG. 5, the equation of motion when an object (rigid body) performs a pendulum vibration with O as a fulcrum is given by Equation (1).

Equation

[0022] When the angle of deflection θ is a small angle (when it can be approximated as sinθ = θ), Solving equation (1), the angular velocity ω = dθ / dt is expressed by the following equation (2).

number

[0023] Furthermore, from equation (2), the period T of the oscillation can be expressed by the following equation (3).

number

[0024] According to equation (3), the acceleration due to gravity g can be calculated using the period T of the object in the following equation (4).

number

[0025] Next, we will consider the motion of a cylindrical body (annular pendulum 2) as shown in Figure 6. First, the moment of inertia I when a cylindrical body rotates around its center of gravity G. G This is given by equation (5).

number

[0026] In the case of the gravitational acceleration measuring device 1 of this embodiment, when the annular pendulum 2 (cylindrical body) rotates around the pivot point O, its moment of inertia Io is expressed by the following equation (6), which is obtained by applying the parallel axis theorem to equation (5).

number

[0027] Therefore, the gravitational acceleration g obtained by the gravitational acceleration measuring device 1 of the present embodiment can be obtained using the following formula (7) obtained by substituting formula (6) into formula (4).

Equation

Example

[0028] In this example, each member of the gravitational acceleration measuring device 1 was manufactured from an aluminum alloy, and a measurement experiment of the gravitational acceleration was conducted using this. The height of the manufactured gravitational acceleration device 1 is approximately 500 mm, and the width is approximately 200 mm. The size of the annular oscillator 2 is such that the outer diameter (= 2a) is 205.91 mm and the inner diameter (= 2b) is 177.94 mm.

[0029] In this experiment, the period of the annular oscillator 2 was observed by the following two methods. <Method 1 Visual observation> The time T 100 required for 100 pendulum oscillations was measured using a stopwatch, and then the period T = T 100 / 100 was obtained. <Method 2 Observation by video camera> The state of the pendulum oscillation was recorded by a video camera 63, and the time T 100 required for 100 pendulum oscillations was measured from the images reproduced frame by frame, and the period T = T 100 / 100 was obtained.

[0030] The actual measurement results are shown in Table 1.

Table 1

[0031] Applying four significant figures of the vibration measurement time, the gravitational acceleration value obtained in this experiment was concluded to be the following values. Visual: 9.805 m / s 2 2 Video: 9.802 m / s

[0032] According to the Geospatial Information Authority of Japan's gravity value estimation calculation site (https: / / vldb.gsi.go.jp / sokuchi / gsigra / calc / ), the gravitational acceleration value near this experimental site is 9.797517 m / s². 2 The results were as follows. The errors and error rates shown in Table 1 are based on these estimated calculated values ​​as the true values. These results in Table 1 confirm that sufficient measurement accuracy can be obtained even when this gravity acceleration device 1 is used to measure gravity acceleration in physics experiments at universities and other institutions.

[0033] As described above, the gravity acceleration measuring device 1 of this embodiment uses only a ring-shaped pendulum 2 as the pendulum (weight), and eliminates as many components that could cause measurement errors as possible, thereby enabling simple and accurate measurement of gravity acceleration. Furthermore, since the gravity acceleration measuring device 1 is highly portable and not limited by installation location, it is expected to be applicable to comparative experiments on gravity acceleration in various locations. [Explanation of Symbols]

[0034] 1 Gravitational acceleration measuring device 2. Ring pendulum 2A Inner surface 2B Outer surface 3. Knife edge 4 Stands 5 Adjustment mechanism 6. Observation methods 31 Point 41 Pillar section 42 Table section 42A Top 51 Adjustment screw 61 Marked line 62 scale 63. Video camera (recording device)

Claims

1. A device for measuring gravity acceleration, The device comprises an annular pendulum having a certain width and thickness, a knife edge having a straight tip, and a stand for fixing the knife edge with the tip pointing upward and horizontal. A gravity acceleration measuring device configured to measure gravitational acceleration by hanging the inner surface of the annular pendulum on the tip of the knife edge, suspending the annular pendulum, and observing the pendulum motion of the annular pendulum with the tip as the fulcrum.

2. The gravity acceleration measuring device according to claim 1, wherein the knife edge is cantilevered and fixed to the stand.

3. The gravity acceleration measuring device according to claim 1 or 2, further comprising an adjustment mechanism for fine-tuning the posture of the knife edge on the stand.

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