CN104537933A - Angular momentum conservation law experiment instrument - Google Patents

Abstract

The invention discloses an experimental instrument for the law of conservation of angular momentum, which comprises a base, a vertical plate, a rotating shaft, a straight rod, and a pendulum ball. The rod is a thin rod with uniform cross-section. One end of the straight rod is fixed on the rotating shaft and can rotate freely around the rotating shaft in the vertical plane. The pendulum ball is connected with the rotating shaft through a cycloid whose length is adjustable. The height markings at the height positions before and after the collision between the ball and the straight rod. The invention can cooperate with the teaching of rigid body mechanics to visually and conveniently verify the law of conservation of angular momentum, which is beneficial to deepening students' understanding of the process and law of rigid body collisions.

Description

Experimental instrument for the law of conservation of angular momentum

technical field

The invention belongs to the field of physical experiment instruments, and relates to a mechanical experiment device, in particular to an experimental instrument for the law of conservation of angular momentum used for studying rigid body collisions.

Background technique

The collision of rigid bodies is a common problem in rigid body mechanics, for example, the collision between a stick and a ball. During the collision process, the rigid body follows the law of conservation of angular momentum, and if it is an elastic collision, it also follows the law of conservation of mechanical energy. At present, there is a lack of an experimental device to realize the collision of rigid bodies and verify the law of conservation of angular momentum.

Contents of the invention

The purpose of the present invention is to design a kind of experimental instrument for the law of conservation of angular momentum, which can realize the collision of rigid bodies and verify the law of conservation of angular momentum.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions: including a base, a vertical plate, a rotating shaft, a straight rod, and a pendulum ball; the vertical plate is rectangular, and the vertical plate is vertically fixed on the base; The straight rod is a thin rod with uniform cross-section, one end of the straight rod is fixed on the rotating shaft and can rotate freely around the rotating shaft in the vertical plane; the pendulum ball is connected to the rotating shaft through a cycloid, and the length of the cycloid is adjustable; Determine the equally spaced height markings of the height positions before and after the collision between the pendulum ball and the straight rod.

The present invention also includes a swing control unit for swinging the ball. The swing control unit includes a guide rail, a telescopic rod, an electromagnet, and an electromagnet controller. To move, the other end of the telescopic rod is connected with an electromagnet for absorbing the pendulum ball, and the electromagnet controller is electrically connected with the electromagnet for controlling the absorption and release of the pendulum ball.

Preferably, the length of the cycloid is equal to the length of the straight rod, and the mass of the straight rod is 2.45 times the mass of the pendulum ball.

Due to the adoption of the above design, the present invention can produce the following beneficial effects: adjusting the length of the cycloid can control the collision point between the pendulum ball and the straight rod; height of ascent. The invention indirectly measures the magnitude of the angular momentum with an intuitive and readable physical quantity, thereby verifying the law of conservation of angular momentum, which greatly simplifies the difficulty of verification. The invention can cooperate with the teaching of rigid body mechanics, and through the collision of rigid bodies, the law of conservation of angular momentum can be verified intuitively and conveniently, which is beneficial to deepening students' understanding of the process and laws of rigid body collisions.

Description of drawings

The present invention will be further described below in conjunction with accompanying drawing.

Fig. 1 is a schematic diagram of the structure of the present invention.

Fig. 2 is a measurement schematic diagram of the present invention.

In the figure: 1. Base, 2. Vertical plate, 3. Rotating shaft, 4. Straight rod, 5. Swing ball, 6. Swing control unit, 11. Leveling screw, 21. Height marking line, 51. Cycloid, 61 . guide rail, 62. telescopic rod, 63. electromagnet, 64. electromagnet controller.

Detailed ways

As shown in FIG. 1 , the present invention includes a base 1 , a vertical plate 2 , a rotating shaft 3 , a straight rod 4 , and a pendulum ball 5 . The vertical board 2 is rectangular, and the vertical board 2 is vertically fixed on the base 1 . The rotating shaft 3 is vertically fixed on the middle and upper part of the vertical plate 2. The straight rod 4 is a homogeneous and equal-section thin rod, and one end of the straight rod 4 is fixed on the rotating shaft 3 and can freely rotate around the rotating shaft 3 in a vertical plane. The pendulum ball 5 is connected with the rotating shaft 3 by a cycloid 51, and the length of the cycloid 51 is adjustable. The vertical plate 2 is provided with equally spaced height marking lines 21 for determining the height positions before and after the collision between the pendulum ball 5 and the straight rod 4 . A leveling screw 11 for adjusting the level of the base 1 is provided under the base 1 .

The present invention also comprises the swing control unit 6 of pendulum ball 5, and swing control unit 6 comprises guide rail 61, telescoping rod 62, electromagnet 63, electromagnet controller 64, and guide rail 61 is fixed on the upper right part of stand plate 2, and telescopic rod 62 One end is movably connected to the guide rail 61 and can move back and forth along the guide rail 61 , and the other end of the telescopic rod 62 is connected with an electromagnet 63 for absorbing the pendulum ball 5 . The electromagnet controller 64 is electrically connected with the electromagnet 63 and is used to control the adsorption and release of the pendulum ball 5: the electromagnet 63 generates magnetism to absorb the pendulum ball 5 when the power is turned on, and the pendulum ball 5 releases to swing downward when the power is off. When using the swing control unit 6, the swing ball 5 is an iron ball.

Preferably, the length of the cycloid 51 is equal to the length of the straight rod 4 , and the mass of the straight rod 4 is 2.45 times the mass of the pendulum ball 5 .

Refer to Figure 2 for the principle of measurement and verification. In this embodiment, the mass of the pendulum 5 is m ₁ , the mass of the straight bar 4 is m ₂ , the lengths of the cycloid 51 and the straight bar 4 are both L, and the height of the pendulum 5 when it swings is h ₀ , the rebound height of the pendulum ball 5 after elastic collision with the straight rod 4 is h ₁ , and the rising height of the end of the straight rod 4 is h ₂ .

According to the law of conservation of angular momentum, there are:

m ₁ v ₁ L＝Jω-m ₁ v ₂ L, namely

Jω＝m ₁ L(v ₂ -v ₁ )(1)

In the formula, v ₁ and v ₂ are respectively the velocity before and after the collision between the pendulum ball 5 and the straight rod 4 , and J is the moment of inertia of the straight rod 4 around the rotation axis 3 .

According to the law of conservation of mechanical energy, there are:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; gh</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; gh</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Depend on $\frac{1}{2}{\mathrm{J\&omega;}}^2=\frac{1}{2}{m}_2{\mathrm{gh}}_2,J=\frac{1}{3}{m}_2{L}^2$ have to:

$\mathrm{<span\; class="notranslate">\; J\&omega;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; gh</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Substituting (2), (3) and (4) into (1), we get:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\sqrt{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Preferably, when That is, when the quality of the straight rod 4 is 2.45 times of the quality of the swing ball 5, the (5) formula can be simplified as:

$\sqrt{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

During the experiment, read the values of h ₀ , h ₁ , and h ₂ in Fig. 2 through the height marking line 21, and the law of conservation of angular momentum can be verified by formula (6).

When the length of the cycloid 51 is shorter than the length of the straight rod 4, the corresponding theoretical conclusions can also be obtained according to the law of conservation of angular momentum, and verified by this instrument, which will not be further discussed here.

Claims (3)

1. a kind of experimental instrument for the law of conservation of angular momentum is characterized in that: comprise base (1), vertical plate (2), rotating shaft (3), straight bar (4), pendulum ball (5); Described vertical plate (2) ) is a rectangle, and the vertical plate (2) is vertically fixed on the base (1); the rotating shaft (3) is vertically fixed on the middle and upper part of the vertical plate (2); ) one end is fixed on the rotating shaft (3) and can freely rotate around the rotating shaft (3) in a vertical plane; the pendulum ball (5) is connected with the rotating shaft (3) through a cycloid (51), and the length of the cycloid (51) is adjustable; The vertical plate (2) is provided with equally spaced height marking lines (21) for determining the height positions before and after the collision between the pendulum ball (5) and the straight rod (4). 2. the law of conservation of angular momentum experimental instrument according to claim 1, is characterized in that: also comprise the swing control unit (6) of pendulum ball (5), and swing control unit (6) comprises guide rail (61), telescopic link ( 62), electromagnet (63), electromagnet controller (64), guide rail (61) is fixed on the upper right part of vertical plate, and one end of telescoping link (62) is movably connected on guide rail (61) and can follow guide rail (61) Move back and forth, the other end of telescopic rod (62) connects electromagnet (63) and is used to absorb pendulum ball (5), and electromagnet controller (64) is electrically connected with electromagnet (63) and is used to control the pendulum ball (5) Adsorption and release. 3. the law of conservation of angular momentum experimental instrument according to claim 1, is characterized in that: the length of described cycloid (51) equals the length of straight rod (4), and the quality of described straight rod (4) is pendulum ball (5) 2.45 times the mass.