A new type of Newton cradle device

Abstract

The invention belongs to the technical field of scientific toys, and discloses a novel Newton's pendulum device, comprising a bracket and a pendulum ball, wherein the pendulum ball is composed of n+1 A pendulum balls and n B pendulum balls, where n≥1 and is an integer; the A pendulum ball and the B pendulum ball are made of the same material, the radius of the A pendulum ball is R, the mass is M, the radius of the B pendulum ball is r, the mass is m, or each pendulum ball is suspended on the bracket by a line, the A pendulum ball and the B pendulum ball are arranged at intervals, the ball centers of the A pendulum ball and the B pendulum ball are located on the same horizontal line and the horizontal line is perpendicular to the line for suspending the pendulum ball, and the distance between the ball centers of adjacent pendulum balls is R+r. The novel Newton's pendulum device of the invention can achieve the same motion effect as the traditional Newton's pendulum.

Description

Technical Field

[0001] The invention belongs to the technical field of scientific toys, and in particular relates to a novel Newton's cradle device. Background Art

[0002] Newton's cradle was first proposed by French physicist Edme Mariette in 1676. It is also called Newton's cradle ball, momentum conservation pendulum ball, perpetual motion ball, physics billiards and bumper ball.

[0003] like Figure 1 As shown in the figure, Newton's cradle is generally composed of 5 metal balls 4 of the same size and a bracket 1. Each metal ball is suspended on the bracket by two thin wires, and the two wires form a certain angle, so that the metal balls just touch each other. When the ball on the far right swings and hits other balls, only the ball on the far left will be ejected; when the two balls on the far right swing and hit other balls at the same time, only the two balls on the far left will be ejected; the ejected balls immediately rebound, and the cycle repeats, making a clicking sound, which is very interesting.

[0004] Newton's cradle is a scientific toy suitable for all ages. It involves important scientific concepts such as elastic collision, conservation of momentum, and conservation of mechanical energy. It often makes people love it and linger on.

[0005] However, throughout history, the masses of the pendulum balls in the Newton's pendulum device are equal. Because when the pendulum balls of equal mass undergo a one-dimensional concentric elastic collision, according to the law of conservation of momentum and the law of conservation of mechanical energy, it can be concluded that the two balls must exchange speeds. The adjacent pendulum balls of equal mass in the Newton's pendulum device undergo elastic collisions in sequence, exchange speeds, and finally achieve the speed exchange of the corresponding pendulum balls on both sides. It is very necessary to further study the structure of the pendulum balls in the Newton's pendulum device in order to improve the structure of the Newton's pendulum device and increase the fun of the Newton's pendulum device. Summary of the invention

[0006] In view of the above situation, the purpose of the present invention is to provide a new type of Newton's cradle device, which uses cradle balls with different masses and radii to achieve the same movement effect as the traditional Newton's cradle.

[0007] The present invention provides a novel Newton's cradle device, comprising a bracket and a cradle ball, wherein the cradle ball is composed of n+1 A cradle balls and n B cradle balls, where n≥1 and is an integer;

[0008] The material of pendulum A and pendulum B is the same. The radius of pendulum A is R and the mass is M. The radius of pendulum B is r and the mass is m.

[0009] or

[0010] Each pendulum ball is suspended on a bracket by a line, and pendulum ball A and pendulum ball B are arranged at intervals. The centers of pendulum ball A and pendulum ball B are located on the same horizontal line and the horizontal line is perpendicular to the line for hanging the pendulum balls, and the distance between the centers of adjacent pendulum balls is R+r.

[0011] According to a specific implementation of the present invention, the pendulum ball is composed of three A pendulum balls and two B pendulum balls, and each pendulum ball is suspended on a bracket by a line.

[0012] According to another specific embodiment of the present invention, the pendulum ball is composed of 3 A pendulum balls and 2 B pendulum balls, each pendulum ball is suspended on a bracket by two lines of equal length, and the suspension points of the two lines on the bracket are symmetrically arranged on both sides of the pendulum ball.

[0013] For the traditional Newton cradle device, since the masses of the balls are equal, the adjacent balls can exchange speeds by simply colliding with each other in sequence. Figure 2 The Newton's cradle device with three cradle balls shown is used as a research model to verify the feasibility of the novel Newton's cradle device of the present invention.

[0014] exist Figure 2 In the figure, the masses of ball A5, ball B6 and ball C7 are M1, m1 and M1 respectively, and M1>m1. The incident velocity of ball A is v0. Then a series of elastic collisions will occur between ball A and ball B, ball B and ball C, ball B and ball A, and ball B and ball C in sequence.

[0015] 1.1 The first collision between balls A and B

[0016] In the first elastic collision between ball A and ball B, taking the system composed of ball A and ball B as the research object, the law of conservation of momentum and the law of conservation of mechanical energy yields:

[0017] M1v0=M1v 甲1 +m1v 乙1 (1)

[0018]

[0019] From equations (1) and (2), we can get that the final velocities of balls A and B after their first collision are:

[0020]

[0021]

[0022] 1.2 Balls B and C collide for the first time

[0023] In the first elastic collision between ball B and ball C, the system composed of ball B and ball C is taken as the research object. According to the law of conservation of momentum and the law of conservation of mechanical energy, we get:

[0024] m1v 乙1 =m1v 乙2 +M1v 丙1 (5)

[0025]

[0026] From equations (4), (5), and (6), we can get that the final velocities of balls B and C after their first collision are:

[0027]

[0028]

[0029] 1.3 Balls B and A collide for the second time

[0030] In the second elastic collision between ball B and ball A, taking the system composed of ball B and ball A as the research object, the law of conservation of momentum and the law of conservation of mechanical energy yields:

[0031] m1v 乙2 +M1v 甲1 =m1v 乙3 +M1v 甲2 (9)

[0032]

[0033] From equations (3), (7), (9), and (10), we can get that the final velocity of balls B and A after the second collision is:

[0034]

[0035]

[0036] 1.4 Balls B and C collide for the second time

[0037] In the second elastic collision between ball B and ball C, taking the system composed of ball B and ball C as the research object, the law of conservation of momentum and the law of conservation of mechanical energy yields:

[0038] m1v 乙3 +M1v 丙1 =m1v 乙4 +M1v 丙2 (13)

[0039]

[0040] From equations (8), (12), (13), and (14), we can get that the final velocities of balls B and C after the second collision are:

[0041]

[0042]

[0043] 1.5 Balls B and A collide for the third time

[0044] In the third elastic collision between ball B and ball A, taking the system composed of ball B and ball A as the research object, the law of conservation of momentum and the law of conservation of mechanical energy yields:

[0045] m1v 乙4 +M1v 甲2 =m1v 乙5 +M1v 甲3 (17)

[0046]

[0047] From equations (11), (15), (17), and (18), we can get that the final velocity of balls B and A after the second collision is:

[0048]

[0049]

[0050] 1.6 Balls B and C collide for the third time

[0051] In the third elastic collision between ball B and ball C, taking the system composed of ball B and ball C as the research object, the law of conservation of momentum and the law of conservation of mechanical energy yields:

[0052] m1v 乙5 +M1v 丙2 =m1v 乙6 +M1v 丙3 (twenty one)

[0053]

[0054] From equations (16), (20), (21), and (22), we can get that the final velocity of balls B and A after the second collision is:

[0055]

[0056]

[0057] 2.1 According to equations (11) and (15), if ball B achieves the velocity exchange between ball A and ball C after four elastic collisions, the mass ratio of the large mass ball (ball A, ball C) to the small mass ball (ball B) must satisfy:

[0058] m1 2 +4m1M1-M1 2 =0 (25)

[0059] From equation (25), we can get that after four elastic collisions, ball B realizes the velocity exchange between ball A and ball C. The mass ratio of the large mass ball to the small mass ball is:

[0060]

[0061] Obviously, the masses of the balls in Newton's cradle do not have to be equal. If the large mass balls and the small mass balls are arranged alternately and the mass ratio between the large mass balls and the small mass balls is 4.236, the speed exchange between the balls on both sides of Newton's cradle can also be achieved.

[0062] In this case, the two adjacent balls cannot exchange speeds directly due to their different masses, but for the large mass balls on both sides of the small mass ball, the speed exchange is achieved after four elastic collisions with the small mass ball in the middle. Although the number of collisions is twice that of a normal Newton cradle, the difference cannot be observed with the naked eye due to the extreme time of each collision.

[0063] 2.2 According to equations (19) and (23), we can find that the condition for both ball A and ball B to be stationary is:

[0064] 9M1 2 m1+M1m1 2 -M1 3 -m1 3 =0 (27)

[0065] From equation (27), we can get that the mass ratio of ball A and ball B that can make both ball A and ball B stationary after 6 collisions of ball B is:

[0066]

[0067] make Then equation (28) can be transformed into:

[0068] x 3 -9x 2 -x+1=0 (29)

[0069] Since equation (29) has no real number solution, its numerical solution is obtained using Mathematica:

[0070]

[0071] It can be seen that if the large mass ball and the small mass ball are arranged alternately, and the mass ratio of the large mass ball to the small mass ball is 9.098, the speed exchange between the balls on both sides of the Newton's cradle can also be achieved.

[0072] In this case, the two adjacent balls cannot exchange speeds directly due to their different masses, but for the large mass balls on both sides of the small mass ball, the speed exchange is achieved after six elastic collisions with the small mass ball in the middle. Although the number of collisions is three times that of a normal Newton cradle, the difference cannot be observed with the naked eye due to the extreme time of each collision.

[0073] According to the feasibility verification process, the masses of the pendulum balls in the Newton's pendulum device do not have to be the same. If the large-mass pendulum balls and the small-mass pendulum balls are distributed at intervals, the large-mass pendulum balls are located on both sides, and the mass ratio of the large-mass pendulum balls to the small-mass pendulum balls is 4.236 or 9.098, the pendulum balls on both sides of the Newton's pendulum can also achieve speed exchange, achieving the same motion effect as the traditional Newton's pendulum. If the large-mass pendulum balls and the small-mass pendulum balls are made of the same material, according to the mass ratio, it can be calculated that the radius ratio of the two is 1.618 and 2.088. The number of pendulum balls of the Newton's pendulum device can be expanded to 5 or even more. Therefore, the novel Newton's pendulum device structure of the present invention is feasible and can achieve the same motion effect as the traditional Newton's pendulum. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a schematic diagram of the structure of a Newton's cradle device in the prior art.

[0075] Figure 2 It is a schematic diagram of the structure of the principle research model of the novel Newton's cradle device of the present invention.

[0076] Figure 3 Schematic diagram of the structure of the novel Newton's cradle device of Example 1.

[0077] Figure 4 Schematic diagram of the structure of the novel Newton's cradle device of Example 2. DETAILED DESCRIPTION

[0078] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0079] Example 1

[0080] like Figure 3 As shown, a novel Newton's pendulum device comprises a bracket 1 and a pendulum ball, wherein the pendulum ball is composed of three A pendulum balls 2 and two B pendulum balls 3;

[0081] A pendulum ball 2 and B pendulum ball 3 are made of the same material. The radius of A pendulum ball 2 is R and the mass is M. The radius of B pendulum ball 3 is r and the mass is m.

[0082]

[0083] Each pendulum ball is suspended on the bracket 1 by a line, and the pendulum ball A 2 and the pendulum ball B 3 are arranged at intervals. The centers of the pendulum balls A 2 and B 3 are located on the same horizontal line and the horizontal line is perpendicular to the line for hanging the pendulum balls. The distance between the centers of adjacent pendulum balls is R+r.

[0084] Example 2

[0085] like Figure 4 As shown, a novel Newton's pendulum device comprises a bracket 1 and a pendulum ball, wherein the pendulum ball is composed of three A pendulum balls 2 and two B pendulum balls 3;

[0086] A pendulum ball 2 and B pendulum ball 3 are made of the same material. The radius of A pendulum ball 2 is R and the mass is M. The radius of B pendulum ball 3 is r and the mass is m.

[0087]

[0088] Each pendulum ball is suspended on the bracket 1 by two lines of equal length, and the suspension points of the two lines on the bracket 1 are symmetrically arranged on both sides of the pendulum ball. The pendulum ball A 2 and the pendulum ball B 3 are arranged at intervals, and the centers of the pendulum ball A 2 and the pendulum ball B 3 are located on the same horizontal line and the horizontal line is perpendicular to the line for suspending the pendulum balls, and the distance between the centers of adjacent pendulum balls is R+r.

[0089] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A novel Newton's cradle device, comprising a bracket and a cradle ball, characterized in that: The pendulum balls are composed of n+1 A pendulum balls and n B pendulum balls, where n≥1 and is an integer; The material of pendulum A and pendulum B is the same. The radius of pendulum A is R and the mass is M. The radius of pendulum B is r and the mass is m. or Each pendulum ball is suspended on a bracket by a line, and pendulum ball A and pendulum ball B are arranged at intervals. The centers of pendulum ball A and pendulum ball B are located on the same horizontal line and the horizontal line is perpendicular to the line for hanging the pendulum balls, and the distance between the centers of adjacent pendulum balls is R+r.

2. The novel Newton's cradle device according to claim 1, characterized in that: The pendulum ball consists of three A pendulum balls and two B pendulum balls, and each pendulum ball is suspended on a bracket through a line.

3. The novel Newton's cradle device according to claim 1, characterized in that: The pendulum ball is composed of 3 A pendulum balls and 2 B pendulum balls. Each pendulum ball is suspended on a bracket through two lines of equal length. The suspension points of the two lines on the bracket are symmetrically arranged on both sides of the pendulum ball.

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