Substituting the value of x c into equation (2) Imitation spreading bird Feather Bird Ornament garden living room bonsai decorative bird feather handicraft bird.The collected feathers of many birds are applied with scissors, tweezers, scalpels, magnifying glasses and other objects used for surgery to connect the shape and color of the feathers, so as to carve out the above carved handicrafts with the theme of birds, or birds flying in the air, or birds perching on the branches, so that the small feathers can also become a spectacular handicraft.Simulation bird, fat bird, feather bird, magnetic bird, fridge, foam bird prop, mold, landscape decoration, fake bird. Halloween Supplies,Halloween Leaf Craft,Halloween Craft Hashtags,Halloween Craft Yarn Xintong Craft Gift Co.,LTD , https://www.ychcraft.com
The relationship between the trajectory and the rotation rate of the steel ball and the ball loading rate
The effect of the grinding machine grinding the ore is determined by its rate of rotation, the rate of loading and the relationship between the two. Obviously these are related to the movement of the steel ball. In order to solve these problems, we must start from analyzing the movement of the steel ball, and based on the clarification of their movement trajectory, step by step how to correctly select the rotation rate and the ball loading rate.
First, the equation of circular motion and the equation of parabolic motion
As shown in the following figure (1), taking the point of departure A as the origin and taking the xAy coordinate, the equation of the center of the circle at the center of the mill and the circle of radius R is
(X-Rsina) 2 +(y+Rcosa) 2 =R 2 ( 1 )
The ball is thrown from the point A at the line speed when the mill is running. According to the parabola drop, the horizontal distance (x) and the vertical distance (y) are respectively
Figure 1 Â The circular motion of the ball and the parabolic trajectory
Substituting the value of t to get
It can be known that the work style:
This is the parabolic equation in which the ball in xAy is parabolic.
Second, the coordinates of the special points on the parabola
In order for the parabola to be accurately drawn, it is necessary to determine the coordinates of its highest point C, its intersection with the x-axis D, and the return point B.
Determine the coordinates of point C: because of this, take the derivative of formula (2) and make it equal to zero, you can find the coordinates x c and y c of point C.
Determine the coordinates of point D: because point D is the intersection of the parabola and the x-axis, so [next]
yD=0 ( 5 )
Can be obtained by formula (2)
Determine the coordinates of point B: point B is the end point of the ball drop, and it is the point at which it starts circular motion, so its coordinates x B and y B are the common solutions when formulas (1) and (2) are joined together. Substituting y in equation (2) into equation (1), and then gradually simplifying it to get
Among them, its three roots x 1 = x 2 = x 3 =0, that is, the coordinate origin A of the intersection of the two tracks. in
In the middle, the fourth root is the x coordinate of the falling point B, that is,
x B =4Rsinacos 2 a ( 7 )
Substituting the value of x B into equation (2), find
Ya=-4Rsin 2 acosa ( 8 )
Comparing equations (7) and (6), it can be seen
x B = 2x D
Comparing equations (7) and (8) with equations (3) and (4), it can be seen
When the departure angle a is known, the coordinates of each special point can be calculated from the above equations, and the parabola when the motion is dropped can be accurately drawn.
If the XOY system with O as the origin is used to represent the coordinates of the return point B, the formulas (7) and (8) are rewritten according to the shift axis rule (the new coordinate is equal to the old coordinate of the old coordinate minus the origin).
The falling angle (β, the angle between the center of the steel ball and the center of the mill and the X axis) can be found as
Some researchers, such as Gow, believe that each ball receives the thrust of the ball behind it as it reaches the point of disengagement. Therefore, the rise is higher than the point of separation, and the parabolic fall is farther than the Davis theory. Although Gao Wu proposed another calculation formula based on this method, it has not been recognized, and Davis theory and actual data are still roughly consistent.
Prev Article
Human resource management system