Will your gravity affect your billiard game?

Consider this diagram in terms of area. The area covered by the blue data in the picture (hit 2 balls) is much larger than the area on the picture that shows the speed required to hit 3 balls.Things become a lot of It is more difficult to achieve a collision involving all four balls.

Let’s make one more. What if I add a 4-ball to the collision chain?

To be clear, this is a comparison of the initial cue ball speed range that resulted in 3 balls hitting 4 balls. Let me review some rough ranges of the initial velocity of the cue ball.

In order to make 1 ball hit 2 balls, the x speed can be from close to 0 m/s to 1 m/s. (I did not calculate speeds greater than 1 m/s.) The y speed may be between 0.02 and 0.18 m/s. That is, the x speed range is 1 m/s, and the y speed range is about 0.16 m/s.

In order to make 2 balls hit 3 balls, the x speed can be from 0.39 to 1 m/s, and the y speed can be from 0.07 to 0.15 m/s. Note that the x speed range has dropped to 0.61 m/s, and the y speed range is now 0.08 m/s.

Finally, for 3 balls to hit 4 balls, the x speed can be from 0.42 to 1 m/s, and the y speed can be from 0.08 to 0.14 m/s. This gives an x ​​range of 0.58 m/s and a y range of 0.06 m/s.

I think you can see this trend: more collisions means a smaller initial value range, which will result in the final ball being hit.

Now we need to test the last case: Nine ball. This is what it looks like:

Okay, that works. But if we consider the extra gravity caused by the interaction between the cue ball and the player, will the last ball still be hit?

This is fairly easy to test. All I need to do is add a certain type of human being.I want to use one Approximately spherical man. I know that people are not actually spheres. However, if you want to calculate the gravity of a real player, you must perform some very complicated calculations. Each part of a person has a different quality, and the distance (and direction) from the ball is also different. But if we assume that this person is a sphere, then it is as if all the masses are concentrated on one point. This It is a calculation we can do. Finally, the gravitational difference between a real person and a spherical person may not be too great.