How to run the fastest on the track? The "fastest curve" you don't know!

Life is like a race track, and we are often curious about how to run the fastest?

When we are rushing forward on a straight track, someone passes us on another track. At this moment, everyone feels as if they are kneeling on the snow and shouting to the sky: "No! This is not fair! My track is obviously the fastest, he is cheating! How can I be the fastest?"

In fact, the big names in the physics world have also struggled with such a "philosophical" question! In 1630, Galileo asked "Which path between two points is the fastest?" At that time, he thought that the line should be a straight line, but later people found that this answer was wrong.

Let’s get to the point:

In the comparison among the big guys, we gradually get a glimpse of the "essence of life" - there is a fastest curve between two points. But this has a premise. If I start sprinting here, but you secretly bring an accelerator, this won't work. It is said that people are not born equal, but today's comparison requires us to start at the same speed!

So what is the fastest curve? The most intuitive way is to look at the picture.

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As shown in the figure above (source: Baidu), if small balls of the same mass and size are released from rest at the top of each track at the same time, it will be found that the ball on one track reaches the end first. The curve of this track is called the brachistocentric curve.

What the fastest curve actually looks like:

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As shown in the figure above, when a circle moves along a straight line, the trajectory formed by a certain point on the boundary of the circle is a cycloid, and the fastest curve we usually see is the curve that is the inverted cycloid.

After learning about the fastest curve, I believe that some diligent and studious kids are curious about the principle of this. Let me briefly share it with you.

Decryption:

Although we have been taught since childhood that the shortest distance between two points is a line segment, when the ball rolls horizontally for the same distance, the ball on the curved trajectory obviously falls higher. In life, it is not difficult to find that under the same conditions, the higher the height of an object's free fall, the faster it falls.

Therefore, the ball rolling on the straight line can only watch itself being surpassed. The exploration of the true face of the fastest curve seems simple, but it involves university physics thinking and calculus, etc. There are Easter eggs for those who are interested!

In addition to mastering the secret of choosing the fastest track, the fastest curve also tells us the truth that "it's not too late"!

As shown in the figure below, balls of different colors fall from different positions at the same time and reach the end at the same time, which is impossible on a straight line. But on the special curve function of the cycloid, physics shows its wonders. Therefore, the fastest curve is also called the isochronal curve. So even if the starting point is different, don't back down, as long as you find the right way, you can still surpass and reach the end! (A smell of chicken soup wafts in~)

Such an interesting curve can not only solve life’s problems, but is also very useful in life!

Roller Coaster Design

Roller coasters are a classic application of the fastest curve in life. Why do we ride roller coasters? Of course, for excitement!

In order to meet customer requirements, engineers used the ingenious concept of the fastest curve, striving to allow people to experience the fastest speed of falling and the most enjoyable feeling.

Skateboarding Tips

At the skatepark, everyone is secretly competing with each other to see who can skate faster. At this time, as long as you master the fastest curve, you will be the coolest guy in the entire skatepark!

No matter if you start from the same point or your opponent cheats and starts ahead, as long as you slide along the trajectory of the fastest curve, you will definitely win!

Contributors: Southwest University Popular Science Space Station, Chongqing Physics Society, Beibei District Science and Technology Association

Audit expert: Zhang Qiaoming

Statement: Except for original content and special notes, some pictures are from the Internet. They are not for commercial purposes and are only used as popular science materials. The copyright belongs to the original authors. If there is any infringement, please contact us to delete them.