Use physics knowledge to explain why the fastest curve is faster than a straight line between two po

For example: place two ping pong balls.

Placed at the starting point of the curved track and the straight track of the same height, the experimental results show that the ball of the curved track reaches the end point first. The ball on the curved track reaches the highest speed first, so it reaches the finish line first. It is the cycloidal that connects the start and end points.

Ignoring other factors, the cycloidal is the fastest descending line.

Beyond the two-dimensional plane, the curve is shorter than the straight line. The earth is round, and any point cannot be connected with another point in the form of a straight line, and if you want to connect it in a straight line, you must fly out in the direction of the tangent line, and it is difficult to connect them together. The curve connection is the shortest distance.

The shortest straight line between two points is only applicable to the two-dimensional plane, and the shortest straight line between two points is not applicable when it is separated from the two-dimensional plane. In addition, the conclusion that the straight line between two points is the shortest in theory, but not in real life. Two points in different dimensions cannot be connected in a straight line, and if they are connected in a straight line, the distance will be correspondingly farther.

In the same way, this method is correct in theory, but it cannot be applied in practice.

On an inclined plane, there are two tracks, one straight and one curved, and the height of the start point is the same as the height of the end point. Balls of the same mass and size slide from the starting point at the same time, and the curved balls go to the end point first. The curve ball reaches the end point first because the ball in the curve track reaches the highest speed first, and the ball reaches the highest speed first.

There is only one straight line between two points, and there are countless curves, so which one is the fastest? Galileo.

The same question was posed in 1630, which he thought should be a straight line, which was later found to be wrong. In 1696, Bernoulli solved this problem as a challenge to other mathematicians. Newton, Leibniz.

Scientists such as Lobida and Bernoulli solved the problem. This maximum speed curve is the cycloid, which is scientifically known as the rotor line.

Galileo Galilei posed the analytic question in 1630: "A mass is under gravity, from a fixed point to a point not below the vertical, regardless of friction."

What curve takes the shortest time. "Curves are circles, that's wrong.

Bernoulli asks for answers to the question of the fastest curve. capacity, the average speed is the fastest.

Because the acceleration of the maximum speed curve is faster and the time to reach another point is shorter, the maximum speed curve is faster than a straight line.

When the object is moving, the kinetic energy obtained is all ** with gravity, and the initial kinetic energy obtained in the curve is more than that obtained in a straight line, and the initial velocity is faster than a straight line.

Because the maximum speed curve is a parabolic motion, it is affected by gravity, and of course it is faster than a straight line.

The maximum speed curve is with the help of inertia, gravitational acceleration, which seems to be a relatively long distance but has enough potential energy to still make up for the disadvantage of the distance, and the speed of the object is very fast.

Maximum speed curveIt means that it takes the shortest timeAverage speedIf you want to say "the fastest", you have to draw a velocity-time image on the third rule (123 from top to bottom), divide the area by the time, the average speed of the third is the largest, and the first is the smallest.

After demonstration and scientific experiments, the red route in Figure 1 is the fastest route, that is, the "fastest curve". The shape of the maximum speed curve is a curve, and the initial acceleration is almost vertical, which gives the object the ability to quickly pass through the horizontal displacement of the second half, and the average speed is the fastest.

Other explanations

If the number of layers divided into coarse celery increases indefinitely, that is, the thickness of each layer becomes infinitely thinner, then the movement of the particle tends to the real situation of the movement of the particle between the two points of space A and B, and the polyline will also increase infinitely, and its shape will approach the curve we require - the fastest curve. And each segment of the polyline tends to be the tangent of the curve.

Thus, an important property of the maximum speed curve is obtained.

The cosine of the angle formed by the tangent and the plumb line at any point.

With the point falls down the height of the flat bench hole square root.

The ratio of is constant. And the curve with this property is the cycloid.

A cycloidal is the trajectory of a circle at any point in its circumference as it rolls along a straight line (without sliding). Therefore, the fastest curve is the cycloid, but in the fastest curve problem, the cycloid is reversed upside down.

a. The condition for the object to do curvilinear motion is that the resultant force and the velocity are not in the same straight line, and the direction of acceleration and the direction of the resultant force are the same, so the direction of acceleration is not in the same straight line as the direction of its velocity, so a is correct b. The motion of the velocity change can also be a uniform linear motion, not necessarily a curved motion, so b is wrong C. The condition for the object to do curvilinear motion is that the resultant force and the velocity are not in the same straight line, but the magnitude of the resultant external force does not have to change, such as flat throwing motion, so c is wrong d. The acceleration changes, but the direction of the force can be on the same straight line as the velocity, and it can be a linear motion, that is, a linear motion with variable acceleration, so d is wrong Therefore, a

a. The condition for the object to do curvilinear motion is that the resultant force and the velocity are not in the same straight line, and the direction of acceleration and the direction of the resultant force are the same, so the direction of acceleration is not in the same straight line as the direction of its velocity, so a is correct

b. The movement of speed change can also be a linear motion with uniform variable speed, not necessarily a curved motion, so B is wrong

c. The condition for the object to do curvilinear motion is that the resultant force and the velocity are not in the same straight line, but the magnitude of the resultant external force does not have to change, such as flat throwing motion, so C is wrong

d. The acceleration changes, but the direction of the force can be on the same straight line as the velocity, and it can be used for linear motion, that is, it can be accelerated in a straight line, so D is wrong Therefore, A

The equilibrium point is a stable state, and there can only be one pressure and one volume in this modular state.

Balancing the grinding process is a process, from one balance point to the next balance point, it must be a curve.

Points 1, 2, 3, and 4 are the equilibrium state, and from 1 to 2 is the equilibrium process.

a, b, the condition for the object to do curvilinear motion is that the resultant force and the velocity are not in the same straight line, the magnitude of the velocity can change, but the direction of the direction of the instantaneous velocity at a certain point is the tangent direction of this point on the curve, so a is correct, b is wrong;

C, D, when rotating the umbrella, the water droplets on the umbrella surface do spiral motion from the inside to the outside, so the velocity direction of the water droplets is always along the tangent direction of its trajectory, so C is wrong, D is correct

Hence the choice: AD

a. The condition for the object to do curve motion is that the resultant force and the velocity are not in the same straight line, the magnitude of the velocity can change, but the direction of the direction of the instantaneous velocity at a certain point is the tangent direction of this point on the curve, so A is correct and B is wrong;

c. When rotating the umbrella, the water droplets on the umbrella surface do spiral motion from the inside to the outside, so the velocity direction of the water droplets is always along the tangent direction of its trajectory, so C is wrong, D is correct

Hence the choice: AD