Steepest Line
Mathematics · Mechanical Interaction
- Dimensions4000×700×1500mm
- PresentationMechanical Interaction
- PricingQuoted by manufacture spec
Purpose & Scientific Principle
Place three tracks in the space, one is a straight line and the other two are curves. The starting points and lengths of the tracks are the same. When two small balls of the same mass and size slide downward from the starting point at the same time, the curved ball reaches the end point first. This is because the ball on the curved track reaches the highest speed first, so it arrives first. However, there is only one straight line between two points, but there are countless curves. So, which one is the fastest? The order in which the balls reach the end depends not only on the length of the track, but also on the speed of the ball's descent. In fact, the cycloidal track is a steepest descent line. In the initial stage of the ball's descent, the ball can gain a greater speed as quickly as possible through a steeper track; and then make full use of the greater speed to complete a relatively flat curve. Therefore, compared with straight lines or other curved tracks, the ball rolling down the steepest line can always reach the end point first. The steepest descent line is widely used in engineering. The curve on the "big roof" house in ancient Chinese architecture is the line of steepest fall. Rainwater falling on the roof can drain away at the fastest speed.
How to Operate
The exhibit consists of three sets of tracks. The starting point and length of the tracks are the same, and the end points of the tracks are different. Participants can place the same three small balls at the starting point of the same set of tracks and release them at the same time to observe the differences in the movement of the balls in different tracks. The audience can gain an in-depth understanding of the fastest drop line through various forms of interaction.
4 0 00 large 70 0 large 1 5 00mm expression
① Place the balls on tracks of different shapes;
② Observe the speed of the ball falling.
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