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Brachistochrone

Mathematics

★Exhibit Content: Brachistochrone, Cycloid ★Interaction: Electromechanical interaction ★Operation: 1. Place the three balls at the top of the tracks; 2. Pull the release mechanism handle and observe which ball reaches the finish first. ★Exhibit Description: The exhibit consists of three tracks, three balls of equal radius and mass, three indicator lights, and an operating lever. The starting and ending heights of the three tracks are the same. Place the balls at the starting positions respectively, pull the operating lever, and the balls roll down simultaneously. No matter how many times you try, the ball on the parabolic track always reaches the finish first. ★Scientific Principle: The order in which the balls reach the finish depends not only on the length of the track but also on the ball's sliding speed. In fact, the curved track is a brachistochrone. In the initial stage of descent, the steeper track allows the ball to quickly gain greater speed; then the greater speed is fully utilized to complete the flat curve. Therefore, compared with other tracks, the ball rolling on the brachistochrone can always reach the finish first. The brachistochrone is widely used in engineering. In ancient Chinese architecture, the curve on the 'large roof' houses is a brachistochrone, allowing rainwater falling on the roof to flow away as quickly as possible.

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Principle Display: ★★★★ Interaction Effect: ★★★★ Ease of Installation: ★★★★★ Durability: ★★★★ Overall Rating: ★★★★

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