EuPhO 2024 — Задача 4. Task E.4 - Deformation of the ball

Автор: Olympiads XYZ · транскрипция на официалните материали

Проверена срещу оригинала на 13.9.2026 от същия модел, който я е транскрибирал (без независима проверка)

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"EuPhO 2024, Kutaisi, Georgia — Experimental Problems" · 4,5 т.

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Условие

In this part you will be dropping the more elastic rubber ball on the piezo element. During the collision between the ball and the piezo, the ball experiences deformations. You can assume that the force FF acting on the ball depends on the ball's elastic deformation xx as a power law:

F=kxα .F = kx^{\alpha}\,.

Find the exponent α\alpha and the material constant kk.

Circuit diagram: piezo capacitor C_p on the left with a switch, a diode in series into a node connecting capacitor C, a discharge switch, and a voltmeter measuring U_C.
Figure 9: .
Plot of elastic energy E_elast in joules (0.000 to 0.020) versus maximum force F_max in newtons (40 to 160), with blue square/diamond experimental points with error bars in both directions.
Figure 10
Plot of log E_elast in arbitrary units (-7.0 to -4.0) versus log F_max in arbitrary units (3.75 to 5.00), with dark-blue diamond experimental points, a red fitted line labelled 'linear fit, γ = 2.34 ± 0.1' and a teal fitted line labelled 'linear fit, γ = 1.94 ± 0.06'.
Figure 11

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Оригинал в Архива: eupho2024_experiment_problems.pdf · официални решения: eupho2024_experiment_solutions.pdf