Mathematical and Physical Journal
for High Schools
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# Problem P. 4645. (May 2014)

P. 4645. An object of mass 0.1 g is fixed to the end of a thin, initially horizontal quartz thread. The declination of the thread is 0.2 mm. The structure is placed into the space between the horizontal plates of a capacitor as shown in the figure. The distance between the plates is 3 cm. The object is given a charge of $\displaystyle 10^{-7}$ C.

$\displaystyle a)$ What should the applied voltage across the plates of the capacitor be in order that the quartz thread gains back its initial undeformed equilibrium position?

$\displaystyle b)$ The motion of the object is started with turning on the previously calculated voltage across the plates. What is the amplitude and the frequency of the initiated oscillatory motion?

(4 pont)

Deadline expired on June 10, 2014.

Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. $\displaystyle a)$ $\displaystyle U=mgd/Q\approx 300$ V.

$\displaystyle b)$ Az amplitúdó $\displaystyle A=2$ mm, a frekvencia $\displaystyle f=\frac{1}{2\pi}\sqrt{\frac{g}{A}}\approx 11{,}1~$Hz. Feltételezzük, hogy a kvarcszál tömege a hozzá erősített test tömege mellett elhanyagolható.)

### Statistics:

 40 students sent a solution. 4 points: Antalicz Balázs, Berta Dénes, Blum Balázs, Bugár 123 Dávid, Büki Máté, Csathó Botond, Di Giovanni Márk, Dinev Georgi, Erdei Ákos, Farkas Tamás, Fehér Zsombor, Fekete Panna, Gróf Tamás, Holczer András, Horváth János, Kaposvári Péter, Kasza Bence, Kenderes Anett, Krokos Ádám László, Marosvári Kristóf, Nagy Zsolt, Németh 017 András, Németh Flóra Boróka, Olosz Balázs, Pázmán Zalán, Seress Dániel, Szántó Benedek, Szász Norbert Csaba, Tanner Martin, Varju Ákos, Virágh Anna. 3 points: Demeter Dániel, Juhász Péter, Kovács András Tamás, Sárvári Péter, Szépfalvi Bálint, Szilágyi Kristóf, Wiandt Péter. 2 points: 1 student. 0 point: 1 student.

Problems in Physics of KöMaL, May 2014