Mathematical and Physical Journal
for High Schools
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# Problem P. 4908. (February 2017)

P. 4908. A point-like mass $\displaystyle m$ is attached to one end of a negligible-mass rod of length $\displaystyle \ell$. The other end is fixed to a hinge about which the system can be rotated. At which angle $\displaystyle \alpha$ will the centripetal acceleration of the object at the end of the rod be the same as the tangential component of the acceleration of the object if the system was released from the vertical, unstable position of the rod?

Does the object pull or push the rod at this instant? (Neglect friction.)

(4 pont)

Deadline expired on March 10, 2017.

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

Megoldás. $\displaystyle \tg\frac{\alpha}{2}=\frac{1}{2}; \qquad \alpha=53{,}1^\circ$. A rúd a csukló felé húzza a $\displaystyle m$ tömegű testet (és a húzóerő $\displaystyle \tfrac15mg$).

### Statistics:

 71 students sent a solution. 4 points: Ardai István Tamás, Bíró Dániel, Bukor Benedek, Csire Roland, Csuha Boglárka, Fehér 169 Szilveszter, Fekete Balázs Attila, Guba Zoltán, Hajdu 046 Ákos, Hajnal Dániel Konrád, Illés Gergely, Illyés András, Jakus Balázs István, Jánosdeák Márk, Klučka Vivien, Kolontári Péter, Kondákor Márk, Kozák András, Krasznai Anna, Magyar Máté, Magyar Róbert Attila, Mamuzsics Gergő Bence, Markó Gábor, Molnár 957 Barnabás, Molnár Mátyás, Morvai Orsolya, Nagy 555 Botond, Náray Balázs, Németh Csaba Tibor, Olosz Adél, Ónodi Gergely, Páhoki Tamás, Papp 121 Krisztina, Pataki 245 Attila, Paulovics Péter, Póta Balázs, Sal Dávid, Schrott Márton, Tibay Álmos, Tófalusi Ádám, Tóth 111 Máté , Weisz Máté, Zsombó István. 3 points: 15 students. 2 points: 4 students. 1 point: 5 students. 0 point: 4 students.

Problems in Physics of KöMaL, February 2017