Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem P. 4260. (May 2010)

P. 4260. An object of mass m can move without friction along the horizontal axis of X. With a thread of length L another object of mass m is connected to it. This object can move only along the vertical axis Y. Initially this object is at the origin of the axes, and the other is at a distance of L on the X axis. Than the objects are left to move. To what speeds will the object accelerates due to the gravitational force? What types of motion do they undergo?

(5 pont)

Deadline expired on June 10, 2010.

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

Megoldás. A felső test a fonál függőleges helyzetében éri el legnagyobb sebességét (\(\displaystyle v_1^{\rm{max}}=\sqrt{2gL}\)), az alsó test sebessége pedig akkor lesz maximális, amikor a fonál \(\displaystyle 35,\!3^\circ\)-os szöget zár be a vízszintessel, ekkor \(\displaystyle v_2^{\rm{max}}\approx0,\!88\sqrt{gL}\). A testek periodikus (de nem harmonikus!) rezgőmozgást végeznek.


24 students sent a solution.
5 points:Béres Bertold, Bolgár Dániel, Galzó Ákos Ferenc, Laczkó Zoltán Balázs, Mayer Martin János, Patartics Bálint, Szabó 928 Attila, Szélig Áron.
4 points:Kungl Ákos Ferenc.
3 points:3 students.
2 points:3 students.
1 point:5 students.
0 point:4 students.

Problems in Physics of KöMaL, May 2010