Mathematical and Physical Journal
for High Schools
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# Problem P. 4574. (November 2013)

P. 4574. A right triangle shaped wedge of mass m=0.5 kg and of angle 30o is placed to the top of a fixed slope of length =1.8 m, and of angle of elevation =30o, as shown in the figure. The vertical height of the wedge is exactly half of the height of the slope H. The wedge is loaded with the small block of mass m as shown in the figure.

This system is assembled in two samples. In case of one of them the small block is fixed to the wedge and in the other case the block is not fixed. The two wedges are released from rest at the same time. Friction is negligible at any surfaces.

a) Determine the ratio of the times during which the wedges reach the bottom of the slopes.

b) What are the forces exerted by the small blocks on the wedges in the two cases?

(5 pont)

Deadline expired on December 10, 2013.

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

Megoldásvázlat. $\displaystyle a)$ $\displaystyle \frac{t_\text{rögzitett} }{t_\text{szabad}}=\sqrt{\frac{a_\text{szabad}}{a_\text{rögzitett}}}=\sqrt{\frac{8}{5}}=1{,}26.$

$\displaystyle b)$ Rögzített hasáb $\displaystyle \frac{3}{4}mg=3{,}68~$N függőleges és $\displaystyle \frac{\sqrt{3}}{4}mg =2{,}12~$N vízszintes irányú erőt fejt ki az ékre, ezek eredője 4,24 N nagyságú. Rögzítésmentes esetben a kényszererő függőleges és $\displaystyle \frac{3}{5}mg=2{,}9~$N nagyságú.

### Statistics:

 79 students sent a solution. 5 points: Antalicz Balázs, Berta Dénes, Blum Balázs, Büki Máté, Csáky Pál, Csathó Botond, Csibi Levente, Fehér Zsombor, Forrai Botond, Géczi Péter Attila, Hegel Patrik, Holczer András, Iván Balázs, Juhász 326 Dániel, Juhász Péter, Kaposvári Péter, Koncz Imre, Mándoki László, Olosz Balázs, Sal Kristóf, Sárvári Péter, Tatár Dániel, Vatamány Lóránd, Verasztó Ádám, Wiandt Péter. 4 points: Berczi Benjámin, Di Giovanni Márk, Dombai Tamás, Farkas Tamás, Fekete Panna, Gerő László, Gróf Tamás, Janzer Barnabás, Juhász Kristóf, Kasza Bence, Kenderes Anett, Kovács Péter Tamás, Marosvári Kristóf, Németh 017 András, Németh Flóra Boróka, Öreg Botond, Pristyák Levente, Sáfrán Péter, Szász Norbert Csaba, Szilágyi András, Varju Ákos. 3 points: 21 students. 2 points: 8 students. 1 point: 2 students. 0 point: 2 students.

Problems in Physics of KöMaL, November 2013