Mathematical and Physical Journal
for High Schools
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# Problem P. 4849. (May 2016)

P. 4849. The total mass of an easily moveable cart and a hemisphere shaped container of radius $\displaystyle R=0.3$ m attached to the cart is $\displaystyle M=2$ kg. Initially a point-like object of mass $\displaystyle m=1$ kg is held at the rim of the hemisphere (such that it touched the rim), and then it is released from rest.

$\displaystyle a)$ What are the velocities of the small object and the cart when the object descended a height of $\displaystyle h=R/2$? (Give both directions and speeds.)

$\displaystyle b)$ What is the radius of the curvature of the path of the motion of the object with respect to the ground, when it reaches its lowest position? (Friction is negligible everywhere.)

(5 pont)

Deadline expired on June 10, 2016.

### Statistics:

 40 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Bartók Imre, Büki Máté, Csorba Benjámin, Csuha Boglárka, Di Giovanni András, Fehér 169 Szilveszter, Fekete Balázs Attila, Forrai Botond, Ghada Alshalan, Iván Balázs, Jakus Balázs István, Kluèka Vivien, Kovács Péter Tamás, Krasznai Anna, Marozsák Tóbiás , Molnár Mátyás, Olosz Adél, Páhoki Tamás, Pázmán Előd, Póta Balázs, Sal Kristóf, Szentivánszki Soma , Tófalusi Ádám. 4 points: Bekes Nándor, Berke Martin, Kasza Bence, Makovsky Mihály, Nagy 555 Botond, Németh 777 Róbert. 3 points: 5 students. 2 points: 3 students. 0 point: 1 student.

Problems in Physics of KöMaL, May 2016