Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem P. 4341. (April 2011)

P. 4341. A long slope of angle of elevation \alpha is made of solid rubber cylinders which can easily revolve about their fixed axles. The rollers, which have mass of m and radius R, are close to each other, but they do not touch each other. To what maximum speed can a crate of mass M be accelerated? (The coefficient of friction between the crate and the rollers is big enough.)

(5 pont)

Deadline expired on May 10, 2011.

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

Megoldás. \(\displaystyle v_{\rm max}\approx \sqrt{\frac{4MgR\sin\alpha}{m}}.\)


50 students sent a solution.
5 points:Jéhn Zoltán, Szemes Gábor Bence.
4 points:Béres Bertold, Hegyfalvi Csaba, Maász Máté.
3 points:44 students.
2 points:1 student.

Problems in Physics of KöMaL, April 2011