Mathematical and Physical Journal
for High Schools
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# Problem P. 4198. (November 2009)

P. 4198. A small block of mass m=1 kg is placed to a plank which moves on a horizontal frictionless surface, as shown in the figure. The mass of the plank is M=4 kg, and its length is L=0.8 m. The coefficient of friction between the plank and the block is =0.4.

a) What is the least constant force F0 with which the plank must be pulled in order to make the block slide down from it?

b) How long does it take for the bock to slide down if the pulling force is F1=3 mg?

c) Till the instant when the block fell off the plank what percent of the force F1 increased the internal energy of the system?

(4 pont)

Deadline expired on December 10, 2009.

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

Megoldás. $\displaystyle a)$ $\displaystyle F_{0}>\mu g (m+M)=19,6$  N.

$\displaystyle b)$ $\displaystyle t=\sqrt{\frac{2LM}{F_{1}-\mu g (m+M)}}=0{,}81$ s.

$\displaystyle c)$ Kb. 5%-a.

### Statistics:

 178 students sent a solution. 4 points: Balogh Gábor, Barta Szilveszter Marcell, Batki Bálint, Béres Bertold, Béres Orsolya Katalin, Bodosi Eszter, Börcsök Bence, Burján Bence, Enyedi Péter, Farkas Martin, Filep Gábor, Fonai Dániel, Galzó Ákos Ferenc, Gujás István, Hegedűs Csaba, Hoksza Zsolt, Illés Dorottya, Jéhn Zoltán, Jezeri András, Kaposvári István, Krammer Rita Amaranta, Kungl Ákos Ferenc, Lőrincz Dóra, Mayer Martin János, Nagy László Bendegúz, Najbauer Eszter Éva, Nánási József, Pál Domonkos, Pálovics Péter, Para Attila, Pataki Bálint Ármin, Patartics Bálint, Pázmán Koppány, Pirka Benjámin Zoltán, Réti Dávid, Sisák Mária Anna, Szélig Áron, Szentes Ákos, Szentgyörgyi 994 Rita, Szigeti Bertalan György, Szikszai Lőrinc, Tamás Zsolt, Török Bálint, Vargha Sára, Varju 105 Tamás, Várnai Péter, Vuchetich Bálint. 3 points: 33 students. 2 points: 37 students. 1 point: 22 students. 0 point: 35 students. Unfair, not evaluated: 4 solutions.

Problems in Physics of KöMaL, November 2009