Mathematical and Physical Journal
for High Schools
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Problem P. 4249. (April 2010)

P. 4249. The two ends of a flexible rope of uniform density are fixed at the same height, as shown in the figure. Starting from the equilibrium position, we perform the following two experiments:

I. We pull down the midpoint of the rope till it reaches point A. (At this time the rope almost has a V-shape.)

II. From the equilibrium position we pull up the midpoint of the rope to the point B. (So now the shape of the rope is like an upside down V.)

The total work we did in the two processes is W. How much work is needed to lift the midpoint of the rope to the point C?

(5 pont)

Deadline expired on May 10, 2010.

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

Megoldás. A kötél \(\displaystyle C\) pontig való felemeléséhez \(\displaystyle W/4\) munkát kell végezni.


25 students sent a solution.
5 points:Batki Bálint, Béres Bertold, Bodosi Eszter, Bolgár Dániel, Fonai Dániel, Galzó Ákos Ferenc, Hartstein Máté, Janosov Milán, Jéhn Zoltán, Kungl Ákos Ferenc, Mayer Martin János, Neumer Tamás, Pálovics Péter, Patartics Bálint, Szabó 928 Attila, Szélig Áron, Szigeti Bertalan György, Varju 105 Tamás, Várnai Péter, Vuchetich Bálint.
2 points:4 students.
1 point:1 student.

Problems in Physics of KöMaL, April 2010