Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem P. 3889. (April 2006)

P. 3889. A syringe is filled with water. Its volume is 20 cm3, and the cross section of its interior part is 4 cm2. The syringe is held vertically such that its nozzle is at its top, and its 100 g piston is pressed and moves with a constant speed. The ejected water has an initial upward velocity of 2 m/s, and the cross-section of the beam of water at the nozzle is 1 mm2. (Neglect the dissipated energy due to friction.)

a) Find the speed of the piston.

b) What is the total work done by us?

c) Express and graph the force exerted on the piston as a function of time.

(4 pont)

Deadline expired on May 11, 2006.

Statistics:

 117 students sent a solution. 4 points: Demeter Dániel, Engedy Balázs, Molnár 811 Kristóf, Nagy 555 Zoltán, Pásztor Attila, Szilágyi Zsombor, Szirmai Péter. 3 points: Balázs Dániel, Blázsik Zoltán, Bogár 560 Péter, Csányi Róbert, Csire Gábor, Filep Tibor, Gresits Iván, Horváth 795 Andrea, Kovács 216 Krisztina, Legoza József, Lovas Lia Izabella, Megyeri Balázs, Nagy 224 Csaba, Nagy 897 Zsolt, Nyíri Dávid Ákos, Pálovics Róbert, Polyák Péter, Sümegi Károly, Szaller Dávid, Szőke Gergő, Szük Dániel, Takács 484 Marcell, Werner Miklós. 2 points: 45 students. 1 point: 35 students. 0 point: 5 students. Unfair, not evaluated: 2 solutions.

Problems in Physics of KöMaL, April 2006