Mathematical and Physical Journal
for High Schools
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# Problem G. 655. (December 2018)

G. 655. A solid brick of mass 27 kg is placed onto a horizontal tabletop. If it is placed onto one of its face then the pressure on the tabletop is 4500 Pa. When another face is in contact with the table then the pressure is 7200 Pa, and facing down to its third side the pressure on the tabletop 2700 Pa. What is the density of the brick?

(4 pont)

Deadline expired on January 10, 2019.

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

Megoldás. Legyen a tégla oldaléleinek hossza $\displaystyle a,$ $\displaystyle b$ és $\displaystyle c$, melyekkel kifejezve a tégla sűrűsége $\displaystyle \varrho=\frac{m}{abc}.$ A megadott nyomások így írhatók fel:

$\displaystyle p_1=\frac{mg}{ab},\qquad p_2=\frac{mg}{bc},\qquad p_3=\frac{mg}{ac}.$

Ezen egyenletek szorzata:

$\displaystyle p_1 p_2 p_3=\frac{(mg)^3}{(abc)^2}=mg^3\varrho^2,$

ahonnan a keresett sűrűség:

$\displaystyle \varrho=\sqrt{\frac{p_1 p_2 p_3}{ mg^3}}=1852~\frac{\rm kg}{\rm m^3}.$

Megjegyzés. Az adatokból azt is ki lehet számítani, hogy a tégla oldalainak hossza kb. 15 cm, 25 cm és 40 cm.

### Statistics:

 94 students sent a solution. 4 points: 72 students. 3 points: 10 students. 2 points: 5 students. 0 point: 1 student. Unfair, not evaluated: 3 solutionss. Not shown because of missing birth date or parental permission: 3 solutions.

Problems in Physics of KöMaL, December 2018