Mathematical and Physical Journal
for High Schools
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# Problem P. 4317. (February 2011)

P. 4317. A skewer of mass m=1 g is hanged with a short thread attached to a fixed point P. A long thread is attached to the bottom end of the skewer, and it is kept in equilibrium with a horizontal force. In this case the angle between the skewer and the vertical is . a) Find the angle between the short thread and the vertical. b) Find the tension in the short thread, if =45o.

(4 pont)

Deadline expired on March 10, 2011.

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

Megoldás. $\displaystyle a$) A forgatónyomatékok egyenlősége miatt a pálcára ható három erő hatásvonalának egy ponton kell áthaladnia, amiből a kis fonal függőlegessel bezárt szögére a $\displaystyle tg \varphi=\frac{tg\alpha}{2}$ összefüggést kapjuk.

$\displaystyle b$) A rövid fonálban ébredő erő nagysága $\displaystyle F'=\frac{\sqrt{5}}{2}mg\approx 11$ mN.

### Statistics:

 105 students sent a solution. 4 points: 69 students. 3 points: 18 students. 2 points: 9 students. 1 point: 5 students. 0 point: 1 student. Unfair, not evaluated: 3 solutions.

Problems in Physics of KöMaL, February 2011