Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem P. 4963. (October 2017)

P. 4963. There is a socket at a height of $\displaystyle H$ above a horizontal tabletop. The charger of our mobile phone has a flexible wire of length $\displaystyle h$ and the length of the small, light and rigid part which is joined to the phone is $\displaystyle s$. The phone which is attached to the charger is put onto the table such that it touches the table with one of its shorter side, but from some positions – when the distance $\displaystyle d$ is greater than the value shown in the to scale figure – the phone slips. The length of the phone is $\displaystyle \ell$, its width is negligible, and it has uniform density.

Determine with construction the numerical value of the coefficient of static friction between the tabletop and the phone.

(4 pont)

Deadline expired on November 10, 2017.

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

Megoldás. Az asztal által kifejtett erő hatásvonala a fonálerő és a nehézségi erő hatásvonalának metszéspontján halad át.

Az asztal által kifejtett erő függőlegessel bezárt szögének tangense (a vízszintes és a függőleges komponens aránya) határesetben éppen a tapadási súrlódási együttható. Az ábráról leolvasható, hogy $\displaystyle \mu\approx \frac{0{,}5}{5}=0{,}1.$

Statistics:

 11 students sent a solution. 4 points: Galló Bence, Lipták Gergő, Markó Gábor, Turcsányi Máté. 3 points: Schneider Anna. 2 points: 4 students. 1 point: 1 student. 0 point: 1 student.

Problems in Physics of KöMaL, October 2017