Problem P. 4513. (February 2013)

P. 4513. Two small insulating discs of mass m are placed to the horizontal tabletop, such that initially the distance between their centres is x₀=5 cm. A small metal sphere of charge Q=8^.10^-8 C is fixed at the top of each disc.

One of the discs if fixed to the tabletop and the other is released, and it slides. The coefficient of friction between the disc and the tabletop is =₀=0.3. Neglect the electrostatic interaction between the charges and the tabletop.

a) What will the distance x₁ be between the centres of the two discs at the moment when the speed of the sliding disc is maximal?

b) What will the distance x_m between the two discs be after the sliding discs stops?

c) What is the relationship between x₀, x₁ and x_m?

(5 pont)

Deadline expired on March 11, 2013.

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

Megoldásvázlat. \(\displaystyle a)\) \(\displaystyle x_1=6{,}25\) cm.

\(\displaystyle b)\) \(\displaystyle x_{\rm m}=7{,}83\) cm.

\(\displaystyle c)\) \(\displaystyle x_0\) és \(\displaystyle x_{\rm m}\) mértani közepe éppen \(\displaystyle x_1\).

Statistics:

90 students sent a solution.
5 points:	51 students.
4 points:	19 students.
3 points:	6 students.
2 points:	7 students.
Unfair, not evaluated:	7 solutionss.

Problems in Physics of KöMaL, February 2013