Problem P. 5517. (November 2023)

P. 5517. The coefficient of friction on the upper part of a slope of length \(\displaystyle \ell_1\) is \(\displaystyle \mu_1\), whilst on the lower part of the slope, having a length of \(\displaystyle \ell_2\) is \(\displaystyle \mu_2\). A small body with zero initial velocity starts at the bottom of a slope and stops just at the bottom. What is the angle of inclination of the slope?

Data: \(\displaystyle \ell_1=20\) cm, \(\displaystyle \ell_2=40\) cm, \(\displaystyle \mu_1=0.1\) and \(\displaystyle \mu_2=0.2\).

(4 pont)

Deadline expired on December 15, 2023.

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

Megoldás. Legyen a keresett hajlásszög \(\displaystyle \alpha\). A munkatétel szerint

\(\displaystyle \left(\ell_1+\ell_2\right)mg\sin\alpha= \ell_1mg\mu_1\cos\alpha+\ell_2mg\mu_2\cos\alpha,\)

ahonnan

\(\displaystyle \tg\alpha=\frac{\mu_1\ell_1+\mu_2\ell_2}{\ell_1+\ell_2}=\frac{1}{6},\)

tehát \(\displaystyle \alpha\approx 9{,}5^\circ.\)

Statistics:

114 students sent a solution.
4 points:	69 students.
3 points:	13 students.
2 points:	4 students.
1 point:	9 students.
0 point:	3 students.
Unfair, not evaluated:	4 solutionss.
Not shown because of missing birth date or parental permission:	3 solutions.

Problems in Physics of KöMaL, November 2023