Problem P. 5299. (February 2021)

P. 5299. A strong uniform-density spring of mass \(\displaystyle M\) and of spring constant \(\displaystyle D\) is accelerated by pulling it at one of its ends with a force \(\displaystyle F\) along a horizontal, frictionless tabletop such that each point of the spring moves at the same acceleration into the direction of the symmetry axis of the spring. What is the length of the spring if its relaxed length was \(\displaystyle \ell_0\gg F/D\)?

(4 pont)

Deadline expired on March 16, 2021.

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

Megoldás. A rugó gyorsulása: \(\displaystyle a=F/M\). A rugót feszítő erő helyről helyre változik, a rugó elejénél \(\displaystyle F\), a végénél nulla. Az átlagos feszítő erő \(\displaystyle F/2\), emiatt a rugó megnyúlása

\(\displaystyle \Delta \ell=\frac{F}{2D},\)

a megnyúlt rugó hossza pedig

\(\displaystyle \ell=\ell_0+\frac{F}{2D}\)

lesz.

Statistics:

24 students sent a solution.
4 points:	Barta Gergely, Hauber Henrik, Kovács Kinga, Ludányi Levente, Páhán Anita Dalma, Török 111 László, Varga Vázsony.
3 points:	Horváth Antal, Kozák Gergely, Szász Levente.
2 points:	1 student.
1 point:	4 students.
0 point:	7 students.
Unfair, not evaluated:	2 solutionss.

Problems in Physics of KöMaL, February 2021