F=ma 2024 Problem 10

Physics · mechanics

Problem

Question: As shown in the figure, a block of mass

m

is connected to the walls of a frictionless box by two massless springs with relaxed lengths

\ell

and

2\ell

, and spring constants

k

and

2k

respectively. The length of the box is

3\ell

. The system rotates with a constant angular velocity

\omega

about one of its walls. Suppose the block stays at a constant distance

r

from the axis of rotation, without touching either of the walls. What is the value of

r

? (A)

\frac{2k\ell}{2k - m\omega^2}

. (B)

\frac{2k\ell}{2k + m\omega^2}

. (C)

\frac{2k\ell}{3k + m\omega^2}

. (D)

\frac{3k\ell}{3k - m\omega^2}

. (E)

\frac{3k\ell}{3k + m\omega^2}

. *Note: This problem references figure(s): `image_question/F=MA_2024_10_1.png`*