Q. A $2\ kg$ block slides on a horizontal floor with a speed of $4\ m/s$. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is $15\ N$ and spring constant is $10,000\ N/m$. The spring compresses by
A) $5.5\ cm$
B) $2.5\ cm$
C) $11.0\ cm$
D) $8.5\ cm$
Explanation
(a) $\frac{1}{2}mv^{2} - f_{k}x = \frac{1}{2}kx^{2}$
$\frac{1}{2} \times 2 \times 16 - 15x = \frac{1}{2} \times 10^{4} \times x^{2}$
$\therefore x = 5.5\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.