Question

A mass of $0.5kg$ moving with a speed of $1.5m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50N/m$. The maximum compression of the spring would be

• A. $0.15m$
• B. $0.12m$
• C. $0.5m$
• D. $0.25m$

Answer 1

Answer: (A)

$0.15m$

Speed of moving mass $v=1.5m/s$

Given : $k=50N/m$ and $m=0.5kg$

The kinetic energy of the moving mass will be converted into potential energy in the spring when the spring is at maximum compression $x_o$.

$\therefore$ $\frac{1}{2}m{v}^2=\frac{1}{2}k{x}_o^2$

Or $x_o=\sqrt{\frac{m}{k}}v$

$⟹$$x_o=\sqrt{\frac{0.5}{50}}\times 1.5=0.15m$