Question

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

Answer 1

Given:

$V=1.5m/sm=.5kgK=50k/m$

from law of conservation of energy,

loss in K.E in the body = gain in P.E stored in the spring

$\frac{1}{2}m{V}^2=\frac{1}{2}K{X}^2$

$X^2=\frac{m{V}^2}{K}$

$X=\sqrt{\frac{m}{K}}\times V$ = $\sqrt{\frac{1}{2\times 50}}\times 1.5$ = $0.15m$