Question

A block of mass 2 kg collides with a horizontal massless spring of force constant 2 N/m. The block compresses the spring 4 cm from the rest position speed of the block at the instant of collision is in m/s

Answer 1

Given,

Mass, $m=2kg$

Displacement, $x=4cm=0.04m$

Kinetic energy = potential energy of spring

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

$v=\sqrt{\frac{k{x}^2}{m}}=\sqrt{\frac{2\times {\left(0.04\right)}^2}{2}}=0.04m{s}^{-2}$

Hence, velocity before collision is $0.04m{s}^{-1}$