Question

A block of $10$ glides on smooth horizontal surface with $20m/s$ towards a spring of spring constant $100N/m$ placed horizontally (as shown in figure). The maximum compression in spring is

Answer 1

Mass of body ,$m=10g=0.01kg$

Spring constant ,$k=100N/m$

Initial velocity of block , $v=20m/s$

Let $x$ be the maximum compression

At maximum compression the whole kinetic energy of block will be stored as elastic potential energy

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

$⟹x^2=\frac{m}{k}{v}^2$

$⟹x^2=\frac{0.01}{100}\times {20}^2=0.04$

$⟹x^2=0.04$

$⟹x=0.2m$