Question

A block of mass $50kg$ is projected horizontally on a rough horizontal floor. The coefficient of friction between the block and the floor is $0.1$. The block strikes a light spring of stiffness $k=100N/m$ with a velocity $2m/s$. The maximum compression of the spring is :

• A. $1m$
• B. $2m$
• C. $3m$
• D. $4m$

Answer 1

The correct option is A $1m$

kinetic energy of block = work done by friction + potential energy of spring

$\frac{1}{2}m{v}^2=f.x+\frac{1}{2}k{x}^2$ equation 1

frictional force

$f=\mu mg=0.1\times 50\times 10=50$

Initial velocity =2 m/s k=100

by putting all these values in equation 1

we get,

$\frac{1}{2}\times 50\times {\left(2\right)}^2=50x+\frac{1}{2}\times 100\times x^2$
$\Rightarrow x^2+x-2=0$

by solving this equation we get

$x=1,x=-2$

$x=-2$ is not possible

then $x=1$

thus the maximum compression of spring is $1m$