Question

A block of mass $2kg$ is dropped from a height of $40cm$ on a spring whose force-constant is $1960N{m}^{-1}$. The maximum distance through which the springs is compressed by:

• A. $5cm$
• B. $15cm$
• C. $20cm$
• D. $10cm$

Answer 1

The correct option is D $10cm$

Given data,

Mass of the body is ( m ) $=2Kg$

spring's constant $\left(K\right)=1960N/m$

height of the body $=0.4m$

Let the maximum distance spring will compressed $=xm$

initial potential energy of body $=mg(h+x)$

final potential energy = spring potential energy $=\frac{1}{2}K{x}^2$

according to the law of conservation of energy,

initial potential energy = final potential energy

$mg(h+x)=\frac{1}{2}K{x}^2$

$2mgh+2mgx=K{x}^2$

$K{x}^2-2mgx-2mgh=0$

$\Rightarrow 1960x^2-2\times 2\times 9.8\times x-2\times 2\times 9.8\times 0.4=0$

$\Rightarrow 1960x^2-39.2x-15.68=0$

after solving this quadratic equations , we get $x=0.1m$

hence, answer is $x=0.1m$