Question

A $2$kg block is dropped from a height of $0.4$m on to the top of a vertical helical spring whose force constant $K$ is $1960N{m}^{-1}$. The spring then suffers a maximum compression of

• A. $0.1m$
• B. $0.01m$
• C. $1m$
• D. $1\times {10}^{-3}$

Answer 1

The correct option is A $0.1m$

Let the final compression of spring be $x$.

Then by conservation of energy,

$E_i=E_F$

$E_i=$gravitational potential energy

$E_F$ spring energy

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

$2\times 10(0.4+x)=\frac{1}{2}\times 1960\times x^2,1960x^2-40x-16=0\therefore x=0.1m$