Question

A $2.0\text{kg}$ block is dropped from a height of $40\text{cm}$ onto a spring of spring consant $k=1960\text{N/m}$. Find the maximum distance the spring is compressed.

• A. $0.080m$
• B. $0.20m$
• C. $0.40m$
• D. $0.10m$

Answer 1

The correct option is D $0.10m$

Decrease in gravitational potential energy = increase in elastic potential energy
$\therefore mg(h+x)=\frac{1}{2}K{x}^2$
$2\times 9.8\times (0.4+x)=980x^2$
$7.84+19.6x=980x^2$
Solving we get $x=0.1\text{m}$