Question

A mass of $2\text{kg}$ falls from a height of $40\text{cm}$ on a spring with a force constant of $1960\text{N/m}$. The maximum compression in the spring is (Take $g=9.8{\text{m/s}}^2$)

• A. $10\text{cm}$
• B. $1.0\text{cm}$
• C. $20\text{cm}$
• D. $5\text{cm}$

Answer 1

The correct option is A $10\text{cm}$

From energy conservation:
Decrease in gravitational potential energy = Increase in elastic potential energy
$mg(h+x)=\frac{1}{2}K{x}^2$
$2\times 9.8(0.4+x)=\frac{1}{2}\times 1960\times x^2$
$50x^2-x-0.4=0$
$x=\frac{1\pm \sqrt{1+4\left(50\right)\left(0.4\right)}}{100}=\frac{1\pm \sqrt{1+80}}{100}=\frac{1\pm 9}{100}=0.1,-0.08$
As $x$ is positive $x=0.1\text{m or}10\text{cm}$