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 (Take $g=9.8m/s^2$):

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

Answer 1

The correct option is A $0.1m$

Let the maximum compression in the spring be $x$.

Initial and final kinetic energy of the system is zero i.e. $\Delta K.E=0$

From work energy theorem : $W_{net}=\Delta K.E$

Or $W_{gravity}+W_{spring}=0$

Or $mg(h+x)-\frac{1}{2}k{x}^2=0$

Or $\left(2\right)\left(9.8\right)(0.4+x)=\frac{1}{2}\left(1960\right)x^2$

We get $50x^2-x-0.4=0$

Solving, we found $x=\frac{1\pm \sqrt{1^2-4\left(50\right)(-0.4)}}{2\left(50\right)}=\frac{1\pm 9}{100}$

Taking positive sign, $x=\frac{1+9}{100}=0.1m$