Question

A block of mass $m=0.1kg$ is connected to a spring of unknown spring constant $k$. It is compressed to a distance $x$ from its equilibrium position and released from rest. After approaching half the distance $x/2$) from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3m/s$. The total initial energy of the spring is

• A. $0.8J$
• B. $0.6J$
• C. $0.3J$
• D. $1.5J$

Answer 1

The correct option is B $0.6J$

For an elastic collision of same mass velocity interchanged when one is rest.

Velocity of block before collision is = 3 m/s

Now $\frac{1}{2}k{\left(\frac{x}{2}\right)}^2+\frac{1}{2}{mv}^2=\frac{1}{2}{kx}^2$

$\frac{1}{2}{kx}^2-\frac{1}{2}\frac{{kx}^2}{4}=\frac{1}{2}{mv}^2\frac{1}{2}{kx}^2\left(\frac{3}{4}\right)=\frac{1}{2}\times 0.1\times 9\frac{1}{2}{kx}^2=\frac{1.8}{3}=0.6$