Question

A block of mass $2.0\text{kg}$ is moving on a frictionless horizontal surface with a velocity of $1.0\text{m/s}$ as shown in figure, move towards another block of equal mass at rest. The spring constant of the spring fixed at one end is $100\text{N/m}$. Find maximum compression of the spring.

• A. $40\text{cm}$
• B. $30\text{cm}$
• C. $20\text{cm}$
• D. $10\text{cm}$

Answer 1

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

Using WE theorem, in COM reference frame
$K_i+U_1=K_f+U_t$
Initial kinetic energy
$K_i=\frac{1}{2}\mu V_{rel}^2=\frac{1}{2}\times \frac{2\times 2}{2+2}(1-0{)}^2=\frac{1}{2}\text{J}$
Initial potential energy
$U_i=0$
for maximum compression $V_{rel}=0$
Final Kinetic energy
$K_f=0$
Final potential energy (when compression is $x$ )
$U_f=\frac{1}{2}k{x}^2=\frac{1}{2}100x^2=50x^2$
$\Rightarrow 50x^2=\frac{1}{2}$
$\Rightarrow x=\frac{1}{10}m=10\text{cm}$