Question

A block of mass $1kg$ is dropped on a spring-mass system as shown in the figure. The block travels $100$ meters in the air before striking the $3kg$ mass. Calculate maximum compression in the spring, if both the blocks move together after the collision. Spring constant of the string $k=1.25\times 10^6.$

• A. $2cm$
• B. $4cm$
• C. $8cm$
• D. $16cm$

Answer 1

Answer: (A)

The velocity of $1kg$ block just before striking
$V=\sqrt{2\times 10\times 100}=20\sqrt{5}m{s}^{-1}$
Applying conservation of momentum, the blocks stick after the collision and move with velocity $v$
Or $1\times 20\sqrt{5}=4v$
Final velocity $v=5\sqrt{5}$ ,
Using energy conservation
$KE+PE=$ const
$\frac{1}{2}\times 4\times {\left(5\sqrt{5}\right)}^2+\frac{1}{2}k{\left(\frac{3g}{k}\right)}^2$
$=0+\frac{1}{2}k.x^2$
$\therefore x^2=\frac{4\times 25\times 5}{1.25\times 10^6}+\frac{30\times 30}{{\left(1.25\times 10^6\right)}^2}$
$x=\frac{20}{1000}m=2cm$