Question

Two blocks of masses $m_1=2kg$ and $m_2=5kg$ are moving in the same direction along a frictionless surface with speeds $10m{s}^{-1}$ and $3m{s}^{-1}$ respectively. An ideal spring with $K=1120N{m}^{-1}$ is attached to the back side of $m_2$ . Find the maximum compression of the spring when the blocks collide.

• A. $0.50m$
• B. $0.25m$
• C. $0.75m$
• D. $1m$

Answer 1

Answer: (B)

Using conservation of linear momentum
$m_1\times 10+m_2\times 3=\left(m_1+m_2\right)V_{CM}$
$2\times 10+5\times 3=7V_{cM}$
$V_{CM}=5m{s}^{-1}$
At maximum compression of spring both particles will acquire common velocity $V_{CM}=5m{s}^{-1}$
Energy conservation
$\Rightarrow \frac{1}{2}\times 2\times 10^2+\frac{1}{2}\times 5\times 3^2=\frac{1}{2}\times 7\times 5^2+\frac{1}{2}k{x}^2$
$\Rightarrow x=0.25m$