Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $m_2=5 \mathrm{~kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3 \mathrm{~m} / \mathrm{s}$ towards the block B kept at rest. A spring with spring constant $\mathrm{k}=3000 \mathrm{~N} /…

Question

Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $m_2=5 \mathrm{~kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3 \mathrm{~m} / \mathrm{s}$ towards the block B kept at rest. A spring with spring constant $\mathrm{k}=3000 \mathrm{~N} / \mathrm{m}$ is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{m}_1 \mathrm{v}_1+\mathrm{m}_2 \mathrm{v}_2=\left(\mathrm{m}_1+\mathrm{m}_2\right) \mathrm{v}_{\mathrm{cm}} \\ & \mathrm{v}_{\mathrm{cm}} \Rightarrow \frac{10 \times 3}{10+5} \Rightarrow \frac{30}{15}=2 \mathrm{~m} / \mathrm{s}\end{aligned}$
$\frac{1}{2} \mathrm{kx}^2=\frac{1}{2}(10)(3)^2-\left[\frac{1}{2}(15)(2)^2\right]$
$\Rightarrow 90-60=30=3000 x^2$
$\begin{aligned} & \mathrm{x}^2 \Rightarrow \frac{30}{3000}=\frac{1}{100} \\ & \mathrm{x} \Rightarrow \frac{1}{10} \mathrm{~m}.\end{aligned}$

Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $m_2=5 \mathrm{~kg}$ that are placed on a…

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