A block of mass m1 = 4kg at rest on a horizontal frictionless surface is connected to an unstretched spring with spring constant 500 N/m whose other end is fixed. A second block of mass m2 = 1kg whose speed is 10m/s collides with the first block. If the two blocks stick together after the one-dimensional collision, find the maximum distance d (in cm) by which the spring is compressed.

Engineering

Physics

Momentum and Energy Conservation for System of Particles

Question

A block of mass m₁ = 4kg at rest on a horizontal frictionless surface is connected to an unstretched spring with spring constant 500 N/m whose other end is fixed. A second block of mass m₂ = 1kg whose speed is 10m/s collides with the first block.

If the two blocks stick together after the one-dimensional collision, find the maximum distance d (in cm) by which the spring is compressed.

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By COM
m₂v = (m₁ + m₂)v'
By COE

$\frac{{(m_{2} v)}^{2}}{2 (m_{1} + m_{2})} = \frac{1}{2} {kx}^{2}$

$\frac{1 \times 10}{\sqrt{5 \times 500}} = x$

$x = \frac{10}{50} = \frac{1}{5} m = 20 cm$