A block of mass 1 kg moving with a speed of 10 m/s on a frictionless horizontal surface collides inelastically (sticks) with another identical block of mass 1 kg, which is initially at rest. The combi

Question

A block of mass 1 kg moving with a speed of 10 m/s on a frictionless horizontal surface collides inelastically (sticks) with another identical block of mass 1 kg, which is initially at rest. The combined mass then moves and compresses a massless spring of spring constant k = 200 N / m . What is the maximum compression (in cm) of the spring?

TestHub · Accepted Answer

Step 1 - perfectly inelastic collision (momentum conserved):

$m_{1} v_{1} = (m_{1} + m_{2}) V$

$1 \times 10 = 2 V \Rightarrow V = 5$ m/s

Step 2 - spring compression (energy conserved):

$\frac{1}{2} (m_{1} + m_{2}) V^{2} = \frac{1}{2} k x^{2}$

$\frac{1}{2} (2) (5^{2}) = \frac{1}{2} (200) x^{2}$

$25 = 100 x^{2} \Rightarrow x^{2} = \frac{1}{4} \Rightarrow x = 0.5$ m $= 50$ cm Answer: 50

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