Question
Two blocks A (5kg) and B(2kg) attached to the ends of a spring constant 1120N/m are placed on a smooth horizontal plane with the spring undeformed. Simultaneously velocities of 3m/s and 10m/s along the line of the spring in the same direction are imparted to A and B then
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Solution
Sol. At max extension velocity of both block is same (v).
momentum conservation
5 × 3 + 2 × 10 = 5v + 2v
v = 5 m/s
Gain in potential energy = loss in KE
$\frac{1}{2}Kx^{2} = \left( \frac{1}{2} \times 5 \times 3^{2} + \frac{1}{2} \times 2 \times 10^{2} \right) - \frac{1}{2}(5 + 2)v^{2}{}$
⇒ x = 25 cm
vcom = $\frac{m_{1}v_{1} + m_{2}v_{2}}{m_{1} + m_{2}} = \frac{5 \times 3 + 2 \times 10}{5 + 2} = 5\mspace{6mu} m/s$
vB/com initially = 5 m/s
Range vB/com =0 to 10
⇒ min vB/ground = 0
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