A 2kg mass and 3 kg mass are used to compress oppoite ends of a spring (k = 750 N/m) by a distance of 40 cm from natural length and released from rest. If the speeds of the two masses as they leave the spring are v2 and v3, find v2 + v3 (in m/s).

Engineering

Physics

Conservation of Energy

SHM of Spring Block System

Momentum and Energy Conservation for System of Particles

Question

A 2kg mass and 3 kg mass are used to compress oppoite ends of a spring (k = 750 N/m) by a distance of 40 cm from natural length and released from rest. If the speeds of the two masses as they leave the spring are v₂ and v₃, find v₂ + v₃ (in m/s).

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2v₂ + 3v₃ = 0

$\frac{1}{2} {kx}^{2} = \frac{1}{2} \times 2 v_{2}^{2} + \frac{1}{2} \times v_{3}^{2}$

$\Rightarrow \frac{1}{2} \times 750 \times (0 .4)^{2} = {v_{2}}^{2} + \frac{3}{2} \times {(\frac{2}{3} v_{2})}^{2}$

$375 \times 0 .16 = \frac{5}{3} v_{2}^{2}$

$v_{2} = \sqrt{225 \times 0 .16} = 6$

$v_{3} = \frac{2}{3} + 6 = 4$

v₂ + v₃ = 10