In the ideal atwood machine arrangement shown, the system starts from rest. Let, the change in kinetic energy (in J) of the system during 3rd second be ΔK. Find 3ΔK.

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$a = \frac{4 - 2}{4 + 2} g = \frac{g}{3}$

v₁ = at₁ = $\frac{2 g}{3}$
v₂ = at₂ = g
$△ k_{a} = \frac{1}{2} M (v_{2}^{2} - v_{1}^{2}) = \frac{1}{2} \times 6 [g^{2} - \frac{4 g^{2}}{9}] = \frac{5 g^{2}}{3} = \frac{500}{3} J$

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