For an Atwood machine consisting of two masses $m_1$ and $m_2$ connected by a light string over a frictionless pulley ($m_1>m_2$), the acceleration $a$ is: $a=\frac{(m_1-m_2)g}{m_1+m_2}$

1. Numerator: The net driving force is the difference in weights: $m_{1}g-m_{2}g=(6-5)g=1g$.
2. Denominator: The total mass being accelerated is $m_1+m_2=6+5=11\text{ kg}$. Substituting: $a=\frac{1g}{11}=\frac{1}{11}g$. In terms of value, $a\approx 0.91{\text{ m/s}}^2$.