# Changes

## Pulley system on a double inclined plane

, 01:29, 14 August 2011
Summary of cases starting from rest
! Case !! What happens qualitatively !! Magnitude of accelerations
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| $\! m_1\sin \alpha_1 - m_2\sin \alpha_2 > \mu_{s1}m_1\cos \alpha_1 + \mu_{s2}m_2\cos \alpha_2$ || $m_1$ slides downward and $m_2$ slides upward, with the same magnitude of acceleration || $\! a = g(m_1 \sin \alpha_1 - m_2 \sin \alpha_2 - \mu_{k1}m_1\sin cos\alpha_1 - \mu_{k2}m_2 \sincos\alpha_2)/(m_1 + m_2)$.
|-
| $\! m_2\sin \alpha_2 - m_1\sin \alpha_1 > \mu_{s1}m_1\cos \alpha_1 + \mu_{s2}m_2\cos \alpha_2$ || $m_2$ slides downward and $m_1$ slides upward, with the same magnitude of acceleration || $\! a = g(m_2 \sin \alpha_2 - m_1 \sin \alpha_1 - \mu_{k1}m_1\sin cos \alpha_1 - \mu_{k2}m_2 \sincos\alpha_2)/(m_1 + m_2)$.
|-
| $\! |m_1 \sin \alpha_1 - m_2 \sin \alpha_2| \le |\mu_{s1}m_1 \cos \alpha_1 + \mu_{s2}m_2 \cos \alpha_2|$ || The system remains at rest || $0$