Blocks on two inclines of a free wedge

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This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.
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Blocksontwoinclinesoffreewedge.png

This article is about the following scenario. A freely movable triangular wedge placed on a fixed frictionless horizontal floor has two inclines I_1 and I_2 making angles \alpha_1 and \alpha_2 with the horizontal. There are blocks of masses m_1 and m_2, resting on the two inclines I_1 and I_2 respectively. All surfaces of contact are frictionless.


Summary of cases

Case What happens
\! m_1 \sin(2\alpha_1) = m_2 \sin(2\alpha_2) The wedge remains stationary and the blocks both slide down their respective inclines.
\! m_1 \sin(2\alpha_1) > m_2 \sin(2\alpha_2) The horizontal push exerted by m_1 exceeds that by m_2, causing the wedge to move in the push direction of m_1. Both m_1 and m_2 slide down.
\! m_1 \sin(2\alpha_1) < m_2 \sin(2\alpha_2) The horizontal push exerted by m_2 exceeds that by m_1, causing the wedge to move in the push direction of m_2. Both m_1 and m_2 slide down.