# Difference between revisions of "Pulley system on a double inclined plane"

From Mech

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! Case !! What happens qualitatively !! Magnitude of accelerations | ! Case !! What happens qualitatively !! Magnitude of accelerations | ||

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− | | <math>\! m_1\sin \alpha_1 - m_2\sin \alpha_2 > \mu_{s1}m_1\cos \alpha_1 + \mu_{s2}m_2\cos \alpha_2</math> || <math>m_1</math> slides downward and <math>m_2</math> slides upward, with the same magnitude of acceleration || <math>\! a = g | + | | <math>\! m_1\sin \alpha_1 - m_2\sin \alpha_2 > \mu_{s1}m_1\cos \alpha_1 + \mu_{s2}m_2\cos \alpha_2</math> || <math>m_1</math> slides downward and <math>m_2</math> slides upward, with the same magnitude of acceleration || <math>\! a = g(m_1 \sin \alpha_1 - m_2 \sin \alpha_2 - \mu_{k1}m_1\sin \alpha_1 - \mu_{k2}m_2 \sin\alpha_2)/(m_1 + m_2)</math>. |

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− | | <math>\! m_2\sin \alpha_2 - m_1\sin \alpha_1 > \mu_{s1}m_1\cos \alpha_1 + \mu_{s2}m_2\cos \alpha_2</math> || <math>m_2</math> slides downward and <math>m_1</math> slides upward, with the same magnitude of acceleration || <math>\! a = g | + | | <math>\! m_2\sin \alpha_2 - m_1\sin \alpha_1 > \mu_{s1}m_1\cos \alpha_1 + \mu_{s2}m_2\cos \alpha_2</math> || <math>m_2</math> slides downward and <math>m_1</math> slides upward, with the same magnitude of acceleration || <math>\! a = g(m_2 \sin \alpha_2 - m_1 \sin \alpha_1 - \mu_{k1}m_1\sin \alpha_1 - \mu_{k2}m_2 \sin\alpha_2)/(m_1 + m_2)</math>. |

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| <math>\! |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|</math> || The system remains at rest || <math>0</math> | | <math>\! |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|</math> || The system remains at rest || <math>0</math> | ||

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## Revision as of 18:13, 18 September 2010

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

View other mechanics scenarios

This article is about the following scenario. A fixed triangular wedge has two inclines and making angles and with the horizontal. A pulley is affixed to the top vertex of the triangle. A string through the pulley has attached at its two ends blocks of masses and , resting on the two inclines and respectively. The string is inextensible. The coefficients of static and kinetic friction between and are and respectively. The coefficients of static and kinetic friction between and are and respectively. Assume that and .

## Summary of cases starting from rest

Case | What happens qualitatively | Magnitude of accelerations |
---|---|---|

slides downward and slides upward, with the same magnitude of acceleration | . | |

slides downward and slides upward, with the same magnitude of acceleration | . | |

The system remains at rest |