Combine separate force diagrams with the taut-string acceleration constraint.
Use a positive direction for each particle
A smooth slope and hanging particle; draw friction separately if the slope is rough.
For two particles joined by a light, inextensible string over a fixed smooth pulley, use one tension magnitude while the string is taut. Their distances moved, speeds and acceleration magnitudes are equal in this simple arrangement. One may move uphill as the other moves downward; their vector accelerations need not be identical.
Draw only forces acting on the particle being considered. For a rough slope, add friction opposite sliding or impending sliding. Find the reaction by resolving normally. Choose positive directions compatible with the string, then write a separate F=ma equation for each particle.
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mBg−T=mBa
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04•Connected Particles on Slopes
Equilibrium & Limiting Cases
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Use an inequality until a limit is specified
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