Connected Particles and Pulleys

This lesson covers problems involving particles connected by strings passing over pulleys, as required by the Edexcel 9MA0 specification. These problems combine Newton's Second Law with the constraints imposed by an inextensible string.

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Key Assumptions

Before solving pulley problems, state the standard assumptions:

• The string is light (massless) — so the tension is the same throughout the string.
• The string is inextensible — so both particles have the same magnitude of acceleration.
• The pulley is smooth — so the tension is the same on both sides of the pulley.
• Particles are modelled as point masses.

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Atwood's Machine (Vertical Pulley)

Two particles of masses m₁ and m₂ (where m₁ > m₂) are connected by a light inextensible string passing over a smooth fixed pulley.

The heavier mass m₁ accelerates downwards, and the lighter mass m₂ accelerates upwards, both with the same acceleration a.

Setting Up the Equations

For m₁ (taking downwards as positive for this particle): m₁g - T = m₁a ... (1)

For m₂ (taking upwards as positive for this particle): T - m₂g = m₂a ... (2)

Solving