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PhysicsClassical Physics

How to Find Tension in a Two-Mass Atwood Machine

For ideal masses of 2.00 kg and 4.00 kg, the heavier mass accelerates downward at 3.27 m/s², the lighter mass accelerates upward at the same rate, and the string tension is 26.1 N.

Question

An ideal Atwood machine has two hanging masses connected by a light, inextensible string over a frictionless pulley. The masses are m1=2.00 kgm_1=2.00\,\mathrm{kg} and m2=4.00 kgm_2=4.00\,\mathrm{kg}. The system is released from rest.

  1. Find the magnitude and direction of each mass's acceleration.
  2. Find the tension in the string.

Use g=9.80 m/s2g=9.80\,\mathrm{m/s^2}.

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Evidence boundary

This solution assumes a taut, massless, inextensible string and a massless, frictionless pulley, so both masses share one acceleration magnitude and the string tension is the same on both sides. A massive pulley, axle friction, string stretch, or slack would require a different model and can produce unequal tensions.