Problem 1
Two masses are joined by a taut, massless inextensible string over a fixed frictionless pulley, so their accelerations have equal magnitude. Mass slides on a frictionless incline of angle ; hangs freely. Take constant and assume , so descends. Ignore the sizes of the bodies and all drag. (a) Draw the force diagrams, choose positive directions, and write Newton’s equation for each mass. (b) Determine the acceleration and tension . (c) Check the near-equilibrium limit when the driving forces almost balance.
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problems.proof.analysis
Adding the equations removes the internal tension, while the inextensible string gives equal acceleration magnitudes. The ideal string and frictionless incline assumptions apply throughout.