Problem 1
Two masses are connected by a massless inextensible string over an ideal pulley. Released from rest, with friction neglected and constant , find the acceleration, string tension, and speed after the heavier mass descends distance . Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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Choose downward for as positive. An ideal string has equal acceleration magnitude and tension on both sides. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.