Problem 1
Two masses are connected by a light inextensible string over a frictionless pulley. Find the acceleration and string tension; is gravitational acceleration. The ideal string and pulley constrain the two masses to accelerations of equal magnitude. (a) Write Newton’s equations for both masses. (b) Find their acceleration and the string tension. (c) If the heavier mass descends a distance from rest, find the speed of both masses. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.
problems.proof.stepOf
problems.proof.analysis
First isolate the parts of the system linked by the stated constraint and choose the governing law; this puts the quantities under a consistent convention. The idealizations exclude interactions not included in the model.
problems.proof.pitfall. Do not omit the sign convention or the model’s physical condition; check the limiting case before accepting a solution.