Problem 1
Two masses m₁ and m₂ are connected by a massless inextensible string over a fixed, frictionless, massless pulley, with m₂>m₁. Both hang freely on opposite sides and are released from rest. Take g=9.8 m/s² and neglect air resistance. (a) Determine the motion directions and write Newton’s equations for both masses. (b) Find the acceleration and string tension. (c) After m₂ descends distance s, find both speeds and check by energy conservation. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
The equation follows by applying the physical law to the chosen system; ideal constraints link the variables. Signs must remain consistent with the defined directions.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.