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
a>0 \text{for m_2 downward}; [a]=m/s^2, [T]=N
problems.proof.analysisCollect results in the order asked. Dimensions and physical signs provide independent checks; they do not replace the derivation but can expose algebraic errors.