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 next part uses the preceding result as input rather than treating parts independently. This keeps conventions and physical state consistent throughout.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.