Physic Labs

Problem 1

Two masses m1,m2m_1,m_2 are joined by a taut, massless inextensible string over a fixed frictionless pulley, so their accelerations have equal magnitude. Mass m1m_1 slides on a frictionless incline of angle α\alpha; m2m_2 hangs freely. Take gg constant and assume m2>m1sin⁡αm_2>m_1\sin\alpha, so m2m_2 descends. Ignore the sizes of the bodies and all drag. (a) Draw the force diagrams, choose positive directions, and write Newton’s equation for each mass. (b) Determine the acceleration aa and tension TT. (c) Check the near-equilibrium limit when the driving forces almost balance.
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m2g−T=m2a,T−m1gsin⁡α=m1am_2g-T=m_2a,\quad T-m_1g\sin\alpha=m_1a
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With m2m_2 descending, the first equation applies Newton’s second law to the hanging mass and the second resolves m1m_1 forces along the incline. The ideal string and frictionless incline assumptions apply throughout.

problems.proof.pitfall. Do not infer the direction of motion by comparing m1m_1 and m2m_2 alone; compare the along-string driving forces m1gsin⁡αm_1g\sin\alpha and m2gm_2g.