Problem 1

Two small masses

m_1>m_2

hang from a light inextensible string over a light frictionless pulley. The string remains taut, motion is vertical, and

g

is constant. Take downward for

m_1

and upward for

m_2

as positive. (a) Find their common acceleration. (b) Find the tension. (c) Evaluate the acceleration for

m_1=3m_2

and check equal masses. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

T=\frac{2m_1m_2}{m_1+m_2}g

problems.proof.analysis

Use the result just found to calculate the quantity requested next. Keep the sign convention consistent throughout.