Question

An object with mass 15.5kg and another one with mass 12.0kg are suspended, joined by a cord that passes over a pulley with a radius of 10.0cm and a mass of 3.00kg.The cord has a negligible mass and does not slip on the pulley.The pulley rotates on its axis without friction.The objects start from rest 3.00 m apart.Treating the pulley as a uniform disk, determine the speeds of the two objects as they pass each other.

Answer 1

According to Newton's second law

$15.5g-T_1=15.5a$

$15g-T_2=-12a$

$T_1r-T_2r=I\epsilon=I\frac{a}{r}$

$I=0.5mr^2=0.5\cdot3\cdot0.1^2=0.015\ (kg\cdot m^2)$

We have $a=0.7g=6.86\ (m/s^2)$

$s=(v^2-v_0^2)/(2a)\to v=\sqrt{2as+v_0^2}=$

$=\sqrt{2\cdot6.86\cdot 3+0}=6.41\ (m/s)$ . Answer