Question

A pulley of mass mp , radius R , and moment of inertia about the center of mass Ic=12mpR2 , is suspended from a ceiling. The pulley rotates about a frictionless axle. An inextensible string of negligible mass is wrapped around the pulley and it does not slip on the pulley. The string is attached on one end to an object of mass m1 and on the other end to an object of mass with m2<m1 .

At time t=0 , the objects are released from rest.


(a) Find the magnitude of the acceleration of the two objects. Express your answer in terms of m1, m2, mp, R and acceleration due to gravity g (enter m_1 for m1, m_2 for m2, m_p for mp, R for R and g for g).

a=


(b) How long does it take the objects to move a distance d? Express your answer in terms of m1, m2, mp, d and acceleration due to gravity g (enter m_1 for m1, m_2 for m2, m_p for mp, d for d and g for g).

t=

Answer 1

a=((m_1-m_2)*g)/(((0.5*m_p)+(m_1+m_2)))
t=sqrt((d*(m_p+2*(m_1+m_2)))/((m_1-m_2)*g))