How to do 69th question?

enter image source here enter image source here

1 Answer
Cesareo R.
Apr 1, 2018

See below.

Explanation:

With #I = 1/2 M R^2#

#{(),(I dot omega = R(T_2-T_1)),(T_1 -m_1 g = m_1 a_1),(T_2 - m_2 g = m_2 a_2),(a_2=-R dot omega),(a_1 = R dot omega):}#

after solving

#{(),(T_1 =(g m_1 (M + 4 m_2))/(M + 2 (m_1 + m_2))),(T_2 = (g (M + 4 m_1) m_2)/(M + 2 (m_1 + m_2))),(a_1 = (2 g (m_2-m_1))/(M + 2 (m_1 + m_2))),(a_2 = - a_1),(dotomega = (2 g ( m_2-m_1))/((M + 2 (m_1 + m_2)) R)):}#

The conclusions are left to the reader.

NOTE

the accelerations are constant.

Related questions
Impact of this question
1116 views around the world
You can reuse this answer
Creative Commons License