How to do 69th question?

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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.

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