The speed of block B in terms of the distance (d) it has descended is [tex]V=\frac{2gd(m_B-\mu_k m_A)}{m_A \;+\; m_B \;+\;\frac{I}{r^2}}[/tex]
How to determine the speed.
In order to determine the speed of block B in terms of the distance (d) it has descended, we would apply the work-energy theorem as follows:
[tex]Work=\Delta KE=KE_f-KE_i[/tex]
The work done due to gravity is given by:
[tex]W_g=(m_B)gd[/tex]
The work done due to friction is given by:
[tex]W_f=-\mu_k (m_A)gd[/tex]
The angular velocity of pulley is given by:
[tex]\omega = \frac{V}{r}[/tex]
Applying the work-energy theorem, we have:
[tex]W_g+W_f= KE_f-KE_i\\\\(m_B)gd-\mu_k (m_A)gd=\frac{1}{2} m_A V^2+\frac{1}{2} m_B V^2+\frac{1}{2} I\omega^2-0\\\\gd(m_B-\mu_k m_A)=m_A V^2+ m_B V^2+\frac{1}{2} I(\frac{V}{r} )^2\\\\2gd(m_B-\mu_k m_A)=(m_A + m_B +\frac{I}{r^2} )V\\\\V=\frac{2gd(m_B-\mu_k m_A)}{m_A \;+\; m_B \;+\;\frac{I}{r^2}}[/tex]
Read more on work-energy here: brainly.com/question/22599382
