Question

Determine the requested tensions T1, T2, T3 and T4 and accelerations a_A, a_Band a_C for the system below which is released from rest. The mass of block A is 8 kg, the mass of block B is 3 kg, and the mass of block C is 5 kg.

Answer 1

$From\: Block\:C:$

$m_c\:g-T_4=m_c\:a_c$

$T_4=m_c\left ( g-a_c \right )$

$From\:Block\:B:$

$T_4=m_B\left ( a_c+g \right )$

$Equaling:$

$a_C=a_B=\frac{g\left ( m_C-m_B \right )}{m_b+m_C}={\color{Blue} 2.45\:\frac{m}{s^{2}}}$

${\color{Blue} T_4=36.75\:N}$

$T_2=2T_4={\color{Blue} 73.5\:N}$

$T_1=T_4$

$a_A=\frac{T_1-m_A\:g}{m_A}={\color{Blue} -5.2\:\frac{m}{s^{2}}}$