The \( 6.2 \, \text{kg} \) mass descends, pulling the \( 4.2 \, \text{kg} \) block with an aiding force.
For \( 6.2 \, \text{kg} \): \( 6.2g - T = 6.2a \Rightarrow 62 - T = 6.2a \).
For \( 4.2 \, \text{kg} \): \( T + 16 - f_k = 4.2a \).
Normal: \( N = mg = 4.2 \times 10 = 42 \, \text{N} \).
Friction: \( f_k = 0.2 \times 42 = 8.4 \, \text{N} \).
Net force: \( T + 16 - 8.4 = 4.2a \Rightarrow T + 7.6 = 4.2a \).
Solve: \( 62 - T = 6.2a \), \( T + 7.6 = 4.2a \).
Substitute: \( 62 - (4.2a - 7.6) = 6.2a \Rightarrow 62 + 7.6 - 4.2a = 6.2a \Rightarrow 69.6 = 10.4a \).
\( a \approx 6.69 \, \text{m/s}^2 \), \( T + 7.6 = 4.2 \times 6.69 \Rightarrow T + 7.6 \approx 28.1
\Rightarrow T \approx 20.5 \, \text{N} \).