To determine the tension $T$ in the connecting string between the two blocks, we need to apply Newton’s second law to each block separately, taking into account the frictional forces acting on each block due to the kinetic friction coefficients provided.

Given Information:

• Force $F = 11.5 \, \text{N}$
• Mass of larger block $M = 1.1 \, \text{kg}$
• Coefficient of kinetic friction for larger block $\mu_1 = 0.19$
• Coefficient of kinetic friction for smaller block $\mu_2 = 0.31$

Let’s denote:

• Mass of the smaller block as $m$.
• Acceleration of the system as $a$.

Step 1: Analyze the Forces Acting on Each Block

1. Larger Block (mass $M$)

   • Applied force $F = 11.5 \, \text{N}$ acts on it.
   • Tension $T$ acts to the left (toward the smaller block).
   • Frictional force $f_1 = \mu_1 \cdot M \cdot g$, where $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity).

   Therefore, the net force on the larger block in terms of $T$ and $a$ is: $F - T - f_1 = M \cdot a$ Substituting $f_1 = \mu_1 \cdot M \cdot g$: $11.5 - T - (0.19 \cdot 1.1 \cdot 9.8) = 1.1 \cdot a$

2. Smaller Block (mass $m$)

   • Tension $T$ acts to the right.
   • Frictional force $f_2 = \mu_2 \cdot m \cdot g$ acts to the left.

   The net force on the smaller block in terms of $T$ and $a$ is: $T - f_2 = m \cdot a$ Substituting $f_2 = \mu_2 \cdot m \cdot g$: $T - (0.31 \cdot m \cdot 9.8) = m \cdot a$

Step 2: Solve for $a$ and $T$

1. Substitute known values and combine the equations