A 1.67-kg block (M1) and a 5.07-kg block (M2) are connected by a massless string. Applied forces, F1 = 11.3 N and F2 = 4.85 N, act on the blocks, as shown in the figure.

a) What is the acceleration of the blocks?

To find the acceleration of the blocks, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

In this case, we have two forces acting on the system: F1 and F2. The net force can be calculated as the difference between these two forces: Net Force (F_net) = F1 - F2.

Now, let's calculate the net force:

F_net = F1 - F2
F_net = 11.3 N - 4.85 N
F_net = 6.45 N

The next step is to calculate the acceleration using Newton's second law:

F_net = m_total * a

We need to find the total mass of the system, which is M1 + M2:

m_total = M1 + M2
m_total = 1.67 kg + 5.07 kg
m_total = 6.74 kg

Now, we can solve for the acceleration (a):

6.45 N = 6.74 kg * a
a = 6.45 N / 6.74 kg
a ≈ 0.959 m/s²

Therefore, the acceleration of the blocks is approximately 0.959 m/s².