Three blocks are connected on the table as shown below. The coefficient of kinetic friction between the block of mass m2 and the table is 0.370. The objects have masses of m1 = 5.00 kg, m2 = 1.40 kg, and m3 = 2.30 kg, and the pulleys are frictionless. Determine the acceleration of each object, including its direction.Determine the tensions in the two cords.

To determine the acceleration of each object and the tensions in the two cords, you can use Newton's second law of motion and apply it to each block separately.

First, let's analyze the system by considering the forces acting on each block:

Block m1:
- The force of gravity acting downwards with a magnitude of F1 = m1 * g, where g is the acceleration due to gravity (9.8 m/s^2).
- The tension T1 in the rope, which is acting to the left.

Block m2:
- The force of gravity acting downwards with a magnitude of F2 = m2 * g.
- The tension T2 in the rope, which is acting upwards.
- The frictional force between m2 and the table, which opposes the motion and has a magnitude of F_friction = μ * F2, where μ is the coefficient of kinetic friction (0.37 in this case).

Block m3:
- The force of gravity acting downwards with a magnitude of F3 = m3 * g.
- The tension T2 in the rope, which is acting upwards.

Now, let's apply Newton's second law to each block:

Block m1: T1 - F1 = m1 * a1, where a1 is the acceleration of m1.
Block m2: T2 - F2 - F_friction = m2 * a2, where a2 is the acceleration of m2.
Block m3: T2 - F3 = m3 * a3, where a3 is the acceleration of m3.

Since the system is connected and the cords are inextensible, the tensions T1 and T2 must be equal.

Now, we can solve the system of equations to find the unknowns: a1, a2, a3, and T2.

1. Solve for T1:
From the equation for m1, we have T1 = m1 * g - m1 * a1.

2. Solve for F_friction:
From the equation for m2, we have F_friction = μ * F2 = μ * (m2 * g - m2 * a2).

3. Solve for T2:
From the equation for m2 and m3, we know that T2 = F2 + F3 = m2 * g - m2 * a2 + m3 * g.

4. Equate T1 and T2:
Set T1 = T2, and solve for a1, a2, and a3.

5. Substitute the values of a1, a2, a3 into the equations and solve for T1, T2.

By solving this system of equations, you will be able to determine the acceleration of each object and the tensions in the two cords.