Two blocks connected by a rope of negligible mass are being dragged by a horizontal force F (Fig. P5.45). Suppose that F = 75.0 N, m1 = 14.0 kg, m2 = 19.0 kg, and the coefficient of kinetic friction between each block and the surface is 0.098.

a)Determine the tension T.
b)Determine the magnitude of the acceleration of the system.

To determine the tension T and the magnitude of acceleration of the system, we need to apply the laws of motion and calculate the forces at play.

First, let's analyze the forces acting on the system:

1. Tension force (T): This force is exerted by the rope and acts on both blocks in the same magnitude.

2. Force of gravity (weight): This force is exerted by the Earth and acts on each block individually. It can be calculated using the formula: weight = mass * gravitational acceleration (weight = m * g).

3. Normal force (N): This force is exerted by the surface and acts perpendicular to it. Since the blocks are on a horizontal surface, the normal force will be equal to the force of gravity acting on each block.

4. Frictional force (f): The coefficient of kinetic friction (μ) between each block and the surface allows us to calculate the frictional force using the formula: f = μ * N.

Now, let's calculate each force and solve the problem step by step:

a) To determine the tension T:
Since the force applied (F) is used to overcome kinetic friction, we can write the equation: F - 2f = T, where 2f represents the sum of the frictional forces acting on both blocks.

1. Calculate the weight of each block:
weight1 = m1 * g = 14.0 kg * 9.8 m/s^2
weight2 = m2 * g = 19.0 kg * 9.8 m/s^2

2. Calculate the normal force on each block:
Since the normal force is equal to the weight (N = weight):
N1 = weight1
N2 = weight2

3. Calculate the frictional force on each block:
f1 = μ * N1
f2 = μ * N2

4. Calculate the total frictional force:
2f = f1 + f2

5. Calculate the tension T:
T = F - 2f

b) To determine the magnitude of the acceleration:
To calculate the acceleration of the system, we need to use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration (ΣF = m * a).

1. Calculate the net force acting on the system:
The net force is the difference between the applied force (F) and the total frictional force (2f):
net force = F - 2f

2. Calculate the mass of the system:
The mass of the system is the sum of the masses of both blocks (m1 + m2).

3. Calculate the acceleration of the system:
Use Newton's second law: net force = mass * acceleration

By performing these calculations, you can determine both the tension T and the magnitude of the acceleration of the system.