The magnitude of the effective friction force exerted on the wagon is 93.9 N and the effective coefficient of friction associated with this force is 1.87.
Step 1: Draw a free-body diagram
A free-body diagram is a diagram that shows all the forces acting on an object. In this case, the forces acting on the wagon are:
The force of the rope, which is 120 N and is acting at an angle of 25° above the horizontal.
The weight of the wagon, which is 20 kg * 9.81 m/s² = 196.2 N and is acting vertically downward.
The normal force of the surface, which is equal to the vertical component of the weight of the wagon.
The force of friction, which is acting in the opposite direction of the motion of the wagon.
Step 2: Resolve the forces into horizontal and vertical components
The horizontal component of the force of the rope is 120 N * cos(25°) = 103.9 N. The vertical component of the force of the rope is 120 N * sin(5°) = 50.3 N.
Step 3: Write down the equations of motion
In the horizontal direction, the net force is equal to the mass of the wagon times its acceleration. This gives us:
103.9 N - F_friction = 20 kg * 0.50 m/s²
Solving for F_friction, we get:
F_friction = 103.9 N - 10 N = 93.9 N
In the vertical direction, the net force is equal to zero. This gives us:
-50.3 N + N_normal = 0
Solving for N_normal, we get:
N_normal = 50.3 N
Step 4: Calculate the coefficient of friction
The coefficient of friction is equal to the force of friction divided by the normal force. This gives us:
µ = F_friction / N_normal = 93.9 N / 50.3 N = 1.87
Therefore, the magnitude of the effective friction force exerted on the wagon is 93.9 N and the effective coefficient of friction associated with this force is 1.87.