A mop is pushed across the floor with a force F of 36.0 N at an angle of Θ = 50.0° (see figure below). The mass of the mop head is 3.75 kg. Calculate the acceleration of the mop head if the coefficient of kinetic friction between the head and the floor is μk= 0.400. (Express your answer to three significant figures.)

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To find the acceleration of the mop head, we need to first determine the net force acting on it parallel to the floor.

First, we find the horizontal (x) and vertical (y) components of the applied force:

Fx = F * cos(Θ) = 36.0 N * cos(50°) = 36.0 N * 0.6428 = 23.141 N
Fy = F * sin(Θ) = 36.0 N * sin(50°) = 36.0 N * 0.7660 = 27.576 N

Next, we find the normal force (N) acting on the mop head, which is simply the net vertical force acting on the mop:

N = mg - Fy = (3.75 kg)(9.81 m/s^2) - 27.576 N = 36.7875 N - 27.576 N = 9.2115 N

Now, we can find the frictional force acting on the mop head:

Friction = μk * N = 0.400 * 9.2115 N = 3.6846 N

Finally, we can determine the net force acting on the mop head parallel to the floor:

Net Force = Fx - Friction = 23.141 N - 3.6846 N = 19.4564 N

Now we can use Newton's second law (F = ma) to calculate the acceleration:

Acceleration = Net Force / Mass = 19.4564 N / 3.75 kg = 5.188 N/kg

Thus, the acceleration of the mop head is 5.19 m/s² (rounded to three significant figures).