To solve this problem, we need to break down the forces and use Newton's second law (F = ma) to find the magnitude of the frictional force on the block and the block's acceleration.
First, we need to break the force F into horizontal and vertical components. The horizontal component is calculated as F * cos θ, and the vertical component is F * sin θ. In this case, F = 18 N and θ = 45°, so the horizontal component is 18 N * cos 45° and the vertical component is 18 N * sin 45°.
Next, we can calculate the magnitude of the frictional force using the equation: friction = μ * (mg + F * sin θ). Here, μ represents the coefficient of kinetic friction (given as 0.25), m represents the mass of the block (given as 3.0 kg), and g represents the acceleration due to gravity (approximately 9.8 m/s²).
Finally, using Newton's second law, we can set up the equation: net force = ma. The net force is the difference between the horizontal force and the frictional force. Rearranging the equation, we have: acceleration = (horizontal force - frictional force) / mass.
By following these steps and plugging in the given values, we can calculate the magnitude of the frictional force on the block from the floor and the magnitude of the block's acceleration.