A student moves a box of books by attaching a rope to the box and pulling with a force of 80.0 N at angle of 45o. The box of books has a mass of 25.0 kg and the coefficient of kinetic friction between the bottom of the box and the sidewalk is 0.43. Find the acceleration of the box.

To find the acceleration of the box, we need to analyze the forces acting on it using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

First, let's calculate the force of friction (F_friction) between the box and the sidewalk. The force of friction can be determined using the equation F_friction = coefficient of friction (µ) × normal force (F_normal).

The normal force (F_normal) is equal to the weight of the box, which is given by the equation F_normal = mg, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).

F_normal = (25.0 kg)(9.8 m/s^2) = 245 N

Now, let's calculate the force of friction.

F_friction = (0.43)(245 N) = 105.35 N

Next, we need to resolve the applied force into its horizontal and vertical components. The horizontal component of the applied force is given by the equation F_horizontal = F_applied × cos(theta), where theta is the angle at which the force is applied.

F_horizontal = (80.0 N) × cos(45°) = 56.57 N

Since the applied force is the only horizontal force acting on the box, it is equal to the net force acting on the box (F_net).

F_net = F_horizontal = 56.57 N

Now, we can rearrange Newton's second law equation to solve for the acceleration.

F_net = ma

56.57 N = (25.0 kg) × a

Dividing both sides of the equation by the mass of the box, we get:

a = 56.57 N / 25.0 kg = 2.26 m/s^2

So, the acceleration of the box is 2.26 m/s^2.