At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of F=86.4 N at an angle of 64 degree.

The acceleration of gravity is 9.8 m/s^2.
The box of books has a mass of 13 kg and the coefficient of kinetic friction between the bottom of the box and the floor is 0.31.
What is the acceleration of the box?
Answer in units of m/s^2

Fb = M*g = 13 * 9.8 = 127.4 N.

Fp = 127.4*sin 0 = 0. = Force parallel to the floor.

Fn = 127.4 - 86.4*sin64. = Normal force.

Fk = u*Fn = Force of kinetic friction.

a = (F*Cos64-Fp-Fk)/M.

To find the acceleration of the box, we need to consider the forces acting on it. In this case, there are three forces: the force applied by the student (F), the force of gravity (mg), and the force of friction (Ff). Let's break down the calculation step by step:

Step 1: Find the vertical component of the applied force:
The vertical component of the applied force (Fv) can be found using the equation:
Fv = F * sin(θ), where θ is the angle between the force and the horizontal axis.
Substituting the given values:
Fv = 86.4 N * sin(64°)

Step 2: Find the force of gravity:
The force of gravity (mg) is given by multiplying the mass (m) of the box by the acceleration due to gravity (g).
mg = m * g

Step 3: Find the force of friction:
The force of friction (Ff) is calculated by multiplying the coefficient of kinetic friction (μk) by the normal force (N), which is equal to mg.
Ff = μk * N

Step 4: Determine the net force:
The net force acting on the box is the vector sum of the applied force and the force of friction. To calculate the net force in the horizontal direction, we subtract the horizontal component of the applied force:
Net horizontal force (Fnet) = F * cos(θ) - Ff

Step 5: Apply Newton's second law:
Using Newton's second law, we can relate the net force to the acceleration of the box:
Fnet = m * a

Finally, we can combine all the steps to find the acceleration of the box:
a = (F * cos(θ) - Ff) / m

Substituting the known values into the equation will give us the answer in m/s^2.