Final answer:
To resolve the gravitational force into its components, use the equations Fx = F * cos(θ) and Fy = F * sin(θ). The normal force can be found by balancing the gravitational force perpendicular to the incline. The acceleration of the box can be calculated using the equation a = F_net / m.
Step-by-step explanation:
To resolve the gravitational force into its components along the rotated coordinate system, we need to find the x and y components of the force. The x component can be found using the equation Fx = F * cos(θ), and the y component can be found using the equation Fy = F * sin(θ), where F is the magnitude of the force and θ is the angle of the force with the horizontal.
To calculate the normal force, we need to consider that the box is being pulled up the incline. The normal force acts perpendicular to the incline and balances the component of the gravitational force that acts perpendicular to the incline. Since the box is being pulled up the incline, the normal force will be less than the gravitational force.
The acceleration of the box can be found using the equation a = F_net / m, where F_net is the net force acting on the box and m is the mass of the box. In this case, the net force can be calculated as F_net = F_applied - F_gravity_parallel, where F_applied is the applied force and F_gravity_parallel is the component of the gravitational force parallel to the incline.