The acceleration of the box sliding on the ramp is approximately 1.49m/s^2.
In this scenario, the motion of a 5.0-kg box sliding on a ramp inclined at 27 degrees above the horizontal is influenced by gravitational forces and friction. The acceleration of the box is determined by considering the net force acting on it. The gravitational component along the ramp is calculated using the formula F gravity =mgsin(θ), where m is the mass of the box, g is the acceleration due to gravity, and θ is the angle of the ramp.
The frictional force opposing the motion is given by F friction =μkmgcos(θ), where μk is the coefficient of kinetic friction. The net force is then F net =F gravity −F friction.
Using Newton's second law (F net =ma), where a is the acceleration, the acceleration of the box is found to be approximately 1.49m/s^2. This accounts for the combined effect of gravity and friction on the motion of the box along the inclined ramp.