Final answer:
The acceleration of the box when a 25 N horizontal force is applied, and after overcoming static friction, is 4.0 m/s². It's calculated by subtracting the kinetic friction force from the applied force and then dividing by the mass of the box.
Step-by-step explanation:
When a force is applied to an object on a surface with friction, there are a few calculations we need to make to determine if the object will move and its subsequent acceleration if it does move.
The maximum static friction force that needs to be overcome to get the box moving is found by using the equation Fs = μs × N where μs is the static coefficient of friction and N is the normal force. Since the box is on a horizontal table, the normal force is equal to the weight of the box mg, where m is mass and g is the acceleration due to gravity (9.8 m/s2). For a 5 kg box, N = 5 kg × 9.8 m/s2, which gives us 49 N. The maximum static friction force is then Fs = 0.40 × 49 N = 19.6 N.
Since the applied horizontal force of 25 N is greater than the maximum static friction force of 19.6 N, the box will indeed move. After the box starts moving, the kinetic friction force takes over, calculated by Fk = μk × N, resulting in Fk = 0.10 × 49 N = 4.9 N.
Once the box is in motion, the net force acting on it is the applied force minus the kinetic friction force. Thus, net force Fnet = 25 N - 4.9 N = 20.1 N. According to Newton's second law of motion (F = ma), the acceleration a of the box can be found by rearranging the equation to a = Fnet / m. This gives us an acceleration of a = 20.1 N / 5 kg = 4.02 m/s2, which we can round to 4.0 m/s2 to one decimal place.