Final answer:
The acceleration of each box connected by an ideal cord on a frictionless table when a 40.0 N force is applied to the 10.0 kg box is 1.82 m/s².
Step-by-step explanation:
The student has asked how to find the acceleration of two boxes connected by an ideal cord and resting on a frictionless table when a horizontal force is applied to one of them. In this system, both boxes will have the same acceleration since they are connected and there is no opposing force due to friction or mass of the cord. The total mass of the system is the sum of the masses of box A and box B, which is 12.0 kg + 10.0 kg = 22.0 kg. The net force applied on the system is 40.0 N, which is the force pulling on the 10 kg box.
To calculate the acceleration, use Newton's second law (Force = mass x acceleration). The acceleration a can be found by dividing the net force (F) by the total mass (m). Therefore, a = F/m = 40.0 N / 22.0 kg = 1.82 m/s². So, the acceleration of each box is 1.82 m/s².