Final answer:
In a scenario where a child pulls a wagon, the horizontal forces involved are the pull force from the child and the opposing frictional force from the ground. To find the acceleration of a wagon with a child inside, one must consider the net external forces and the mass of the system. Calculations are based on the net force, which is the sum of pushing forces minus the force of friction.
Step-by-step explanation:
When a child pulls a wagon, the two horizontal forces present are the pull force exerted by the child and the frictional force by the ground. If we consider the situation where two children are pushing horizontally in opposite directions on a wagon with a third child inside, and we want to calculate the acceleration of the system (child plus wagon), we define the system of interest as the child in the wagon including the mass of the wagon itself.
For the free-body diagram, we identify all the external forces acting on this system: the force exerted by the first child (75.0 N), the force exerted by the second child (90.0 N), the frictional force (12.0 N initially, with a variation case of 15.0 N), the weight of the system and the normal force from the ground. Remembering that net force equals mass times acceleration (F = ma), we can calculate the acceleration when the total external force is the difference between the pushing forces minus the frictional force. Therefore, with a friction of 12.0 N, the acceleration is calculated as (90.0 N - 75.0 N - 12.0 N) / 23.0 kg.
If the friction increases to 15.0 N, the calculation changes slightly, reflecting this higher resistance to motion, resulting in a different acceleration value for the wagon system.