Final answer:
The Cart and Horse Paradox is misunderstood because it doesn't account for external forces acting on the system. Internal forces between the horse and cart cancel out, but the horse's interaction with the ground creates an unbalanced force that moves the horse and cart forward.
Step-by-step explanation:
The Cart and Horse Paradox exemplifies a common misunderstanding of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This might imply that forces cancel out, leading to no movement. However, this is not the case because the forces act on different objects. When considering the system of interest, we can define it as the horse and cart together or each individually.
If we take the horse and the cart as a single system, the internal forces they exert on each other indeed cancel out within that system. Nevertheless, this system also interacts with the external environment. The horse exerts a force on the ground through its hooves, pushing backward. According to Newton's third law, the ground reacts by exerting an equal and opposite force on the horse, pushing it forward. This force does not cancel out with any other force within the system and thus results in the forward motion of the entire horse-cart system.
Therefore, when analyzing movement, it is important to consider both the internal forces within a system, which cancel each other out, and the external forces acting upon the system, which can cause it to accelerate. This understanding allows us to see how movement is initiated despite the existence of action-reaction force pairs.