Final answer:
According to Newton's First Law, the horizontal force P that should be applied to the cart so that the cord AB just becomes slack is zero.
Step-by-step explanation:
To determine the horizontal force P that should be applied to the cart so that the cord AB just becomes slack, we need to consider Newton's First Law. Newton's First Law states that an object at rest will stay at rest, and an object in motion will stay in motion with the same velocity, unless acted on by an external force.
In this case, if the cart is at rest, Newton's First Law tells us that no external force is acting on the cart. Therefore, the horizontal force P that should be applied to the cart should be zero.