Question

according to newton's third law, when a horse pulls on a cart, the cart pulls back on the horse with an equal force on the horse. if in fact the cart pulls back on the horse as hard as the horse pulls forward on the cart, how is it possible for the horse to move the cart?

Answer 1

The horse exerts a force on the cart. But that force applies only to the cart, not also to the horse.

The cart in turn exerts a force on the horse. But that force applies only to the horse, not the cart also.

Hence the net force on the cart remains as it was--a positive force in the direction of the horse's movement. Therefore the cart begins to accelerate and move.

Answer 2

Basically the Third Law of Motion state that "The mutual forces of action and reaction between two bodies are equal, opposite and collinear." Therefore the goal of this Law is just to suffice the State of Equilibrium wherein 1-1 = 2-2 or Simply 0. Having the Laws working properly and effectively of the real world is simply amazing XD

Answer 3

according to action-reaction forces,they are CONTACT forces when the horse pulls cart there is transmission of force via the rope that is being used and there is not maximum effect of action-reaction forces seen here
let us consider the case when a man pushes a box ON A FRICTIONLESS PLANE assuming both have same mass m
here when they have no friction and same mass action reaction forces can be seen

even when we assume the horsew and cart are in direct contact,when we draw free body diagram(all forces acting on it)for cart we see that only action force put by horse acts in the horizontal direction which results in motion
hope this helped you understand!