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

Provided they have the same force?

It isint possible?

Answer 2

Consider all the forces acting on the horse and the cart. F(pull) is what acts on the cart. This force is directed toward the horse. The is no or little friction forces acting on the cart. This is why the net force applied to the cart is not zero, therefore the cart has to move. Horse is pulled back by the cart with the force equal to F(pull) in magnitude and opposite in direction according to the Newton's law. However, there are friction forces acting on horse's hooves. These friction forces are larger in the magnitude compared to the F(pull). What's interesting is that in this particular case these friction forces are directed the same way the horse moves. This is not unusual. Consider friction forces between a highway surface and car tires.

Answer 3

This also explains why if the cart was heavier and the horse applied the same force to run it would run slower. Something that in your textbook would be referred to as inertia. I have purposely ignored frictional forces. One could easily includethem.