A horse can pull a cart even though “every action has an equal and opposite reaction” because those equal and opposite forces always act on different bodies, not on the same one, so they do not cancel each other and still allow acceleration of the horse–cart system as a whole.

Quick Scoop

  • The horse pushes backward on the ground with its hooves.
  • The ground pushes the horse forward with an equal and opposite frictional force; this is what actually drives the horse (and cart) ahead.
  • The horse pulls the cart forward, and the cart pulls the horse backward with equal tension forces, but these act on different objects.
  • What matters for motion is the net force on each object or on the whole system, not the action–reaction pair itself.

Step‑by‑step: What forces act?

Think of three main players: horse, cart, and ground.

  1. On the cart
    • Forward force: pull by the horse through the harness (tension TTT).
 * Backward force: friction from the ground on the cart’s wheels or axle.

 * The cart moves forward if the pull TTT is greater than the opposing friction.
  1. On the horse
    • Backward force: pull from the cart (also tension TTT, equal and opposite to the force the horse exerts on the cart).
 * Forward force: friction from the ground on the horse’s hooves, produced because the horse pushes the ground backward.

 * The horse moves forward if the forward friction from the ground is larger than the backward pull from the cart.
  1. On the horse–cart system together
    • Internal forces (horse pulls cart, cart pulls horse) cancel in the system picture because they are equal and opposite and internal.
 * The only important horizontal external forces are:
   * Forward: friction of ground on horse (and sometimes on wheels).

   * Backward: friction on the cart wheels, air resistance, etc.

 * If the forward friction from the ground is larger than the total backward friction, the _whole_ system accelerates forward.

Where does Newton’s third law fit?

Newton’s third law is not violated here; you just have to track which object each force acts on.

  • Horse pulls cart forward with force TTT.
    • Cart pulls horse backward with force TTT.
    • These two forces form an action–reaction pair, but they act on different bodies.
  • Horse pushes ground backward.
    • Ground pushes horse forward with an equal and opposite frictional force.
* This pair also acts on different bodies (horse vs Earth).

Because Newton’s second law says acceleration depends on the net force on one object (or system), action–reaction pairs never “automatically cancel” in the way that confuses people; they only cancel if you sum forces on the same object.

A simple story version

Imagine the horse complaining:

“If the cart pulls me back as hard as I pull it forward, we’ll never move!”

The physics reply:

  • “You do two things at once:
    • You pull the cart, yes; the cart pulls you back equally.
    • But you also push the ground backward, and the ground pushes you forward.
  • As long as your push on the ground is strong enough, the ground’s forward shove on you beats the drag from the cart, and both of you roll ahead.”

So, the horse–cart motion is possible because of Newton’s third law plus friction with the ground, not in spite of it.

One‑line TL;DR

The horse pulls the cart while pushing the ground backward; the ground’s forward reaction on the horse is what overcomes friction and moves the horse–cart system ahead, even though each action has an equal and opposite reaction on another body.

Information gathered from public forums or data available on the internet and portrayed here.