Horse and Buggy (Dr. H Gets Pulled Around)?

Question

This is perhaps the oldest and most famous "brain twister" in classical physics. Which is correct?

a) If action always equals reaction, a horse cannot pull a buggy because the action of the horse on the buggy is exactly cancelled by the reaction of the buggy on the horse. The buggy pulls backward on the horse just as hard as the horse pulls forward on the buggy, so they cannot move.

b) The horse pulls forward slightly harder on the buggy than the buggy pulls backward on the horse, so they move forward.

c) The horse pulls before the bugy has time to react so they move forward.

d) The horse can pull the buggy forward only if the horse weighs more than the buggy.

e) The force on the buggy is as strong as the force on the horse, but the horse is joined to the earth by its flat hoofs, while the buggy is free to roll on its round wheels.

You must finally select one of the answer choices. Otherwise, if it is not obvious which choice you have made from the details of your resonse (and I won't spend much time trying to make a determination) you cannot be selectd for Best Answer.

Answer: E. True, the force on the horse is as strong as the force on the buggy, but you are interested in motion-acceleration, not force. A thing's acceleration depends on its mass as well as the force on it.

Well, who has the most mass -- the horse or the buggy? It doesn't matter, because the horse has joined itself to the earth by its flat hoofs. So in effect one force pulls on the buggy (sorry Helmut) and an equal and opposite reaction pulls on the horse AND EARTH. To pull back the horse also requires pulling back the massive earth, while the buggy being less massive than the earth, moves much more easily. But as the buggy moves forward, the whole earth moves SLIGHTLY backward.

If the horse pulls the buggy a foot forward, how far backwards does the earth move? Suppose the buggy weighs 1000 pounds. The mass of the earth is 10,000,000,000,000,000,000,000 times greater. So the plantet moves a 10, 000,000,000,000,000,000,000th part of a foot backwards, (continued)...

(continued)...
which is hard to notice! Incidentally, you can save some ink by writing 10,000,000,000,000,000,000,000 (it has 22 zeros) as 10superscript 22.

Interesting range of responses and reasoning!

Answer 1

Logically, you know that the horse can pull the buggy, therefore the correct answer is "e)" The system is not confined to the horse and buggy, The horse also exerts a force on the Earth, The buggy exerts a force on the Earth, and the Earth exerts an equal and opposite force on the horse and the buggy, etc. If you look at the direction and magnitude of all of the forces, including friction, you will see that the horse can indeed pull the buggy.

If the Earth was not part of the system, and the horse and buggy were just floating, then indeed the horse would have no way of pulling the buggy right?

Answer 2

Answer B. Buggy at rest has static frictional forces that the horse must overcome. Horse must exert enough force exceeding the static frictional forces the buggy creates in order to move the buggy forward. Bonus comment: Maintaining the motion involves dynamic frictional forces which are usually less than static frictional forces.

Answer 3

The horse does not pull the buggy. It pushes it.

Answer 4

Helmut is right