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Horse - Carriage problem - Newton's III law of motion

Students of basic physics are well aware of the Newton's Laws of Motion which states that "Every Action has an equal and opposite reaction." 

Here is a famous paradox related to the above mentioned law. Consider a horse pulling a carriage. In this process, the horse applies a force (say F) on the carriage to pull it. Now, according to the Newton's III law, the carriage will apply and equal but opposite force (i.e. -F). Thus the net resultant Force should be F+(-F)=0. In other words, the horse would never be able to pull the carriage, no matter what amount of Force it applies on the carriage! Yet, we see horses pulling carriages everyday! So, where's the catch? Is the Newton's III law wrong?

Absolutely not. The catch in the above mentioned paradox lies in the fact that of the two forces applied on each other by the horse as well as the carriage, the force applied by horse translates into more work than the force applied by carriage.

This is because, when the horse pulls the carriage, it is actually applying force on the wheels of the carriage to overcome the force of friction offered to the wheels of the carriage by the floor below. Whereas, the opposite but equal force applied by the carriage on the horse acts on the feet of the horse to overcome the frictional force between the feet of the horse and the floor. Now, the force of friction between the wheels of the carriage and the floor is less than the frictional force between the feet of the horse and the floor. Thus even though both the forces are equal and opposite, the force applied by horse on the carriage translates into more work than the force applied by the carriage on the horse. Thus, the horse is able to pull the carriage.

NOTE: If you remove the wheels of the carriage and make the horse pull the bare cart on the floor, it will become more difficult for the horse to pull now as the frictional force experienced by the horse and the carriage with the floor will almost be equal. 

-Gurudev
MADE IN INDIA
gurudevp@vsnl.net
On 2 December 2002

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