A horse is urged to pull a wagon. The horse refuses to try, citing Newton’s thir

Question

A horse is urged to pull a wagon. The horse refuses to try, citing Newton’s third law as a defense: The pull of the horse on the wagon is equal but opposite to the pull of the wagon on the horse. “If I can never exert a greater force on the wagon than it exerts on me, how can I ever start the wagon moving?” asks the horse.

A. How would you respond to the horse? In other words, how could you convince him that Newton’s third law doesn’t prevent him from pulling the wagon?

2. The horse seems to imply that he can’t move the wagon for the following reason: The backward force exerted by the wagon on the horse equals—and therefore cancels—the forward force exerted by the horse on the wagon. Do those two forces cancel each other? Explain.

3. Is it possible for the horse to feel a net forward force even though the wagon pulls back on him just as strongly as he pulls forward on the wagon? Explain.

4. At this point, how would you respond to the horse?

Thank you!

Explanation / Answer

I think you need to bear in mind two things: equal forces acting on bodies does not lead to equal acceleration; and a body accelerates when subject to unbalanced force. There is a Newton's 3rd law force pair between the horse and the wagon, and these are equal and antiparallel, true. However, there are more forces acting on the horse. As well as being pulled by the wagon, it is also pushing against the ground, a normal reaction that, due to the inclination of the hooves against the ground, yields a force component parallel to the ground away from the wagon. The normal reaction on the wagon is due to its weight and this is pretty much verticle - i.e. negligible horizontal component. You also have friction acting against the acceleration on both bodies. For the wagon, since it is supported by rotating axles, this is going to be comparitively low. For the horse, whatever the friction is is irrelevant, since it is the total force (normal + friction) that acts on the wagon - i.e. the force the horse exerts on the wagon, that is matched by the wagon itself, includes the horse's friction but NOT the wagon's. The force exerted on the horse by the wagon includes the wagon's friction, but this is lower. Overall, the force is balanced in the horse's favour. Simple. The horse puts a force forward on the wagon, right? This causes the wagon to exert a force backward on a horse. This force pushes the horse into the ground, causing a net backward force on the earth, and a forward force from the ground to the horse. The force of the earth on the horse and the wagon on the force cancel, leaving only a net force on the wagon and the earth.

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