# The Catch 22 of Newton's 3rd Law

## Main Question or Discussion Point

I'm long past the days of general physics, but a friend who's taking it now posed an interesting thought experiment, of which to my embarassment, I was unable to answer! He said, imagine a horse is urged to pull a wagon. The horse refuses to try, citing Newton's third law as his 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. How would you argue with the horse?

Stupid, I know...but it's driving me crazy! Anyone remember this stuff???

## Answers and Replies

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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.

Hi. 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.

Doc Al
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pattiecake said:
The horse refuses to try, citing Newton's third law as his 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. How would you argue with the horse?
Realize that the two forces in Newton's 3rd law always act on different bodies! (In this example the horse and the wagon are the two bodies.) Equal and opposite forces only "cancel" and produce equilibrium if they act on the same body.

To find out how things will move, you need to consider all the forces acting on the body (as others have explained). For example, the horse is also being pushed forward by the ground.