BrainDen.com - Brain Teasers

# The Donkey and Cart Paradox

## Recommended Posts

This is a common Physics paradox:

A donkey starts to pull a cart (he exerts a force in one direction). The cart therefore exerts the same amount of force on the donkey (a force in the opposite direction). (Newton's third law: For every action, there is an equal and opposite reaction.) So how can the donkey pull the cart if the cart exerts the same amount of force on the donkey in the opposite direction? Should he not move?

The two forces may be of the same strength and opposing in direction, but they act on different objects: one on the donkey and one on the cart. Thus they cannot be added together to cancel each other out.

Also, two other forces exist: the forces between the wheels/ground and the hooves/ground. Because the friction between the hooves and ground is greater than with the wheels, the donkey pulls the cart. So really, the donkey is pushing on the ground to pull the cart. The ground does a good job in moving things!

##### Share on other sites

The opposite reaction to the Donkey's force would be pressure from the harness exerting force on the Donkey's body. Newton's third law doesn't require a "pull" from the cart, but merely a force equal to the pull of the Donkey. That force would be produced by inerta and friction. However, the cart is on two very efficient levers (the wheels) which greatly aids the Donkey's ability to overcome the inertia and friction. If you overcome the force of inertia and friction on an object, you get movement.

Now, put that donkey on a couple wheels and position him so the cart is creating the pull, say on a very steep hill, and I bet the result is different.

##### Share on other sites
This is a common Physics paradox:

A donkey starts to pull a cart (he exerts a force in one direction). The cart therefore exerts the same amount of force on the donkey (a force in the opposite direction). (Newton's third law: For every action, there is an equal and opposite reaction.) So how can the donkey pull the cart if the cart exerts the same amount of force on the donkey in the opposite direction? Should he not move?

This is not a paradox. It's a misapplication of Newton's 3rd law.

Newtons 2nd Law says that an object of mass m, acted upon by a net force F, experiences an acceleration a,

in the direction of F, such that F=ma. The cart accelerates because it experiences an imbalance of forces.

Newton's 3rd law is different. It does not apply to an object.

It does not say that the vector sum of the forces acting upon an object is zero.

It says that at the interface between two objects, equal and opposite forces are exerted.

The ground, the donkey and its harness all combine to exert an unopposed force to the cart, so it accelerates.

That happens because these objects are in contact, and Newton's 3rd law is obeyed at these points of contact.

Take a baseball hit by Alex Rodriguez's bat. Ball and bat exert equal and opposite forces on each other [N3].

No other force acts on the ball, so the ball accelerates. [N2]

Because the ball exerts an equal force on the bat [N3], the bat slows down [N2].

The motion of objects does not contradict a right application of Newton's 3rd law.

##### Share on other sites
• 2 months later...

The cart is not resisting the donkey. The donkey is planting its foot in the ground and trying to pull it back. The equal and opposite reaction would be the the donkey, with the cart, moving forward.

Also, it that statement were true, then Newton's second law, a stationary object is stationary until it is influenced by an outside force, would be false, because the object would be resisting, and therefore not moving.

The real question is whether Newton meant matter as the object, or energy. If it is energy, then potential energy would have to be converted into kinetic energy in order to counter the force.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.