Newton's 3rd Law: Horse & Cart Motion Explained

[JimmyRay]

The question is, "If a horse pulls on a cart, the cart pushes on it with an equal but opposite force, therefore there should be no motion involved. If this is true how can the horse ever move the cart?". Does Newton's 3rd law not apply because the horse and the cart act as one mass?

 

[arildno]

No, that is not true.
The forces do not cancel each other, since they act on two different objects..
(Did you read my latest reply to your first thread, BTW?)

 

[Sirus]

In a way, the horse and cart do act as one mass. They do not move relative to each other. However, there is a net force here, because the horse pushes on the ground, and the ground pushes on the horse. The forces are the same, but the horse will not move the Earth very much, while the horse will be moved a lot by the Earth when it returns the force. Therefore, the horse pushes off of the Earth and so pulls the cart.

 

[JimmyRay]

Yes arildno I JUST read it and replied I didn't notice it before, (I went on to page 4 trying to find it because I missed it, lol).

Ohhhh ok, they are not affecting each other I see. The horse's force goes on the Earth and is pushed off by it and THEN the horse moves and THAT causes the cart to move, right?

 

[arildno]

That's the truth of the matter!
For later reference:
Under your own profile, there's an option:
"Find all threads started by JimmyRay"
Suppose the cart has mass M, the horse has mass m, the force between them is called F, and the force from the ground on the horse (for simplicity) G
Then, we may formulate Newton's 2.law for both cart and horse (we assume the will get the same acceleration a):
F=Ma (cart)
G-F=ma (horse)
Now, let's add these equations together:
G=(M+m)a
That is, G must be so strong to provide the acceleration "a" to the SYSTEM composed of cart+horse!
Hence, Newton' 3.law is seen as the proper way in which forces add up when we add together objects into systems of objects.

 

[JimmyRay]

wait wait wait... that kind of confused me...
If you add the equations of F=ma and G-F=ma you get...
G=(m+m)a

(That seems like the formula for finding the force of gravity between two objects...?)

Right now I can't relate what you've done with the formulas to answering my question...

But I do understand that the horse pushes off the Earth and THAT's where Newton's 3rd law applies, and not between the cart and the horse.

 

[arildno]

When I added the force law for THE CART with the force law for THE HORSE, I find the force law for THE SYSTEM CART+HORSE.
More precisely, we gain the force law for the two object's COMMON CENTER OF MASS.

 

[Gokul43201]

wait wait wait... that kind of confused me...
If you add the equations of F=ma and G-F=ma you get...
G=(m+m)a

No, the equations are F = ma and G-F = Ma

There's no reason to assume the horse and cart have the same mass.

 

[Gokul43201]

But I do understand that the horse pushes off the Earth and THAT's where Newton's 3rd law applies, and not between the cart and the horse.

No, Newton's Third Law applies here too. The force on the horse from the cart (F) is equal to the force on the cart from the horse.

These equal forces are acting on two different objects. There's no reason to say that something shouldn't move as a result of this.

 

[JimmyRay]

Equal forces acting on two different objects, omg... lol

It was so obvious, sorry guys...

 

[Sirus]

Nothing to be sorry about.