# (INTERSTING!)question aboutnewton law of motion

1. Jul 29, 2006

### wonderkid

question:

a hourse is 'bound' together with a cart to carry goods.
according to newton's third law,when 2 bodies interact,they exert equal and opposite forces on one another.
then,if horse exerts a force to move forward,there should be an equal and opposite direction force exerted by the cart that acting on horse.
then net force between these two bodies will be zero.
BUT WHY THE HORSE STILL CAN MOVE FORWARD IF THE NET FORCE BETWEEN CART AND HORSE ARE ZERO?

2. Jul 29, 2006

### Staff: Mentor

The horse does not move forward with respect to the cart, in accorance with Newton's law.

3. Jul 29, 2006

### HallsofIvy

Notice the words "with respect to the cart" in russ watters' answer!

There is a force, forward, applied to the cart by the horse and an equal-but-opposite force applied to the horse by the cart. There is no net force and so the distance between the horse and cart does not change.

There is also a force to the earth, backward, applied by the horse to the ground. The ground applies an equal-but-opposite force, forward to the horse. Since the horse and earth are not bound together the horse (and cart) moves forward. Theoretically, the earth moves slightly backward but the difference in masses is so great, it is infinitesmal.

4. Jul 29, 2006

### Staff: Mentor

That's correct. If the horse pulls on the cart, then the cart pulls back on the horse with an equal and opposite force. Note that these "equal and opposite" forces act on different bodies and thus cannot be added together to get a net force.
I'll rephrase that: In order for the cart to start moving, the horse must exert a force on it. Right! And thus there is an equal force pulling back on the horse. If that were the only force acting on the horse, then cart and horse would just pull themselves closer to each other. But, of course, the ground also exerts a force on the horse.
No! Let's look at each body separately:
-Cart: Only one force acts on the cart, so obviously the "net" force on the cart can't be zero!
-Horse: Two forces act on the horse: the cart's force pulling back, and the ground pushing forward.

If you choose to look at the "Cart + Horse" as a single system, then the forces between Cart and Horse will cancel each other, since they both act on the same system. But then the only force of interest for understanding the motion of "Cart + Horse" is the external force of ground on horse.
Because the net force on each object is not zero!

5. Jul 29, 2006

### Danger

Wonderkid, it might be helpful for you to update the question to a tractor trailer (semi). You can see that if you weld the fifth wheel linkage so that they form a solid body, the (straight-line) dynamics of the system don't change. The reason for the update is that it's very difficult to weld a horse. They tend to start kicking when you attach the ground clamp.
Anyhow, the net force of the system is primarily the vehicle vs the Earth. You also have to contend with frictional losses through both rolling resistance and the axle bearings, and air resistance. While those might appear inconsequential on the surface, remember that in a tornado the air resistance can be more powerful than the motor.
I specified straight-line dynamics above because obviously the thing won't handle corners.

6. Jul 29, 2006

### Gokul43201

Staff Emeritus
Russ, Halls : There is absolutely nothing in Newton's Law that prevents the horse from moving forward "with respect to the cart".

7. Jul 29, 2006

### Danger

True up to a point, Gokul. There will be relative movement until the elastic limit of the attachment (harness etc.) is reached. If it doesn't break, then the cart has to move with the horse; if the cart is too heavy, then the horse will stop moving at that point.
That ambiguity is actually why I used the trailer example.

8. Jul 29, 2006

### Staff: Mentor

The reason why the horse does not move with respect to the cart is not because Newton's law's prevent it, but because horse and cart are assumed to be attached. But all that is beside the point of the OP's question, which has to do with understanding Newton's 3rd law.

9. Jul 29, 2006

### Gokul43201

Staff Emeritus
Last edited: Jul 29, 2006
10. Jul 29, 2006

### Hootenanny

Staff Emeritus
I think it may be high time that an explanation of Newtons 3rd law was added to out FAQ in general physics.

11. Jul 29, 2006

### Staff: Mentor

?? F=ma: if f=0, a = 0?

12. Jul 29, 2006

### Gokul43201

Staff Emeritus
What if the horse and cart were attached by an ideal spring? What about two bodies that are gravitationally or electrostatically coupled? The reason that there is no relative acceleration in the OP's case is because of the rigid harness and that's it.

13. Jul 30, 2006

### Staff: Mentor

The horse and cart aren't attached by an ideal spring, so it really isn't relevant: I was answering the question that was asked.
That is a way to look at it without using the laws of motion, but the OP was asking about the laws of motion, so I answered the question in those terms. Just saying that they are attached rigidly doesn't explain how that jives with the laws of motion. Besides, if the cart and horse are attached by a spring, you still need to apply f=ma in addition to the spring force equation to find the acceleration of each or between the two.

Last edited: Jul 30, 2006
14. Jul 31, 2006

### Mk

I just bought a box of those off ebay!