# Conceptual questions on newtons third law

1. Sep 21, 2014

### Kontilera

Hello!
I'm a highschool teacher in physics. I will teach Newtons third law this coming week and found the following question (regarding a horse pulling a carriage):

"If the force on the carriage is equal and opposite to the force on the horse how can the horse pull the carriage? Is the answer:

(a) The horse cannot pull the carriage because the carriage pulls as hard on the horse as the horse pulls on the carriage.

(b) The carriage moves because the horse pulls slightly harder on the carriage

(c) The horse pulls the carriage before it has time to react.

(d) The horse can pull the carriage only if the horse is heavier than the carriage.

(e) Another explanation. What might it be?"

For me, the correct answer is (e). I think of the force from the carriage as being the force due to the inertia of the carriage. I.e. when the horse match the force of the carriage, it implies the acceleration.

How would you formulate the correct answer?

Thanks!

2. Sep 21, 2014

### A.T.

Yes, the others are all worng

No, it doesn't imply acceleration. The horse and carriage could exchange equal and opposite forces without acceleration. Acceleration is related to the sum of all forces on an object, and there are other forces acting on the horse and carriage, than just the ones between them.

See here:
https://www.lhup.edu/~dsimanek/physics/horsecart.htm
And dozens of other sites you can find with a simple web search.

3. Sep 21, 2014

### Drakkith

Staff Emeritus
The answer is that when the horse pulls the carriage, the friction between it and the ground is more than the friction between the carriage wheel and axle, allowing the carriage to accelerate. A.T.'s link explains it.

4. Sep 21, 2014

### Riadh

The simplest way I found to think about such problems is to remember that bodies can be either in constant motion (zero motion included) or accelerating. If the carriage is in constant motion then there is equilibrium between all the forces.. the horse being the forward force opposed by the friction with the road and in the axles. If the road is inclined then uphill will give an extra resistive component force and a downhill will be a helping component. How the carriage reached to its constant velocity is by accelerating first. In this case the forces are not in equilibrium (not equal) unless you add the inertial force (m*a) as a resistive force to the motion.

5. Sep 21, 2014

### sophiecentaur

The whole thing is a false dichotomy. Newton's Third Law implies nothing about equilibrium or the lack of it.

6. Sep 21, 2014

### Matterwave

The answer is very simple, as sophiecentaur said. The question is a false dichotomy, it is using words to try to trick you. The equal and opposite forces specified in Newton's law are on different objects. The force the carriage exerts on the horse has nothing to do with whether or not the carriage accelerates since this force is applied on the horse and not the carriage. The force the carriage exerts on the horse makes the horse have to work harder to move (after all it is easier to move without the carriage), but this just means a slower acceleration than without the carriage.

7. Sep 22, 2014

### Meir Achuz

Even in high school, you have to introduce a free body diagram.
Then tell them that the only forces affecting the motion of the carriage are forces that act ON the carriage. The force of the carriage on the horse does not act ON the carriage and is irrelevant to the motion of the carriage.

8. Sep 22, 2014

### Staff: Mentor

This sounds very much like a homework question in sheep's clothing. Even if the OP is a HS teacher, it would have been better to post in Introductory Physics forum, since the teacher is still a student of introductory physics.

Chet

9. Sep 22, 2014

### FactChecker

Others may have covered this, but here is my two cents:
The force between the horse and the cart are equal and opposite. If the horse was only pushing against the cart, there would be no net motion. A horse inside a trailer can not move the trailer no matter how hard he pushes. But the horse is pushing against the earth, so the horse and cart combination can move versus the earth.

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