The Physics of a Horse Pulling a Carriage

Date: 07/13/2005 at 01:33:12
From: Lina
Subject: Physics - Newton forces

Hi Dr. Math

I have a question about the forces that enable an object to be moved.
The question is: "How can a horse pull a carriage?"

I know that Newton's Law states that an object will not move or stop
in its track unless there is an unbalance force acting on it.  And
that F(a on b) = F(b on a).

So if it is like that then where does the horse get its starting 
force from?  And when it does start to pull the carriage, how can it 
stop if the force that it exerts on the carriage is the same amount 
that the carriage exerts on it?

Also, I know that there is some friction acting too, but I'm confused
about where the friction comes from and how it fits into the whole thing.

Also, does the force only act between the carriage wheel and the 
ground, and the horse's hooves and the ground or what?

Thanks for your time.

Date: 07/13/2005 at 14:23:25
From: Doctor Edwin
Subject: Re: Physics - Newton forces

Hi, Lina.

Great question!  It's always exciting to really think about something 
that you usually just take for granted.

In school, we usually aren't taught about action and reaction very 
well.  I remember the example I was taught was, "If you're standing 
in a boat and you throw a rock, the boat moves backwards."  But 
that's not a good way to describe it.  The rock-and-boat example, 
like the horse-and-cart example, is actually TWO action-and-reaction 
pairs.  When I'm on the boat, I push against the rock.  That's the 
action f(me on rock).  The reaction is that the rock pushes on me 
with the same force f(rock on me).  The result of my pushing on the 
rock is that the force on it is unbalanced and it accelerates away 
from me.  The result of its pushing on me is that I accelerate away 
from it.  In doing so, I push against the boat.  It pushes back.  The 
results are that the boat moves along with me, and I am accelerating 
more slowly than I would if I weren't pushing on the boat.

Now, let's look at the horse example.  The first action is that the 
horse pushes backward against the ground with force f(horse on 
ground).  So what's the reaction to that?  What's the result of the 
action?  What's the result of the reaction?  (Hint: the result of the 
reaction is a lot easier to observe than the result of the action). 
Can you carry it through from here?

Now, what's the importance of friction?  Would it be possible for the 
horse to push sideways on the ground if there were no friction?

The other situation to consider is when all the forces are balanced.  
The cart and horse are in motion, and not accelerating.  In that 
case, there are two forces that must be in balance.  The first is the 
force that the horse exerts by pushing backward against the ground.  
Can you tell what the second is? 

Write back and let me know how much of this makes sense. 


- Doctor Edwin, The Math Forum
  http://mathforum.org/dr.math/