Action-Reaction in Freefall
We are studying Newton's laws and my student
wanted to know: When an object falls in a vacuum, what are the
action-reaction forces, since there is no air resistance?
The action force is Earth pulling the object down, the reaction
force is the object pulling Earth up. Since the object has a tiny
mass compared to Earth, it is the item that sees the acceleration.
A good conceptual physics source that will help you is:
Paul Hewitt "Conceptual Physics" Addison-Wesley
There is no air resistance, but Earth's gravity pulls down on the
object as the object's gravity pulls upward on Earth with EXACTLY
the same magnitude of force. More accurately, their mutual
gravitational attraction pulls the objet and Earth together, toward each other.
Usually, when we say an object is falling, we are not paying much attention
to the thing that it is falling toward. Let us take the case of a
to Earth. Earth is so much more massive than the ball that is seems
unaffected by it, and we rarely think of the Earth as falling toward the ball,
but actually, both objects are falling toward each other. As the ball falls,
it gains momentum, and the Earth gains exactly the same momentum, but in the
opposite direction. But the Earth is so massive, compared to the ball, that
its momentum change implies an extremely small velocity change,
which we usually
If the action is the object being pulled down toward Earth, the
reaction is Earth being pulled up toward the object. Action and
reaction are both due to the force of gravity, are equal in magnitude,
and opposite in direction. From Newton's second law the force on any
object is equal to mass*acceleration. Since the force on Earth and
the force on the object are equal so is their mass*acceleration product.
As the mass of the earth is overwhelmingly large compared with any
terrestrial, falling object, the object's acceleration down towards
Earth is overwhelmingly large compared with Earth's imperceptible
acceleration up towards the object. For all practical purposes
Earth is usually regarded as stationary.
The accelerations of the object toward Earth and Earth toward the object
continue until the two collide (i.e. the object lands on the ground) and
the impact of the two produces another equal and opposite pair of
forces: the Earth pushes up on the object until it comes to a stop and
the object pushes down with equal force on the Earth until it too comes
to a stop.
If air is present there will be additional actions/reactions between the
object and the air molecules as well as between the Earth and the air
molecules, but provided the object is not so light that air currents
greatly effect it or is not dropped from such a height that it reaches
very high velocities the forces of the action/reaction described above
are the dominant ones.
The action/reaction forces are the same as in a vacuum, even though
there is no air resistance. Think of everything in terms of
conservation of momentum. The air only slows down the object
because the air molecules are basically "still" to the falling
object and so the object accelerates the air molecules around
it. This transfers a tiny bit of momentum from the object to the
air molecules. This continual loss of momentum to the air slows the
falling object down. In a vacuum, since there is no air, an object
will not meet air resistance and hence will not slow down until it
hits something else massive. At this point the action/reaction
forces are exactly as Newton described them, but the full momentum
is transferred instead of the full momentum minus the air
resistance. The air resistance is strong enough to slow things down
until the object hits critical velocity, where the air resistance is
equal to the effects of gravity and the object cannot fall any
faster. This speed is dependent on the mass and drag coefficient of
the object. Look more up on terminal velocity to read more details on this.
Newton's 3rd Law is rather subtle and it pays to be careful when applying it.
The 3rd Law says that if some object (call it A) is exerting a
force on a second object (call it B), then B is exerting a reaction
force on A which is equal in magnitude and opposite in direction.
Notice that this law implies that all forces must be caused by some
object (no object, no force). So there are always two
objects. Incidentally, this means there are never three objects in
an action-reaction chain. Forces in more complicated systems can
always be broken down into two-body action-reaction pairs.
In the example you give, the object falling in a vacuum (and
accelerating) is accelerating because of the gravitational force
exerted on it downward (toward the center of the earth) by the
earth (I presume this object is near the earth). The reaction
force is therefore the force exerted upward on the earth by the
object. This is true whether the object is falling in air or in a vacuum.
If the object is falling in air, the air exerts an upward
(retarding) force on the object. The reaction to that force is, of
course, the object pushing down on the air.
This may be confusing, but it is an important idea. I find it
helpful to remember that you climb a mountain by pressing down on
the mountain with your feet. Why does pressing down make you go
up? Because the earth kindly exerts a reaction force upward on your feet!
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
If the object falls in a vacuum due to gravity, then the gravity between the
Earth and the object is the force of concern. The Earth pulls on the
falling object, and the falling object pulls on the Earth. They both feel
the same amount of force. The object is strongly affected by the force,
feeling almost 10m/s^2 of acceleration. The Earth is so huge that it is not
affected. This is similar to a truck hitting a fly. Both feel the same
force, but only the fly notices.
Thanks for your question. Newton's Third Law of motion is often
quoted as "For every action, there is an opposite and equal
reaction" -- or "forces come in pairs". The most classic example of
this is when someone fires a rifle. The force of the explosion that
forces the bullet down the barrel also pushes back, so the person
firing the rifle feels a "kick" as the rifle accelerates backwards.
When I was teaching this to my physics class, I taught my students
to view this Law of motion this way:
"If ________(A)________ pushes/pulls on _______(B)_______ , then
_______(B)_______ pushes/pulls on _________(A)________."
For example, "If I push on the wall, then the wall pushes back on
me." For gravity, "If the earth pulls on me, then I pull on the
earth." This one seems a bit hard to belive, but that is how
gravity works. When I jump up away from the earth, the same force
pulling me back down to the earth is also pulling the earth up to
me. I will accelerate more quickly than the earth because I have
much less mass than the earth does -- which is why it seems that all
of the effect of these forces is on me and not on the earth -- but
the force pulling me down toward the earth is same as the force
pulling the earth up toward me.
A tug-of-war is also another "classic" example of this. If both
teams are evenly matched, then the force pulling north is about
equal to the force pulling south and the rope (and the flag in the
middle of the rope) will not accelerate. If the teams are unevenly
matched, then forces will be uneven (say the north is pulling
stronger than the south) then the flag will accelerate in the
direction of the stronger force.
So, this is a long way of saying when an object falls in a vacuum,
the object is pulling up on the earth with the same force that the
earth is pulling down on the falling object. That sounds a little
bit weird, but that is the way it is. No air resistance is
required. If fact, when air is included, you get another force
pair, the air pushing on the falling object and the falling object
pushing back on the air!
I hope this helps!
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Update: June 2012