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Name: Kelly
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Question:
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?



Replies:
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

---Nathan A.Unterman


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.

Richard Barrrans


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 ball falling 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 just ignore.

Tim Mooney


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.

-Paul Cadden-Zimansky


Kelly,

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.

Matt Voss


Dear Kelly,

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


Kelly,

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.

Dr. Mellendorf


Dear Kelly,

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!

Regards,

Todd Clark



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