Action Reaction force on the earth

In summary, the force of gravity acts downward upon a body as it sits in a chair, with the reaction force being the body pulling the Earth upwards. This is possible because of Newton's Law of Universal Gravitation and Third Law of Motion. However, the forces are equal in magnitude but opposite in direction, resulting in no acceleration of the Earth due to the person's gravitational pull.
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Zack K
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"As you sit in your chair and study your physics (presuming that you do), the force of gravity acts downward upon your body. The reaction force to the force of the Earth pulling you downward is the force of your body pulling the Earth upwards". I read this somewhere just a bit ago and it's confusing me. How is it possible for you to be able to pull the Earth towards you with the same force? A mathematical explanation would be good also.
 
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Zack K said:
"As you sit in your chair and study your physics (presuming that you do), the force of gravity acts downward upon your body. The reaction force to the force of the Earth pulling you downward is the force of your body pulling the Earth upwards". I read this somewhere just a bit ago and it's confusing me. How is it possible for you to be able to pull the Earth towards you with the same force? A mathematical explanation would be good also.
Just apply Newton's Law of Universal Gravitation and Newton's Third law of motion.
The force of the Earth (of mass M) on a body of mass m is:
$$ F_{M on m} = m\frac{GM}{R^2}\hat{R} $$

By the third law, there must be an equal and opposite force of the body on the earth:

$$F_{m on M} = - M\frac{Gm}{R^2}\hat{R}$$

So the forces are equal in magnitude but opposite in direction.

If you consider a person falling to the Earth rather than sitting in a chair, the gravitational forces are still equal and opposite, but not the accelerations. Since F = mass × acceleration the Earth does not accelerate very fast toward the person. Acceleration of the Earth is so small it cannot be measured. Work out the acceleration of the Earth from a falling 100 kg mass using the above equation.

AM (Edited in response to A.T.'s comment below)
 
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Zack K said:
"As you sit in your chair and study your physics ...
Andrew Mason said:
Work out the acceleration...
If you sit in your chair, there is no acceleration, because the contact forces cancel the gravitational forces.
 
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A.T. said:
If you sit in your chair, there is no acceleration, because the contact forces cancel the gravitational forces.
Thanks. Your point is well taken, although the contact forces don't exactly cancel the gravitational forces. They still exist, of course. But the gravitational and contact forces sum to 0, so there is no acceleration. I have edited my earlier post accordingly.

AM
 
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1. What is an action-reaction force on the earth?

An action-reaction force on the earth refers to the equal and opposite forces that occur when two objects interact with each other. This means that for every force that is exerted on an object, there is an equal and opposite force exerted back.

2. How does an action-reaction force affect the earth?

An action-reaction force can affect the earth in various ways, depending on the objects involved and the magnitude of the force. For example, when a person jumps, the force they exert on the ground causes the ground to push back with an equal force, propelling the person upwards. This is how we are able to walk, run, and move on the earth's surface.

3. Can an action-reaction force cause the earth to move?

Yes, an action-reaction force can cause the earth to move, but the movement would be very small and imperceptible to us. This is because the force of the earth's mass is much greater than any force we could exert on it.

4. What are some examples of action-reaction forces on the earth?

Some common examples of action-reaction forces on the earth include walking, throwing a ball, riding a bike, and even sitting on a chair. In all of these actions, there is a force being exerted on the earth and an equal and opposite force being exerted back.

5. Is the action-reaction force always equal in magnitude?

Yes, according to Newton's third law of motion, the action and reaction forces are always equal in magnitude but in opposite directions. This means that if one force is stronger than the other, it will result in a net force and cause movement.

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