Reciprocity

claimed by ksomu3

This topic covers why forces on each other are equal.

The Main Idea

Reciprocity is the idea that the force object 1 exerts on object 2 is the same as the force object 2 exerts on object 1. This idea comes from Newton's Third Law of Motion. Forces are results of interactions. If i put my hand on a table, I am exerting a contact force on the table, but at the same time the table is using a exerting force on me. Though it seems like I am putting in more effort, the forces are the same. Forces come in pairs. The two forces are called "action" and "reaction" pairs. When forces are in these pairs, the magnitude of the two forces equal each other. However, in vector form, the two forces would be in opposite directions of each other, so one force would have a negative sign on it.

A Mathematical Model

Here is a formulaic representation of reciprocity. F12=-F21. This shows that

[math]\displaystyle{ {\mathbf{F}}_{12}= {\mathbf{-F}}_{21}\ This is the equation in vector format. When the vector of one force is in one direction. Usually, the vector is in the other direction; ::\lt math\gt \vec{\mathbf{F}}_{12}= vec{\mathbf{F}}_{21}; What are the mathematical equations that allow us to model this topic. For example \lt math\gt {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

This equation on the left side. shows that object one is acting on object 2;

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

If you exert 20 N on the table, what would be the normal force of the table on you?

Since you are exerting 20 Newtons, due to reciprocity the table will be exerting a normal force of 20 Newtons.

Middling

A 60 kilogram man stands on the surface of the Earth. What is the force Earth exerts on the man? What is the force the man exerts on the Earth?

60x9.8=588N. Due to reciprocity 588 is the force on both Earth and the man.

Difficult

This problem is from our test.

Two blocks of mass m1(under rod) and m3(above rod) are connected by a rod of mass m2. A constant unknown force F pulls upward on the top block while both blocks and the rod move upward at a constant velocity v near the surface of the Earth. The direction of the gravitational force on each block points down. Find F1on2, the force exerted by the bottom block on the rod.

Fnet1=0 due to constant v. F2on1-m1gy=0. F2on1=m1gy F1on2=-m1gy

Connectedness

1. The first physics I ever learned was Newtons laws. Before heading into any science class, I always thought, every reaction gets an equal and opposite reaction. I didnt really understand it. That is a fundamental principle that we use in almost all physics problems. It has been test questions and homework questions. The thing that intrigues me the most is how an ant can be pushing against a rhino and though the rhino is so much bigger, they are still exerting the same force.
2. I am an industrial engineering major and though there is very minimal use of physics in that field, I do believe it is something that will help us go about our days knowing that force isn't how much effort you put in but about the action reaction pairs.
3. Forces are something we deal with everyday. Everything we touch, me typing this page right now is all the result of forces. An important industry that deals with this is the automobile industry. If we understand the forces of the wheels on the road, we will know how to make wheels that best suit an automobile.

History

Isaac Newton was born in Woolsthorpe, England. When he was a child, one day he was resting under an apple tree when suddenly an apple fell on his head. He thought about why things fall down and not fall back up. He spent years figuring out the phenomenon. After all this, he came up with three laws of motion. This is when he discovered gravitation as a force. Where Newton's Law comes into play is that the Earth is exerting a force on us to stay with it since closer objects exert stronger forces on each other. We are also exerting a force on Earth so that we stay on the ground and don't go flying off. The date of this story is not known, and some even believe it to be a myth. However William Stukeley, author of Memoirs of Sir Isaac Newton's Life noted that he had a conversation with Newton and Newton talked about why an apple falls to the ground due to gravitational interaction.

See also

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References

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