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โš™๏ธย ap physics c: mech

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๐Ÿชย Unit 7

ย ย โ€ขย ย โฑ๏ธ2 min read

7.1 Gravitational Forces

Daniella Garcia-Loos

daniella garcia-loos

โฑ๏ธ November 5, 2020

๐Ÿ“…

Unit 7: Gravitation

Overview

Gravitation may be the last and shortest unit, but you can see the applications of everything you've learned so far in this unit! From momentum to energy to forces, everything has accumulated to this point.

Big Ideas

  • Fields:

    • How does the moon stay in orbit despite its great distance from the Earth?

  • Conservation:

    • Why is navigation technology dependent on the orbits of Earthโ€™s artificial satellites?

Exam Impact

Unit 5 will cover approximately 6%-14% of the exam and should take around 5 to 10, 45-minute class periods to cover. The AP Classroom personal progress check has 10 multiple choice questions and 1 free response question for you to practice on.

7.1: Gravitational Forces ๐ŸŽ

When an object is large enough/massive enough it will create its own gravitational field which can interact with other objects that have gravitational fields.

Newton's Law of Universal Gravitation: Every object attracts every other object in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance/radius between their centers.

You can see the equation form of the law below:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-R575Q4av2rVv.png?alt=media&token=13757e37-3a0a-46c7-aabc-f91f8b3e6b42

In which Fg is the force of gravity, m1 and m2 are masses, r is the distance between the two masses, and G is the universal gravitational constant which is 6.67*10^(-11) ((m^3)(kgs^2)).

Essentially, this law is an extension of Newton's Third Law in which every action has an equal and opposite reaction.

Here's a diagram that illustrates the law:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-B2xNxCE4HRBS.png?alt=media&token=2ee12c67-e3d3-474b-a579-4c9b42de0377

Taken from Wikimedia Commons

Now, we can use this equation to find the acceleration due to gravity on an object!

If object is on/near earth's surface:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-voyeDb831yiH.png?alt=media&token=083c70b3-776a-425f-8710-a6f09e804e5a

g is the acceleration due to gravity and we can cancel out the mass, therefore:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-yffW0byxgn2S.png?alt=media&token=4b9683c3-27bd-49e3-b6c2-8b33ac7e97c9

if the object is far from the earth's surface, we use the distance from the earth to the object rather than the earth's radius:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-10-13%20at%2012.35-0VW6R7PX35EK.png?alt=media&token=7a303f8e-46ce-4b20-8ca7-7f2b5453e5e1

Additionally, it should be noted that gravity is a conservative force, meaning that its path is independent of it and the total work on a closed path is zero. Note that work done by a conservative force is equal to the negative change in potential energy. However, it is not uniform!

This might be intuitive to some, but the further away the object is, the weaker the gravitational force acting on it from the other object will be. You can see this below:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-uzvVI6CBRJiu.png?alt=media&token=56199292-640d-450b-bd14-b0c182b857e7

Taken from Physics Stack Exchange

Unit 7.1 Practice Problems

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-uQbW2Nxjxsru.png?alt=media&token=3a49b184-da54-4b58-bb30-97e860dc66b5

Taken from College Board

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-PYo0a5eQeQl2.png?alt=media&token=f4f27e4a-30f6-4404-a1c0-a5233437aca0

Answer

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3OakoEChAqHA.png?alt=media&token=4c1539e1-de6b-46b2-b43c-9f87e0e1f70e

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-FtbxE6pjRJeg.png?alt=media&token=9d8a665b-33ec-44df-8e78-635505b8f54b

Answer

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-4SzXMXaVd6cn.png?alt=media&token=27a8400c-d6ca-4231-8b75-6b0a0e8dde0b

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