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AP Physics C: Mech

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Unit 7

# 7.1 Gravitational Forces

Daniella Garcia-Loos

### AP Physics C: MechanicsΒ βοΈ

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## 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 Earthβ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 π

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:
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:

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

Taken from Physics Stack Exchange

### Unit 7.1 Practice Problems

Taken from College Board

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πUnit 1: Kinematics
πUnit 2: Newton's Laws of Motion
π’Unit 3: Work, Energy, and Power
π³Unit 4: Systems of Particles and Linear Momentum
π²Unit 5: Rotation
πUnit 6: Oscillations
πͺUnit 7: Gravitation