Gravitational and Electric Forces: AP Physics 1 Study Guide
Introduction
Hey there, future physicists! Ready to dive into the universe's most attractive forces? We're going to talk about gravitational and electric forces — think of them as the ultimate cosmic magnets, pulling all masses and charges together. Let's get ready to get seriously attractive (or repulsive, in the case of electric forces), shall we? 🌌⚡
Gravitational Force
Gravity: the ultimate clingy friend of the universe. This force is the reason planets orbit stars, moons orbit planets, and why you don't float away while reading this. Gravity is the cosmic equivalent of a very dedicated hug—it always pulls things towards the center.
Imagine a planet or other celestial body drawing objects toward itself like a giant cosmic vacuum cleaner. This relentless force keeps all the planets, moons, and even you grounded. Gravity never lets go and is always attractive, which is more than we can say for that odd soda you left in the fridge too long. 🍻
The gravitational force is a longrange force, which means it doesn't have to physically touch anything to exert its influence. It's kind of like that meme that's been circulating the internet since 2006—it simply never dies.
When Does Gravity Get Important?
Gravity really flexes its muscles when the masses involved are enormous, like planets and stars. For everyday stuff like your pencil, the force is so small it's practically nonexistent. Now, before you start blaming gravity for every time you trip, just know that it’s also steering the Earth's course around the Sun, orchestrating the dance of planets and guiding comets through space. You might say it's the DJ at the universe's hottest club. 🎶🌍
The gravitational force is described by the simple equation:
[ F_g = mg ]
where:
 ( F_g ) is the force of gravity in Newtons (N).
 ( m ) is mass in kilograms (kg).
 ( g ) is the acceleration due to gravity, which is about ( 9.8 , \text{m/s}^2 ) on Earth's surface.
Newton's Universal Law of Gravitation
Newton was a pretty bold guy who decided to explain every single gravitational interaction in the universe with one tidy equation:
[ F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} ]
where:
 ( F_g ) is the gravitational force in Newtons (N).
 ( G ) is the gravitational constant, approximately ( 6.67 \times 10^{11} , \text{Nm}^2/\text{kg}^2 ).
 ( m_1 ) and ( m_2 ) are the masses of the two objects in kilograms.
 ( r ) is the distance between the centers of the masses in meters.
Just to clarify, ( G ) is a very tiny number, meaning the gravitational force between small objects (like ice cream cones and physics textbooks) is usually very weak. But don't tell your ice cream cone it's insignificant; it's sensitive about these things. 🍦
The law tells us that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. In simpler terms: more mass = stronger attraction, more distance = weaker attraction. It’s like a universal dating rule: close up, more attractive; far away, less attractive. 💕💔
Electric Force
Now, let's get jolted into the world of electric forces! Electric forces are like gravity's dramatic sibling: they can both attract and repel. If you’ve ever been shocked by a doorknob or played with a balloon to make your hair stand, you have experienced electric forces in action.
Electric force is governed by Coulomb's law:
[ F_e = k_e \cdot \frac{q_1 \cdot q_2}{r^2} ]
where:
 ( F_e ) is the electric force in Newtons (N).
 ( k_e ) is Coulomb’s constant, approximately ( 8.99 \times 10^9 , \text{Nm}^2/\text{C}^2 ).
 ( q_1 ) and ( q_2 ) are the charges of the objects in Coulombs (C).
 ( r ) is the distance between the charges in meters.
Coulomb's law, much like Newton's law of gravitation, states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It’s like placing two electric charges in a social network: depending on their 'charge,' they either become besties or unfollow each other immediately! 💁♂️❌
Common Ground and Differences
Both of these forces share a lot in common: they are central (acting along the lines joining the centers), conservative (path independent), and follow the inversesquare law.
However, a key difference is that gravitational force is always attractive, while electric force can either attract or repel depending on the types of charges involved. This means two positive charges will repel, as will two negative charges, but a positive and a negative charge will attract, possibly forming the cutest atomic couple ever. 😍⚛️
Practice Problems
Let's make physics fun with some practice problems!

Two objects with masses of 10 kg and 5 kg are located 3 meters apart. What is the gravitational force between them?
 a) 0.22 N
 b) 2.2 N
 c) 22 N
 d) 220 N
 Answer: a) 0.22 N
 Explanation: [ F = \frac{G \cdot m_1 \cdot m_2}{r^2} = \frac{(6.67 \times 10^{11} , \text{Nm}^2/\text{kg}^2) \cdot 10 , \text{kg} \cdot 5 , \text{kg}}{3^2 , \text{m}^2} = 0.22 , \text{N} ]

A planet with a mass of ( 5 \times 10^{24} , \text{kg} ) is located ( 1.5 \times 10^{11} , \text{m} ) away from a star with a mass of ( 2 \times 10^{30} , \text{kg} ). What is the gravitational force between them?
 a) ( 2.22 \times 10^{11} , \text{N} )
 b) ( 2.22 \times 10^{13} , \text{N} )
 c) ( 2.22 \times 10^{15} , \text{N} )
 d) ( 2.22 \times 10^{17} , \text{N} )
 Answer: d) 2.22 x 10^{17} N
 Explanation: [ F = \frac{G \cdot m_1 \cdot m_2}{r^2} = \frac{(6.67 \times 10^{11} , \text{Nm}^2/\text{kg}^2) \cdot (5 \times 10^{24} , \text{kg}) \cdot (2 \times 10^{30} , \text{kg})}{(1.5 \times 10^{11} , \text{m})^2} = 2.22 \times 10^{17} , \text{N} ]

A satellite with a mass of 500 kg is located at a distance of 1000 km from the center of Earth, which has a mass of ( 5.97 \times 10^{24} , \text{kg} ). What is the gravitational force acting on the satellite?
 a) ( 1.96 \times 10^4 , \text{N} )
 b) ( 3.92 \times 10^4 , \text{N} )
 c) ( 7.84 \times 10^4 , \text{N} )
 d) ( 1.57 \times 10^5 , \text{N} )
 Answer: c) 7.84 x 10^4 N
 Explanation: [ F = \frac{G \cdot m_1 \cdot m_2}{r^2} = \frac{(6.67 \times 10^{11} , \text{Nm}^2/\text{kg}^2) \cdot 500 , \text{kg} \cdot (5.97 \times 10^{24} , \text{kg})}{(1000 \times 10^3 , \text{m})^2} = 7.84 \times 10^4 , \text{N} ]
Key Terms to Review
 Gravitational Constant: Represented by ( G ), it’s the fundamental physical constant that quantifies the strength of the gravitational force between two objects.
 Gravitational Force: The attractive force between two masses. It depends on the masses of the objects and the distance between them.
Now that you're a pro at gravitational and electric forces, get ready to ace those AP Physics 1 exams. Remember, whether you're calculating the orbital path of a distant planet or merely dropping your pen, gravity’s got your back. And with electric forces? Let’s just say you’ve got the power! 🎓🔥
Go out there and make Alphys gyroscopic! (See what I did there? 'Alphys' instead of 'alphas'? No? Okay, only physicists would get that joke. 😅)