Gravitational Force

Ethan Williams

11 min read

Next Topic - Kinetic and Static Friction

Study Guide Overview

This study guide covers Newton's Law of Universal Gravitation, the gravitational field model, and the concept of weight as a gravitational force. It also distinguishes between apparent weight and true gravitational force, exploring the effects of acceleration and the equivalence principle. Newton's Shell Theorem and its implications for gravitational forces inside and outside spherical masses are explained. The guide also reviews inertial vs. gravitational mass and their equivalence. Finally, it provides exam tips focusing on key topics, common question types, and last-minute advice.

#AP Physics C: Mechanics - Gravitation 🚀

Hey there! Let's get you totally prepped for the gravitation section of the AP Physics C: Mechanics exam. This guide is designed to be your go-to resource, especially the night before the test. Let's make sure you feel confident and ready!

#Gravitational Interactions Between Objects

#Newton's Law of Universal Gravitation

The gravitational force between two objects is:
- Directly proportional to the product of their masses.
- Inversely proportional to the square of the distance between their centers of mass.
$F = G \frac{m_1 m_2}{r^2}$

Where:
- $F$ is the gravitational force.
- $G$ is the gravitational constant.
- $m_1$ and $m_2$ are the masses of the two objects.
- $r$ is the distance between their centers of mass.

Key Concept

Gravity is always an attractive force, pulling objects towards each other.

- The direction of the force is always along the line connecting the centers of mass of the two objects. - The **center of mass** of a system is the point where the gravitational force can be considered to act.

Memory Aid

Think of gravity like a cosmic hug – the bigger the objects, the stronger the hug, and the further apart they are, the weaker the hug.

#Gravitational Field Model

Fields help us understand non-contact forces, like gravity, by showing how they affect objects in space.
Gravitational field strength ( $g$ ) at a point is the gravitational force per unit mass:

$g = \frac{F}{m}$
The acceleration of an object due to gravity is numerically equal to the gravitational field strength at that location. 💡

Exam Tip

Remember that gravitational field strength ( $g$ ) is measured in N/kg, which is equivalent to m/s²

#Weight as Gravitational Force

Weight is the gravitational force exerted by a large astronomical body on a smaller nearby object.
Mathematically:

$Weight = F_g = mg$

Where:
- $m$ is the mass of the object.
- $g$ is the gravitational field strength.

Practice Question

json
{
  "mcqs": [
    {
      "question": "Two objects of masses m and 2m are separated by a distance r. What is the ratio of the gravitational force on the object of mass m to the gravitational force on the object of mass 2m?",
      "options": ["1:4", "1:2", "1:1", "2:1"],
      "answer": "1:1"
    },
    {
      "question": "A satellite is orbiting Earth at a certain altitude. If the satellite were moved to a higher orbit, which of the following would increase?",
      "options": ["The gravitational force on the satellite", "The satellite’s orbital speed", "The satellite’s period", "The satellite’s centripetal acceleration"],
      "answer": "The satellite’s period"
    }
  ],
  "frq": {
    "question": "A satellite of mass m orbits a planet of mass M at a radius R. (a) Derive an expression for the orbital speed of the satellite. (b) If the radius of the orbit is doubled, how does the orbital speed change? (c) Calculate the period of the satellite’s orbit in terms of G, M, and R.",
    "scoring_guidelines": {
      "part_a": "(3 points) Setting gravitational force equal to centripetal force: GmM/R^2 = mv^2/R. Solving for v: v = sqrt(GM/R)",
      "part_b": "(2 points) Since v is proportional to 1/sqrt(R), if R is doubled, v decreases by a factor of sqrt(2).",
      "part_c": "(3 points) Using v = 2πR/T and the result from part (a). Solving for T: T = 2πsqrt(R^...

How are we doing?

Give us your feedback and let us know how we can improve

Previous Topic - Newton's Second Law Next Topic - Kinetic and Static Friction