Tru Physics

Chapter 10: Free Fall Motion

—

by

Tru Physics
in

10.1 Introduction to Free Fall Motion

Free fall is a type of motion experienced by objects that are falling under the influence of gravity. It occurs when an object is dropped from a height or is projected upwards and then falls back to the ground due to the force of gravity.

10.1.1 Definition of Free Fall 

In physics, free fall is defined as the motion of an object that is only affected by the force of gravity and (generally) experiences no other forces. This means that the object falls freely towards the ground, accelerating at a constant rate.

10.1.2 Importance of Free Fall in Physics

Free fall is a fundamental concept in physics and is used to describe the motion of objects under the influence of gravity. This concept is important in many areas of physics, including kinematics, dynamics, and astrophysics.

10.1.3 Real-Life Examples of Free Fall

Free fall can be seen in many everyday situations, such as when an apple falls from a tree or when a skydiver jumps out of an airplane. These examples illustrate how objects experience free fall when they are not restrained by any forces other than gravity.

Skydiving out of an airplane is a great example of free-fall at work. However, in this scenario, quadratic air resistance plays a significant role in the motion of the skydiver. This factor should be accounted for.
Skydiving out of an airplane is a great example of free-fall at work. However, in this scenario, quadratic air resistance plays a significant role in the motion of the skydiver. This factor should be accounted for.

10.2 Equations for Free Fall

10.2.1 Deriving the Theoretical Basis for Free Fall

The equation for free fall is derived by considering an object that is subjected to a constant acceleration due to gravity. The acceleration of an object in free fall is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth. By Newton’s Second Law, we can write: \Sigma \vec{F} = m \cdot \vec{a}. Seeing as gravity is the only force at play here, we can now write: m \vec{g} = m \vec{a}. This simplifies nicely when we cancel m from both sides are are just left with: \vec{g} = \vec{a}.

10.2.2 Using Equations to Calculate Free Fall Motion

Generally, we want to calculate quantities such as position, velocity, and acceleration of an object as it falls under the influence of gravity. Understanding this motion is a powerful tool for making predictions about how objects will move in different situations.

Equation:

y_f = \dfrac{1}{2}a_yt^2 + v_{i,y}t +y_i

where y_f is the final y position relative to the chosen coordinate system and y_i is the initial position. a_y is really just g, the acceleration due to gravity (9.8 \dfrac{m}{s^2}), and v_{i,y} is the initial velocity in the y-direction. So, for an object dropped from rest, v_{i,y}=0 \dfrac{m}{s}. Finally, t is time, measured in seconds.

NOTE: You must be consistent in choosing a coordinate system. For example, if you choose down to be the negative direction, then you will plug in -9.8 \dfrac{m}{s^2} for a_y. Do not forget the negative sign if this is how you choose to organize your coordinate system!

10.3 Factors Affecting Free Fall

10.3.1 Air Resistance

One of the factors affecting free fall is air resistance. Air resistance, also known as drag, is a force that opposes the motion of an object as it falls through the air. Air resistance can slow down an object’s descent, causing it to fall more slowly than it would if there were no air resistance. The magnitude of the air resistance force depends on several factors, including the velocity of the object, the size of the object, and the density of the air.

There are two main types of air resistance: quadratic air resistance and linear air resistance. Quadratic air resistance is a model in which the air resistance force is proportional to the square of the velocity of the object. In other words, as the object’s velocity increases, the air resistance force increases faster. This type of air resistance is often used to model the motion of an object moving through the air at high speeds, such as a skydiver falling through the air.

Linear air resistance is a model in which the air resistance force is proportional to the velocity of the object. In other words, as the object’s velocity increases, the air resistance force increases, but at a constant rate. This type of air resistance is often used to model the motion of an object moving through the air at low speeds, such as a feather falling through the air.

Generally, we say that air resistance can be written as the sum of both types mentioned above: f(v) = f_{linear} + f_{quadratic} = bv + cv^2 and thus the total drag vector can be written as: \vec{f} = -f(v) \hat{v}

Note that b = \beta D and c = \gamma D^2 where D is the diameter of a sphere representing the object in question, while \beta and \gamma are coefficients that are determined by the nature of the medium itself. At standard temperature and pressure, a spherical projectile might have values similar to \beta=1.6 \cdot 10^{-4} \frac{N \cdot s}{m^2} and \gamma=0.25 \frac{N \cdot s^2}{m^4}. These values, however, are subject to a great deal of variability, and real-world data should be consulted before choosing values for experimental or research work.

10.3.2 Initial Velocity

Another factor that affects free fall is the initial velocity of the object. If an object is projected upwards with an initial velocity, it should have a sign (positive or negative) that is opposite the sign chosen for g. So, if you choose g to be positive, then all motion in the downward direction is also positive. Thus, launching a projectile upward would result in a negative value for v_{i,y}. On the other hand, if g is chosen to be negative, that would make upwards the positive direction. Then, v_{i,y} will be positive for an object launched upwards.

10.4 Free Fall on Different Planets

10.4.1 Differences in Free Fall on Earth, Moon, and Other Planets

The acceleration due to gravity is different on other planets, which means that the motion of objects in free fall will also be different. On Earth, the acceleration due to gravity is approximately 9.8 \frac{m}{s^2}, while on the Moon it is approximately 1.62 \frac{m}{s^2}. On other planets, the acceleration due to gravity can be significantly different from that on Earth.

10.4.2 The Role of Gravity in Free Fall

Gravity is the force that drives free fall, and its strength is determined by the mass and distance of the objects involved. The stronger the gravitational force, the greater the acceleration of an object in free fall. On different planets, the strength of gravity can be significantly different, which affects the motion of objects in free fall.

10.5 Applications of Free Fall in Real Life

  • Sports and Athletics: In many sports, free fall is a crucial component. For example, in gymnastics, divers use the principles of free fall to perform various aerial maneuvers and flips. Skiers and snowboarders also use free fall as they soar through the air and perform tricks.
  • Engineering and Architecture: Free fall is also important in engineering and architecture. Engineers design roller coasters and other thrill rides to maximize the sensation of free fall. When designing tall structures such as skyscrapers, architects consider the effects of free fall and ensure that the structures are sturdy enough to withstand the forces involved.
  • Astronomy and Space Exploration: In astronomy and space exploration, free fall plays a crucial role in our understanding of the solar system and beyond. Some scientists use the principles of free fall to calculate the orbits of planets and other celestial bodies. They also use free fall to study the behavior of objects in microgravity, which is an important aspect of space research.

Chapter Summary

Recap of Key Points

  • Free fall is the motion of an object that is subject only to the force of gravity. It is an important concept in physics and is used to calculate the motion of objects under the influence of gravity.
  • The equations for free fall can be derived from simple assumptions and used to calculate the motion of objects. Factors such as air resistance and initial velocity can affect the motion of objects in free fall.
  • Free fall occurs on different planets and is affected by the strength of the gravitational force on each planet. It has important applications in sports, engineering, architecture, astronomy, and space exploration.

Significance of Free Fall Motion

Free fall is an exciting and fascinating aspect of physics that has important real-life applications. Understanding the principles of free fall can help us better appreciate the world around us. This can also enable us to make more informed decisions about the things we build, the activities we participate in, and the research we conduct.

Enroll on Canvas

This course uses Canvas for homework assignments, quizzes, and exams. These assignments are open to everyone. Anyone is allowed to enroll in the Canvas course. In fact, this is highly encouraged as it will help you track your progress as you go through the course. Graded feedback will help you get an idea for what your grade would actually be in a Physics 1 college course. Use this link to enroll in the Canvas course.

Continue to Chapter 11: Projectile Motion
Back to Chapter 9: Newton’s Laws of Motion

Are you enjoying this content? Read more from our Physics 1 course here!

Do you prefer video lectures over reading a webpage? Follow us on YouTube to stay updated with the latest video content!

Comments

3 responses to “Chapter 10: Free Fall Motion”

  1. Newton’s Laws of Motion – Tru Physics

    […] Continue to Chapter 10: Free Fall Motion […]

    Reply
  2. Newton’s Laws of Motion – Tru Physics

    […] Continue to Chapter 10: Free Fall Motion […]

    Reply
  3. Chapter 11: Projectile Motion – Tru Physics

    […] Back to Chapter 10: Free Fall Motion […]

    Reply

Have something to add? Leave a comment!