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is a fascinating phenomenon where objects move solely under the influence of gravity. This topic explores the kinematics of , using modified equations to describe an object's motion as it accelerates downward at 9.8 m/s².

We'll dive into how position, , and acceleration change during free fall. By understanding these concepts and applying the right equations, you'll be able to analyze and predict the motion of falling objects in various scenarios.

Free Fall Kinematics

Kinematic equations for free fall

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  • for free fall derived from general kinematic equations with modifications:
    • Acceleration always due to gravity ([g](https://www.fiveableKeyTerm:g)[g](https://www.fiveableKeyTerm:g)) approximately 9.8m/s29.8 m/s^2 near Earth's surface
    • denoted by yy instead of xx
    • Positive yy-direction typically chosen upward
  • Four kinematic equations for free fall:
    • y=y0+v0t−12gt2y = y_0 + v_0t - \frac{1}{2}gt^2 relates position, , , time, and
    • v=v0−gtv = v_0 - gt relates velocity, initial velocity, time, and
    • v2=v02−2g(y−y0)v^2 = v_0^2 - 2g(y - y_0) relates velocity, initial velocity, position, initial position, and acceleration due to gravity
    • y−y0=12(v+v0)ty - y_0 = \frac{1}{2}(v + v_0)t relates position, initial position, velocity, initial velocity, and time
  • Solve free fall problems by identifying known variables and choosing appropriate equation including unknown variable to calculate

Changes during free fall motion

  • Acceleration:
    • Acceleration during free fall always due to gravity (gg) constant and downward
    • Magnitude of acceleration approximately 9.8m/s29.8 m/s^2 near Earth's surface (skydiving, falling objects)
  • Velocity:
    • Velocity of object in free fall changes linearly with time due to constant acceleration
    • Initially moving upward, velocity decreases until zero, then becomes increasingly negative downward (thrown ball, launched rocket)
    • Initially moving downward, velocity becomes increasingly negative downward (falling raindrop, skydiver)
  • Position:
    • Position of object in free fall changes parabolically with time due to changing velocity
    • Initially moving upward, continues to rise until velocity reaches zero, then falls back down (tossed coin, jumping athlete)
    • Initially moving downward, continues to move downward at increasing rate (falling hailstone, dropped book)

Calculations in free fall analysis

  • Calculate object's position, velocity, or acceleration at specific time during free fall:
    1. Identify known variables like initial position (y0y_0), initial velocity (v0v_0), acceleration due to gravity (gg), and time (tt) at which to calculate unknown variable
    2. Choose appropriate kinematic equation including unknown variable to calculate
    3. Substitute known values into equation and solve for unknown variable
  • Example calculating velocity after 2 seconds for object dropped from 50 m height:
    • Given: y0=50my_0 = 50 m, v0=0m/sv_0 = 0 m/s, g=9.8m/s2g = 9.8 m/s^2, t=2st = 2 s
    • Choose equation: v=v0−gtv = v_0 - gt
    • Substitute values: v=0−(9.8)(2)v = 0 - (9.8)(2)
    • Solve: v=−19.6m/sv = -19.6 m/s, object moving downward at 19.6 m/s after 2 seconds (falling stone, skydiver)
  • explain the constant acceleration in free fall due to the gravitational force
  • Gravitational potential energy decreases as an object falls, converting to kinetic energy
  • applies in free fall, with total mechanical energy remaining constant in ideal conditions
  • combines free fall with horizontal motion, resulting in parabolic trajectories
  • In real-world scenarios, affects free fall by opposing motion and potentially leading to

Key Terms to Review (26)

Acceleration due to gravity: Acceleration due to gravity is the rate at which an object accelerates when falling freely towards a massive body, like Earth, due to gravitational pull. On Earth's surface, this value is approximately $9.8 \text{ m/s}^2$.
Acceleration Due to Gravity: Acceleration due to gravity, often denoted as 'g', is the acceleration experienced by an object due to the Earth's gravitational pull. This constant acceleration affects the motion of objects near the Earth's surface, influencing various physical phenomena such as free fall, mass, weight, and gravitational fields.
Air resistance: Air resistance is the force exerted by air against the motion of an object moving through it. This force opposes the object's motion and increases with speed.
Conservation of Energy: The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. This fundamental concept links various phenomena, illustrating how mechanical, kinetic, and potential energies interconvert while keeping the total energy constant in a closed system.
Drag force: Drag force is a resistive force exerted by a fluid (such as air or water) against the motion of an object moving through it. It acts in the direction opposite to the object's velocity.
Drag Force: Drag force is the resistive force that opposes the motion of an object moving through a fluid, such as air or water. It acts in the opposite direction of the object's motion and plays a crucial role in various physics topics, including free fall, projectile motion, solving problems with Newton's laws, and fluid dynamics.
Free fall: Free fall is the motion of an object under the influence of gravitational force only. It neglects air resistance and assumes a uniform acceleration due to gravity.
Free Fall: Free fall is a state of motion where an object is falling under the sole influence of gravity, without any other external forces acting upon it. This term is closely connected to the topics of motion with constant acceleration, projectile motion, Newton's second law, and gravitational effects near Earth's surface.
G: The acceleration due to gravity, commonly denoted as 'g', is a fundamental physical constant that represents the acceleration experienced by an object in free fall near the Earth's surface. It is a measure of the strength of the Earth's gravitational field and plays a crucial role in the understanding of various physical phenomena, particularly in the context of free fall and the relationship between mass and weight.
Galileo: Galileo Galilei was an Italian physicist and astronomer who made pioneering observations that laid the foundation for modern physics, particularly in mechanics. He is best known for his work on the motion of objects and the laws governing free fall.
Galileo Galilei: Galileo Galilei was an Italian astronomer, physicist, engineer, and philosopher who played a pivotal role in the scientific revolution of the 17th century. His groundbreaking contributions and discoveries had a profound impact on our understanding of motion, gravity, and the cosmos, laying the foundations for modern physics and astronomy.
Initial position: Initial position refers to the starting point of an object in motion before any forces act upon it. This concept is crucial when analyzing free fall, as it helps to establish where the object begins its journey and allows for the calculation of various kinematic equations that describe its motion under the influence of gravity.
Initial Velocity: Initial velocity refers to the speed and direction of an object at the start of its motion or at the beginning of a particular time interval. It is a fundamental concept in the study of kinematics, which is the branch of physics that describes the motion of objects without considering the forces that cause the motion.
Kinematic Equations: Kinematic equations are a set of mathematical relationships that describe the motion of an object, including its position, velocity, and acceleration, without considering the forces that cause the motion. These equations are fundamental in the study of classical mechanics and are widely used in the analysis of various types of motion, such as free fall, projectile motion, and uniform acceleration.
Newton's Laws of Motion: Newton's Laws of Motion are a set of three fundamental principles that describe the relationship between an object and the forces acting upon it, governing the motion of objects in the physical world. These laws form the foundation of classical mechanics and are essential in understanding the behavior of objects in various contexts, including the Scope and Scale of Physics, Algebra of Vectors, Free Fall, Newton's First Law, Impulse and Collisions, and Center of Mass.
Parabolic Motion: Parabolic motion is a type of projectile motion where an object follows a curved path described by a parabola. This motion is characterized by the combined effects of gravity and the initial velocity imparted to the object.
Position-Time Graph: A position-time graph is a graphical representation that shows the position of an object as a function of time. It is a fundamental tool used to analyze and understand the motion of an object in physics, particularly in the context of kinematics, which is the study of motion without considering the forces that cause it.
Projectile motion: Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity. It involves two components of motion: horizontal and vertical.
Projectile Motion: Projectile motion is the motion of an object that is launched into the air and moves solely under the influence of gravity and without any additional force acting on it. It is a type of motion that follows a curved trajectory, with the object's position and velocity changing over time in a predictable manner.
Terminal velocity: Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration. It occurs when the drag force equals the gravitational force acting on the object.
Terminal Velocity: Terminal velocity is the maximum speed that an object can reach while falling through a fluid, such as air or water, due to the balance between the downward force of gravity and the upward force of drag. This concept is fundamental in understanding the motion of objects under the influence of gravity and air resistance.
Vacuum Chamber: A vacuum chamber is an enclosed space where the air pressure is significantly lower than the surrounding atmosphere, creating a near-vacuum environment. This specialized apparatus is commonly used in various scientific and industrial applications, including the study of free fall phenomena.
Velocity: Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the speed and the direction of an object's motion, making it a more complete description of an object's movement compared to just speed alone.
Velocity-Time Graph: A velocity-time graph is a graphical representation that depicts the relationship between an object's velocity and time. It is a fundamental tool in understanding and analyzing the motion of an object, as it provides a visual representation of the object's speed and direction of motion over a given time period.
Vertical Position: Vertical position refers to the displacement or location of an object measured in the upward or downward direction, perpendicular to the Earth's surface. It is a crucial concept in the study of free fall motion, where the vertical position of an object changes over time due to the influence of gravity.
Y-direction: The y-direction refers to the vertical axis in a coordinate system, typically perpendicular to the horizontal x-axis. It represents the upward and downward motion of an object or the direction of forces acting on an object in a two-dimensional plane.
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Glossary
Glossary
3.6 Finding Velocity and Displacement from Acceleration