Free fall is a fascinating phenomenon where objects move solely under the influence of gravity. This topic explores the kinematics of free fall, using modified equations to describe an object's motion as it accelerates downward at 9.8 m/s².
We'll dive into how position, velocity, 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
- Kinematic equations for free fall derived from general kinematic equations with modifications:
- Acceleration always due to gravity ($g$) approximately $9.8 m/s^2$ near Earth's surface
- Vertical position denoted by $y$ instead of $x$
- Positive $y$-direction typically chosen upward
- Four kinematic equations for free fall:
- $y = y_0 + v_0t - \frac{1}{2}gt^2$ relates position, initial position, initial velocity, time, and acceleration due to gravity
- $v = v_0 - gt$ relates velocity, initial velocity, time, and acceleration due to gravity
- $v^2 = v_0^2 - 2g(y - y_0)$ relates velocity, initial velocity, position, initial position, and acceleration due to gravity
- $y - y_0 = \frac{1}{2}(v + v_0)t$ 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 ($g$) constant and downward
- Magnitude of acceleration approximately $9.8 m/s^2$ 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:
- Identify known variables like initial position ($y_0$), initial velocity ($v_0$), acceleration due to gravity ($g$), and time ($t$) at which to calculate unknown variable
- Choose appropriate kinematic equation including unknown variable to calculate
- Substitute known values into equation and solve for unknown variable
- Example calculating velocity after 2 seconds for object dropped from 50 m height:
- Given: $y_0 = 50 m$, $v_0 = 0 m/s$, $g = 9.8 m/s^2$, $t = 2 s$
- Choose equation: $v = v_0 - gt$
- Substitute values: $v = 0 - (9.8)(2)$
- Solve: $v = -19.6 m/s$, object moving downward at 19.6 m/s after 2 seconds (falling stone, skydiver)
- Newton's laws of motion explain the constant acceleration in free fall due to the gravitational force
- Gravitational potential energy decreases as an object falls, converting to kinetic energy
- Conservation of energy applies in free fall, with total mechanical energy remaining constant in ideal conditions
- Projectile motion combines free fall with horizontal motion, resulting in parabolic trajectories
- In real-world scenarios, drag force affects free fall by opposing motion and potentially leading to terminal velocity