Free Fall Stuntman’s Free Fall – Great Adventure

Questions: Do heavier objects fall faster than lighter ones when starting from the same position? Does air resistance matter? If the free fall motion has a constant acceleration, what is this acceleration and how was it found? How do we solve problems involving free fall?

Galileo (1564 – 1642) and the leaning tower of Pisa Free fall experiment.

Actually, it all started with a cannonball… Well, and before the cannonball, it started with a philosopher & scientist named Aristotle. In ancient Greece around 400 BC, he proposed that the rate at which an object falls depends on its mass. In other words, Aristotle believed that the heavier the object, the faster it falls.

Galileo’s Ball and Channel Experiment

Galileo’s Ball and Channel Experiment He varied the starting position of the ball along the channel. He measured the times for the ball to travel the various lengths. He raised the channel until it was steep enough to simulate free fall.

Galileo’s Finding “ We compared the time for the whole length with that for the half, or with that for two-thirds, or three-fourths, or indeed for any fraction; in such experiments, repeated a full hundred times, we always found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane, i.e., of the channel, along which we rolled the ball. Galileo “Two New Sciences” I other words time is the same, no matter what the mass of the ball is.

Lets get back to the future of the past In the late 1500s, an Italian scientist named Galileo Galilei decided to prove Aristotle wrong. Galileo theorized that all objects will land at the same time when they are dropped from the same height. To prove this to his critics, he set up a little experiment.

A story about a cannonball Galileo carried a cannonball and a wooden ball up the 300 steps of the Leaning Tower of Pisa. Dropping the two different balls at exactly the same time, the crowd was amazed with what they saw… The two balls, with extremely different masses, landed at the exact same time! Disclaimer: this story may or may not be true, but a similar and well-documented experiment was performed by Benedetti Giambattista in 1553.

Elephants & feathers What did Galileo prove? Objects fall to the ground at the same rate because acceleration due to gravity is the same for all objects. For example, an elephant and a feather fall with the same acceleration even though they have different masses.

Free Fall Explained Since the ratio of weight (F) to mass (m) is the same for the 10-kg cannonball and the 1-kg stone, they both fall at the same rate of acceleration. Why? Weight-mass ratios for each are identical! It takes a larger force to keep the larger mass accelerating because a larger mass has more inertia.

Gravity & Acceleration The rate at which objects accelerate towards Earth is 9.8 m/s/s. This acceleration is the same for all objects, regardless of their mass. In other words, falling objects accelerate at a constant rate of 9.8 m/s2. Gravity = g = 9.8 m/s2

Gravity & Acceleration Notice, the ball isn’t traveling at 9.8m/s2, it’s accelerating at 9.8 m/s2. It’s velocity is continually increasing. Only the acceleration remains constant. Each picture was taken 1 second apart, but notice how the ball travels a greater distance between each second.

Apollo 15 -Astronaut David Scott on the Moon (1971) Hammer and Feather on the Moon https://www.youtube.com/watch?v=KDp1tiUsZw8 http://www.archive.org/details/NIX-LV-1998-00046

Does Air Resistance Matter? Despite the fact that all objects are supposed to fall at the same rate, you know that this is not always the case.

Hammer & Feather in the presence of air

Hammer & Feather in the absence of air

Air Resistance The force of friction or drag acting on an object in a direction opposing its motion as it moves through air.

Falling and Air Resistance Air resistance does not depend upon the weight of the object. Falling and Air Resistance The amount of air resistance force an object experiences depends on the object’s speed and exposed surface area. 1. Speed The greater the speed, the greater the air resistance. 2. Exposed Surface Area The greater the surface area, the greater the air resistance.

Speed in Free Fall If you know the acceleration of an object in free fall, you can predict its speed at any time after it is dropped. The speed of a dropped object will increase by 9.8 m/sec every second.

Objects in Free Fall If a falling object starts at rest, it will be moving at 9.8 m/sec after one second 19.6 m/sec after two seconds 29.4 m/sec after three seconds, and so on.

How Fast & Far? V= gt t = √2d/g

Terminal Velocity As an object falls, the air resistance is continually increasing. Eventually, the force of the air resistance will match the force of gravity pulling the object down. When this happens, the overall force is 0 N and the object stops accelerating. The object is now falling a constant velocity, which is called the terminal velocity.

Projectile Motion Rather than dropping a ball straight down, what happens if you throw it horizontally? An object that is thrown is called a projectile. Will a projectile that is thrown horizontally land on the ground at the same time as an object that is dropped?

The yellow ball was given a horizontal push at the same time as the red ball was dropped. Even though the yellow ball moves horizontally, the force of gravity continues to act on it in the same way it acts on the red ball. The yellow ball falls at the same rate as the red ball. Thus both balls will hit the ground at exactly the same time.

To Find Distance from t and g: d=vit + ½ g t2

Acceleration due to Gravity, g g=-9.8m/s2 (we often use -10m/s2) g= v f –v i t When vi=0: vf=gt Note: the down direction is usually assumed negative.

Equations of Motion for Uniform Accelerated Motion vf= vi+ gt vavg = ½ (vf +vi) d= ½ (vf + vi)t d= vit + ½ gt2 vf2 = vi2 + 2gd d is the displacement (or Δd) Assume that ti=0

Example 1: Free Fall A ball is dropped from rest from the top of a building. Find: The instantaneous velocity of the ball after 6 sec. How the ball fell. The average velocity up to that point. Answers: -60m/s, 180m, -30m/s

Example 2: Free Fall on the Moon A hammer is dropped on the moon. It reaches the ground 1s later. If the distance it fell was 0.83m: Calculate the acceleration due to gravity on the surface of the moon. Calculate the velocity with which the hammer reached the ground and compare to the velocity it would have, if it was dropped on the earth’s surface. Answer:-1.66m/s2, -1.66m/s, -9.8m/s