WHAT IS FREE FALL?
All the objects dropped near the surface of the Earth in the absence of air resistance fall towards the Earth with the same constant acceleration.
The study of falling objects was first conducted by great philosopher Aristotle and it was believed that heavier objects fell faster than lighter once. Galileo proved this theory to be wrong and formulated the laws governing the motion of objects in free fall. But up to the year 1600, Galileo’s theory was not accepted by the scientific community.
GALILEO’S FREE FALL EXPERIMENT
Galileo discovered the law of falling objects by observing that two different weights dropped simultaneously from the leaning tower of Pisa hit the ground at approximately the same time. He performed many systematic experiments on objects moving on inclined planes. He rolled balls down an inclined plane and measured the distance they covered in successive time intervals.
The purpose of the incline was to reduce the acceleration so that he could make accurate measurements of the time intervals.
He conducted the experiment at various angles by gradually increasing the angle of inclination.
When the angle becomes 90 degree, i.e., vertical, the falling ball is equivalent to a free fall.
This experiment and the results made a high impact in the scientific community. This paved the way for Newton in his development of the laws of motion.
TRY THIS OUT!
Purpose: To understand the concepts in free fall.
Experiment: Drop a coin and a feather from the same height simultaneously.
Observation: Coin comes first and then feather.
Reason: This is due to air resistance. If the air resistance on these objects are negligible, both will have the same motion and hit the floor at the same time.
What if you conduct this experiment in vacuum?
In vacuum, air resistance is zero so the feather and coin would fall with the same acceleration. Such a motion is called free fall.
If you drop a coin and feather on moon, they fall with the same acceleration to the lunar surface. This is because moon has no atmosphere.
ACCELERATION DUE TO GRAVITY
During the free fall, the body feels weightlessness. Gravity is the only force acting upon the motion of a free falling object.
- The free fall acceleration is represented by g, called acceleration due to gravity having an average value of g is 9.8 m/s2 on the surface of the Earth.
- g is directed downward toward the center of earth.
- The magnitude of g decreases slightly with the altitude.
Note: There is a change in g if we move towards the center of Earth. At the center of Earth g=0.
A HYPOTHETICAL SITUATION
Suppose you could drill a hole through the center of the Earth, the end of the hole being the other side of the earth. So, the length of the hole is equal to the diameter of earth.
If you jump into the hole, can you reach the other side?
At the moment of jump, the initial velocity is zero and the acceleration is g. As you move down, your speed increases because of acceleration due to gravity. Your weight would be 0 and speed becomes very high as you flew through the center of the Earth. For our hypothetical journey, we will assume the Earth to be of uniform density and neglect air friction and the high temperature of this trip. Beyond the center of Earth, the gravity will pull you back to the center and so you would decelerate and slow down to a stop just as it reached the other surface. Momentarily the gravity will pull you back to the center of the earth and then to that point from where you jump. This will continue indefinitely.
Hence you will execute simple harmonic motion about the center of Earth i.e., just like a pendulum.
If there is air resistance and other dissipating forces exist, there would be a loss of velocity on each swing reducing the back and forth amplitude each time. Finally, you would come to near rest at the central core of Earth. During the whole journey, only one force is acting, which is the gravitational force. In this example, half of the journey i.e., from Earth surface to the center of the Earth is equivalent to a body falling freely from rest and the other half is similar to a body that is thrown upwards from the surface of the Earth.
So are you ready for gedanken fall?