 # Free Fall  View Notes

Define Free Fall

The free fall definition is the movement of an object or body only under the influence of gravity. The acceleration caused by this external force on the object, hence the motion of the object will be accelerated. Thus, free fall motion is also popularly known as the acceleration due to gravity. The acceleration in this motion is constant because the gravitational force rather than the pull is downwards and has a constant value. And the scenario will even be the same when a body has zero gravity. For example, say that the body is thrown upwards. Hence, the term acceleration due to gravity means that motion of an object under free fall with constant acceleration (g) towards the Earth can be calculated as,

g = 9.8m/s²

Motion Under Gravity Free Fall (Newtonian Mechanics)

• The uniform gravitational field with zero air resistance: A small vertical distance close to the surface of the Earth where an object falls. As long as the air resistance is lower than the force of gravity on the body, or equivalently the terminal velocity of the body is much greater than the body’s velocity.

The initial velocity is v₀

The vertical velocity with respect to time is v(t)

The initial altitude is y₀

The altitude with respect to time is y(t)

The time elapsed is represented by t

The acceleration due to gravity (9.8 $\frac{m}{s²}$ near Earth’s surface) is denoted by g

∴ v(t) = v₀ - gt

y(t) = v₀t + y₀ - $\frac{1}{2}$gt²

• The uniform gravitational field in the presence of air resistance: In the case of the uniform gravitational the mass of an object be considered as m, and the cross-sectional area be A, and if the Reynolds number is above the critical limit such that the v of the square of the fall velocity is proportional to the air resistance, has an equation of motion under gravity free fall

m$\frac{dv}{dt}$ = mg - $\frac{1}{2}$ρC$_{D}$Av²

[where the air density is represented by ρ, and the drag coefficient is represented with C$_{D}$, which even though depends on the Reynolds number yet commonly popular as a constant].

Let us think of a body which was at rest but now falling with no change In the density of the air with altitude, then the equation will be

v(t) = v$_{∞}$tanh ($\frac{gt}{v_{∞}}$),

Now when the terminal speed is provided, the equation will be,

v$_{∞}$ = $\sqrt{\frac{2mg}{ρC_{D}A}}$

The vertical position of the body as a function of time can be found if the speed of the body against time can be integrated over time,

y = y₀ - $\frac{v_{∞}^{2}}{g}$ ln cos h($\frac{gt}{v_{∞}}$).

The uniform gravitational field with air resistance applies to parachutists and skydivers motion while doing the activity and falling from a height.

Solved Examples

Question: Is the acceleration due to gravity or the value of ‘g’ a constant?

Let an object (say a ball) be dropped from a height on the surface of the Earth, but that height is minimal in comparison to the radius of the Earth (almost negligible).

The force acting during free fall motion is equal to the force of gravitation between the falling body and the Earth

Therefore we can put this in the form of an equation,

F = $\frac{GMm}{(R+h)²}$

[where M = mass of the Earth, and G = the universal gravitation constant. And we also assume that (R+h) is almost equal as R, where R = radius of the Earth]

∴F = G$\frac{Mm}{R²}$ [Equation (1)]

And according to Newton’s second law, F = ma

And the acceleration due to gravity which is represented by g is also calculated by force per unit mass, then

F = mg [Equation (2)]

From equation (1) and (2) we can equate,

mg = G$\frac{Mm}{R²}$

or, g = G$\frac{M}{R²}$ [Equation (3)]

Therefore, from equation number 3, we can see that the value of 'g' is not as constant as indifferent to G's value, which is a universal constant. The value of the due to gravity depends upon the mass and radius of the object, and from which we can conclude that it will not be the same everywhere. But the free fall acceleration remains constant during the free fall motion. Therefore the equation of motion can be easily used if only the acceleration value is replaced by 'g' in all those equations.

Fun Facts

The motion of an object under free fall: Long ago, Galileo discovered that all objects would experience the same ‘g,’ i.e., the acceleration due to gravity when the air resistance was not present. Later in 1971, astronaut D. Scott tried to experiment with this theory with practical proof as he on the Moon’s surface released a feather and a hammer from the same vertical length or height. The result was that the feather and the hammer both reached the ground of the Moon at the same time. This happened because, on Moon, the gravitational pull is only one-sixth compared to that of Earth’s.

1. Give a Few Examples of the Free Fall Concept for Better Understanding.

Answer: There are many examples of free fall in our environment from which the free fall meaning can be understood even better:

The motion of a spacecraft is also an example of the motion of an object under free fall. In space when the propulsion is off, then the spacecraft first goes up for a few minutes and then travels downward.

Free fall definition in physics proves that a falling skydiver also experiences the free fall motion before opening their parachute because that person in that state experiences drag force which when he/she reaches terminal velocity equals their weight.

A body also experiences free fall motion when it is dropped from the top of a column like from the top of a drop tube.

2. What is the Concept of Free Fall in Terms of General Relativity?

Answer: Many aspects of physics tried to explain the free fall meaning, but among them, one simplified explanation is the free fall in terms of general relativity. According to general relativity, the motion of an object under free fall is an inertial object moving along a geodesic (a curve representing the shortest distance between two points) is subject to no force.

The Newtonian theory of the free fall concept will only agree to general relativity when the object is far from space and time curvature, where the space-time is flat. If this doesn’t happen, then the Newtonian theory and the general relativity’s concept of free fall disagree.

It is only the general relativity that can say about the precession of orbits, the inspiral of compact binaries due to gravitational waves or the orbital decay, the frame-dragging, and geodetic precession, which altogether is called the relativity of direction.

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