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Gravity and Air Resistance

Gravity is the attraction between two objects. We all know that gravity is the reason why all things fall to the ground. As we stand on the Earth, we experience this force of gravity F_grav. The force of gravity F_grav=mg. This is easily confused with the acceleration of gravity g. The acceleration of gravity is experienced when the force of gravity is the only thing that is acting on an object. On and near the surface of the Earth, the acceleration of gravity is 9.8m/s^2. This acceleration of gravity is the same for all objects regardless of the mass. The value of g depends on where you are located from the Earth's center.It can seen from the chart that the change in g from the center of the Earth follows that g is inversely proportional to the distance from Earth's center squared. These values were found using the formula g=GM/d^2 whch states that gravitational acceleration is equal to the gravitational constant G = 6.672x10^-11 Nm^2/kg^2  times the mass of the Earth divided by the distance squared.



Air resistance is dependent on the density of the fluid, the speed of the object, the drag coefficient (which is dependent on the shape of the object) and also the cross sectional area of the object. The more air molecules the object collides wth, the greater the air resistance. F_drag=(1/2)ρ(v^2)CA.


Newton's second law states that F=ma. The force that causes the acceleration of an object is dependant on the mass of the object. An object will acclerate if there is an unbalanced force acting on the object and the amout of acceleration is drectly proportional to the amount of force acting upon it.


Say for example, an elephant and a feather was dropped from the top of the building. What is happening with gravity, air resistance, acceleration of gravity and terminal velocity? When the objects are initially drop, they will both experience an unblanaced downward force of gravity so the objects will begin to accelerate. As the objects gain speed, the objects will start to feel an upward force of air resistance. The elephant is the bigger, heavier object and will have greater air resistance than the feather. But, if the elephant encounter more air resistance, why does it fall faster than the feather? Wouldn't the object with the greater air resistance fall slower?


This is not the case. The elephant will also have to accelerate for a longer period of time before there is sufficient upward air resistance to balance the downward force of gravity (it requires a greater speed to accumulate sufficient upward air resistance force to balance the downward force of gravity). Terminal velocity is when the air resistance force is large enough to balane the downward forrce of gravity and there is zero acceleration. Objects will continue to fall to the ground at this speed as it is the final velocity of the object. Larger, heavier objects will take longer to reach this terminal velocity and that is why heavier, larger objects fall faster than lighter, smaller objects as some larger, heavier objects never reach terminal velocity and they continue to accelerate as it falls, approaching terminal velocity but never fully reaching. The elephant will accelerate for longer and therefore reach the ground faster than the feather.

So what happens in a free fall scenario or when the objects are placed in a vacuum? IN this case, air resistance is neglected and the larger, heavier object experiences a greater force than the smaller object. This tends to produce greater accecleration but the mass of the object resists the acceleration. The greater mass of the elephant offsets the influence of the greater force so increasing the mass decreases the acceleration.

The ratio of force to mass is the same for the elephant and for the mouse. The acceleration is 10m/s^2 which is called the gravitational field strength expressed as 9.8m/s^2 near the Earths surface as stated above. All objects accelerate with this acceleration of gravity when dropped from the air.

CHART 1: Shows the different values of g depending on where you are from the Earth's center. (chart taken from Physics Classroom 2014)

FIGURE 1: Shows the free body diagram of the elephant and feather after falling for 1 second, 2 seconds and 5 seconds. The feather hits terminal velocity but the elephant does not (image taken from the Physics Classroom 2014)

FIGURE 2: (left) shows different F_grav of the elephant and mouse but the same acceleration. (right) shows the force and mass ratio for both the elephant and mouse are the same. (images taken from the Physics Classroom 2014)

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