Mechanics of the Free Fall

Mechanics of the Free Fall

When a body is dropped from a height H it falls down freely due to the force of gravity. This is as per the first law of motion that states that any body is in a state of rest or is in a state of uniform motion until it is acted by an external force. When one holds the body at a height H above the surface of the earth one is exerting a force in the opposite direction to prevent is from falling. So the body starts falling down under the natural force of gravity.

Is this uniform motion or in other words does the body cover equal distances in equal intervals of time?. No, the motion is accelerated where the acceleration due to gravity is equal to 9.81 m/s * s. In other words it will cover unequal distances in equal intervals of time as the body approaches the surface of the earth.

Let us apply newtons second law of motion to the falling object. At any point the external force on the body is m * a. Here a is equal to the gravitational force of attraction and hence is equal to g. So the force of downward pull is m * g.

Let us calculate the time taken to reach the ground from the height H.
The laws of motion are S = u * t *t + 0.5 * g *t * t — (1)
Here u is the initial velocity and is equal to 0.
S is the distance traveled or is equal to H.
H = 0.5 * g * t * t or H = 4.9 t * t. This can also be derived using the law of conservation of energy. So at any point during the free fall the potential energy is equal to the kinetic energy 0.5 * m * v * v = m * g * h. v or the velocity of the body after time t under an acceleration of g can be calculated as v = u + gt where u is the initial velocity. So when the body is just dropped from a height h the initial velocity is 0. So v = gt. Applying the law of conservation of energy is 0.5 * m * g * g * t * t = m * g * h. So h is 0.5 * g * t * t. In fact all the equations of motion can be derived using the law of conservation of energy.

So the time taken by a body to fall from a height of 49 meters is sqrt(10) seconds, to fall from a height of 100 meters is sqrt(20.4) or 4.51 seconds Comparatively, the time taken by a human to race through 100m is 10 seconds so one can imagine the extent of the natural force of gravity.

Using the same equation (1) one can calculate the distance traveled by a body is say half a minute. In half a minute or in 30 seconds a body will reach the surface of the earth from a height of 4410 meters or 4.4 km. It can also be seen that in 1 minute or in 60 seconds a body can fall from a height of 17640 meters or 17.64 kilometers. One can also immediately verify that the body does not cover equal distances in equal intervals of time.

Another interesting aspect of the free fall is that the equations of motion are independent of the mass. But mass may affect the motion if there is resistance due t wind and if the surface of the body is not uniform. This may cause an upward drag and the motion may not be uniform for all masses. But without air resistance or in vacuum the motion will be as described above.

You May Also Like

About the Author: admin