mechanics of free fall

By | July 10, 2022

When a body is dropped from a height H, it will fall down freely due to gravity. This corresponds to the first law of motion, which states that every body is in a state of rest or in a state of uniform motion until an external force acts on it. Holding the body at a height H above the earth’s surface exerts a force in the opposite direction to prevent it from falling. So the body begins to fall down under natural gravity.

Is it a uniform motion, or in other words, does the body cover equal distances at equal intervals of time? No, the movement is accelerated when the acceleration of gravity equals 9.81 m/s * s. In other words, it travels unequal distances at equal time intervals as the body approaches the earth’s surface.

Let’s apply Newton’s second law of motion to the falling object. At each point the external force on the body is m * a. Here a is equal to the gravitational force and therefore equal to g. So the force of the downward pull is m * g.

Let’s calculate the time it takes to reach the ground from height H.

The laws of motion are S = u * t * t + 0.5 * g * t * t — (1)

where u is the initial velocity and equals 0.

S is the distance traveled or equals H.

H=0.5*g*t*t or H=4.9t*t. This can also be derived from the law of conservation of energy. The potential energy is therefore equal to the kinetic energy 0.5 * m * v * v = m * g * h at any time during free fall. v or the velocity of the body after time t under an acceleration g can be calculated as v = u + gt where u is the initial velocity. So if the body is simply 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 of the equations of motion can be derived using the law of conservation of energy.

The time it takes for 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 it takes for a human to traverse 100m is 10 seconds, so one can imagine the magnitude of natural gravity.

With the same equation (1) one can calculate the distance traveled by a body, which is about half a minute. In half a minute or 30 seconds a body reaches the earth’s surface 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 prove immediately that the body does not cover the same distances at equal intervals of time.

Another interesting aspect of free fall is that the equations of motion are independent of mass. But mass can affect motion when there is resistance from wind and when the surface of the body is not uniform. This can cause upward resistance and motion may not be uniform for all masses. But with no air resistance or in a vacuum, the movement will be as described above.

Thanks to Srinivasa Gopal | #mechanics #free #fall

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