Free fall




>> The falling of an object from a height under force of gravitation of earth is called FREE FALL.

•  The acceleration produced in a freefalling body due to gravitational force of earth is called ACCELERATION DUE TO GRAVITY.

•   Acceleration due to gravity is denoted by 'g'.
•  This Acceleration produced in a freely falling        body does not depend on the mass of the body.

● This was first concluded by Galileo Galili and was experimentally demonstrated by Robert Boyle [ feather 🪶  and hammer 🔨 experiment]


Calculation of acceleration due to gravity: 

Force of gravitation = GMm÷r²  ----------(i)

By Newtons 2nd law of motion
        F = ma  --------------(ii)

From equation (i) and (ii) 

        ma = GMm÷r²

>>       a = GM÷r²
     
      Therefore,  a= GM÷r²

Now ,this acceleration is produced due to force of gravitation.  So this is acceleration due to gravity denoted by letter 'g'.

So,   [  g = GM÷r²  ].

In general the value of 'g' = 10 
But the actual value of 'g' = 9.8 m/s².

● The value of acceleration due to gravity on earth 🌎  is 'g' = 9.8m/s².

[ The acceleration due to gravity on moon 🌙 is 1/6 of gravity on earth ].

■ Variation of acceleration due to gravity. 

~ Radius of earth 🌎  is minimum at the pole and maximum at the equator.

>< Acceleration due to gravity is maximum at the pole and minimum at the equator.
      
        i.e,    g(pole) > g(equator).


Equation of motion for freely falling body:

》Equation of motion for freely falling body is given by :

(i)   V = u + at  becomes  V = u + gt.

(ii)  S = ut + 1/2at² becomes  h = ut + 1/2gt².

(iii) V²= u² + 2as   becomes   V² = u² + 2gh.


• when an object falls freely from a height its initial velocity , u = 0.

• when an object thrown vertically upward then it's velocity at maximum height , V = 0.

• when an object is thrown vertically upward then it's velocity decrease so the acceleration due to gravity 'g' should be taken Negative (-).

• when an object is falling freely vertically download then it's velocity increase . So the acceleration due to gravity should be taken positive.

 ■ time  taken to reach maximum height:
         
                   t = u÷g

■ Time taken to reach the ground when falls freely:
  
                   t = v÷g

■ Maximum height during upward motion:

                   h = u²÷2g

■ Height covered by an object during free fall :

                   h = v²÷2g

NOTE:

~ Time taken to reach the maximum height = Time taken to fall from the same height. 

~ velocity of a body at the the same level will always be same..



         ............[Thanks for 📚 reading guys]............