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Free Fall

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MOTION OF OBJECTS UNDER THE INFLUENCE OF GRAVITATIONAL FORCE OF THE EARTH:

As g is constant near the earth, all the equations for the uniformly accelerated motion of objects become valid with acceleration a replaced by g. The equations are:

v = u + at

s = ut + 1/2at2

v2 = u2 + 2as

where u and v are the initial and final velocities and s is the distance covered in time, t. In applying these equations, we will take acceleration, a to be positive when it is in the direction of the velocity, that is, in the direction of motion. The acceleration, a will be taken as negative when it opposes the motion.

notes

Free Fall:

Whenever objects fall towards the earth under this force alone, we say that the objects are in free fall. Is there any Whenever objects fall towards the earth under this force alone, we say that the objects are in free fall. Is there any But due to the earth’s attraction, there will be a change in the magnitude of the velocity. Any change in velocity involves acceleration. Whenever an object falls towards the earth, an acceleration is involved. This acceleration is due to the earth’s gravitational force. Therefore, this acceleration is called the acceleration due to the gravitational force of the earth (or acceleration due to gravity). It is denoted by g. The unit of g is the same as that of acceleration, that is, ms–2.

As 

F = ma             (`because`a = g)  ...(1)

F = mg                                         ...(2)

and  `"F" = "G"("Mm")/"d"^2`    (`therefore` Universal law of gravitation)            ...(3)

From (ii) and (iii)

`therefore`  `"mg" = "G"("Mm")/"d"^2`

`therefore`  `"g" = "GM"/"d"^2`

M = Mass of the earth.

d = Distance between the object and the earth.

G = Gravitational constant

If the object is placed on the earth then d = R (radius of the earth) 

`therefore`  `"g" = "GM"/"R"^2`

Earth is not a sphere it is flattened at poles.

Hence R- Radius at pole and Re - Radius at equator   Re > Rp

`"g" ∝ 1/"R"`

`therefore` The value of 'g' is more at poles = (9.9 m/s2) and less at the equator = (9.8 m/s2)

description

  • Motion of objects under the influence of gravitational force of the earth
  • Escape velocity
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