body falling in a vacuum

Force balance involving the volume force only

VELOCITY AS A FUNCTION OF TIME, v(t).

Consider an object falling in a vacuum, where the only force acting on the object is gravitation.
Thus according to Newton's second law, the motion is governed by the differential equation

    (1.1)

    (1.2)

where = the mass of the object (kg),
= the velocity of the object (m/s),
= time (s),
= the acceleration of the object (m/s2),
= the gravitational acceleration (m/s2).

Since g is a constant, eqn (1.2) tells us that the object falls with a constant acceleration. Note that the velocity of any object is independent of its mass.

If the initial velocity of the object is zero, then

    (1.3)

Newton's Second Law of Motion

where F = the unbalanced force on the object (N)
       ma = inertia, the resistance of the object to being accelerated




The unbalanced force is the force of gravity, the weight of the object. Thus

where Fg = the gravitational force (N)

Gravitation is designated as a "volume" force because it acts on the entire volume of the object through its center of mass.

Force Acting on the Object
Gravity Acts on the entire volume of the object


Solution of equation (1.1) subject to (1.3) gives

    (1.4)

The velocity varies linearly with time and the acceleration equals g at all times.

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