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
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
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
The velocity varies linearly with time and the acceleration equals g at all times.
Copyright
1998-1999
Rensselaer Polytechnic Institute. All Rights Reserved.