Freely Falling Bodies
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| Free falling bodies |
Free Falling Bodies
Free
falling bodies refer to any objects moving up or down under the effect of its
weight so, gravity is the only acceleration that acting on the moving body in
that case. The earth’s gravity is a constant which equals 9.8 and take the
acceleration unit of m / sec2. The gravity acceleration of any
falling object always affects towards the center of the earth and is
perpendicular to its surface.
In
physics science, Free falling bodies motion was discussed widely and described
mathematically by Newtonian equations. There are many examples of free-falling
bodies in everyday life as follows:
-
Any object
thrown upwards and allowed to fall freely again to the ground.
-
A ball which
falls down to the earth from the second floor.
Terminal Velocity
During
the falling of the body, the
speed of the body is directly proportional to the resistance of the air so, the
air resistance will increase as the speed increases. When the air resistance
equals the weight of the falling body, the body starts falling with a constant
speed which is known as the terminal velocity.
Equations of free-falling bodies
In these
equations, the gravitational acceleration is used instead of the acceleration
of normal motion. The resistance of the air is neglected as well in most cases.
There are three equations for this vertical motion that are known as Newtonian
equations of free-falling bodies, they are formulated as follows:
§ The second
equation: y = v0t – 0.5
gt 2
§ The third
equation: v 2 = v02 -
2gy
Where,
-
v0: is the initial velocity of the free-falling object
(m/s).
-
v: is the final velocity of the free-falling
object (m/s).
-
y: is the altitude from which the object
is falling (m).
-
t: is the time of the fall (sec.).
-
g: is the acceleration of the motion due
to gravity, g = 9.8 m/sec2
Problem Solving
In
all problems of free-falling bodies, you have to follow two main steps:
1.
Extract the
given data carefully then choose the equation which fit your data.
2.
Substitute in
this equation by the given data to get the required variables.
Example: A body is thrown upward with an
initial velocity of 40 m/s. Find a) the highest point that this body will reach
and b) the time which is required to reach this altitude.
The given
Data:
-
v0: 40 (m/s).
-
v: 0 (m/s).
-
g: 9.8 m/sec2
The required variables:
-
y: ??? (m).
-
t: ??? (sec.).
Solution
a)
According to
the given data, the third equation will be used to get the altitude:
v 2 = v02 -
2gy
02
= 402 – 2*9.8*y
y
= 81.6 m
b)
The first
equation will be used to calculate the time which the body requires to reach
this altitude:
v = v0 – gt
0 = 40 – 9.8*t
t = 40 / 9.8
t = 4.08 sec
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