PROJECTILE MOTION INSIDE INTERNATIONAL
SPACE STATION
INTRODUCTION
Projectile motion is a
form of motion that follows or traces out a parabolic path. The predominant
reason for the origin of projectile motion is acceleration due to gravity. When
an object is simply given a horizontal initial velocity, gravity which is always
acting downward will exert a vertical pull on the object. The resultant of
horizontal and vertical components is a parabolic motion. The magnitude of
horizontal and vertical components may or may not be equal since it depends on
the angle of trajectory. However both horizontal and vertical components are
totally independent of each other. In this post, we intend to determine time of
flight, maximum attainable height and maximum attainable distance of an object
undergoing projectile motion inside the International Space Station (ISS).
ASSUMPTIONS
1. Air, wind and other
frictional resistance are neglected
2. Temperature effects do
not impede the motion
3. The ground surface is
perfectly horizontal
4. The projectile moves
along a two dimensional path
CALCULATION
Consider an object of
mass ‘M’ kg, moving with an initial velocity ‘u’ at an angle ‘θ’ with respect
to the horizontal. Let ‘g’ be the acceleration due to gravity on ISS. It is
important to note that projectile motion is independent of the mass of the
object in a vacuum. However in air or other media, the drag coefficient being
different for various object shapes and sizes, it is no longer independent of
mass. The ISS is always in a state of free fall, hence experiences
weightlessness. Thereby all the objects inside the ISS will also experience
weightlessness. Hence it is safe to assume that the acceleration due to gravity
is zero.
The equation of
projectile motion in this case is given by,
where,
h – Horizontal distance
at which the projectile attains maximum height (m)
k – Maximum height
attained by the projectile (m)
a – Focal length of the
parabola (m)
A projectile motion is
represented in figure.1 with all the coordinates
 |
| Fig .1 A projectile motion |
Now, the other aspects
of the parabolic motion such as total time taken, maximum height and maximum
distance attained will be discussed
The time of flight ‘T’ is
given by,
where,
T – Time of flight or
total time taken (s)
u – Initial velocity of
projectile (m/s)
θ – Angle of projectile
(degree)
g – Perceived acceleration
due to gravity inside ISS (0 m/s2)
The value ‘ꝏ’ or ‘infinity’
implies that the projectile motion will never be completed because due to lack
of gravity, the projectile will continue to move at 45° rather than falling
down to the surface.
The maximum height
attained (H) by the object is given by,
The value ‘ꝏ’ indicates that
the object will never achieve any maximum height since the projectile will
always keep moving upward at the launch angle instead of falling down.
The maximum distance
attained (d) by the object is given by,
The value ‘ꝏ’ indicates that
the object will never achieve any maximum distance since the projectile will
always keep moving upward at the launch angle instead of falling down.
Equations (3), (5) and
(7) indicate that projectile motion cannot be completed inside the ISS since it
is always in a state of free fall.
CONCLUSION
Thus it can be observed
from the calculations that the projectile motion can never be completed inside
the ISS.
