Fictitous Force and Free falling Elevator



A non inertial Frame of Reference is the frame of reference which is having acceleration($a_{0}$) Example Free Falling elevator
Newtons law are valid in inertial frame of refrence only. We cannot apply them as it is in non inertial frame of refrence as it left out the acceleration of the object because of the frame of refrence.
Let me provide simple example to illustrate this.
a)You are moving in car which is accelerating. From your frame of reference,a block on the road would be accelerating in opposite direction.
Now if we apply newton’s law, we will find acceleration to be zero as no net is acting. But the block has acceleration from car frame of refrence.
So to fix this issue,we will add one fictitous quantity in the Newton law equation like
$F=F_{0}+ma$
Where F0 is the fictitous and it is in opposite direction of accleration frame
$F_{0}=-Ma_{0}$
Where $a_{0}$ is the acceleration of Non inertial frame of refrence
Now let me further illustrate this with example of free falling elevator
b) A free falling elevator is an non inertial frame of reference. The acceleration of the elevator as defined from the observer on the ground will be
g=-gk
Where k is the unit vector along vertical axis in the upward direction
Let us take an unattached object of mass M in the elevator.
From the frame of refrence of free falling elevator,Two forces are acting on the mass
Fictitous due to non inertail frame of refrence
$F_{fic}=Mg$
It is opposite to the acceleration of the elevator
Gravitational on the Mass
$F_{G}=-Mg\mathbf{k}$
So the total on the body from elevator frame of refrence
$F_{T}=F_{fic}+F_{G}=0$
Which mean body is unacclerated in the elevator frame of refrence. The body will appear to be suspended in the air ,if it has no initial relative velocity to the elevator
c) A rotating merry go round is a non inertial frame of reference.
The acceleration of the person sitting in merry go round as defined from the observer on the ground will be
$a=\frac {mv^2}{r}
Few more important things about Fictitous
  • Fictitous are called pseudo .
  • It simple represent the effect of the acceleration of the non inertial frame of refrence
  • They dont have any physical significance
  • Whenever we work the problem in non inertial frame of refrence,always make sure to include fictitous in the newton law


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