In a test of a “g -suit,” a volunteer is rotated in a horizontal circle of radius 6.5 m . What must the period of rotation be so that the centripetal acceleration has a magnitude of 2.4 g ? What must the period of rotation be so that the centripetal acceleration has a magnitude of 10 g ?
Solution:
Let us go to the basics first.
We know that centripetal acceleration is given by:
a = v2/R .......................Eqn.1
velocity, v = distance/time.
=> v = Circumference / time
=> v = 2πR / t
Thus, eqn.1 becomes
a = v2/R
=> a = (2πR / t)2 / R
=> a = 4π2R / t2 ........................Eqn.2
Now, Case: a volunteer is rotated in a horizontal circle of radius 6.5 m . What must the period of rotation be so that the centripetal acceleration has a magnitude of 2.4 g ?
Thus, substituting values in eqn.2,
a = 4π2R / t2
=> 2.4*9.8 = 4π2*6.5 / t2
=> t2 = 4π2*6.5 / 2.4*9.8
=> t = 3.301 seconds (Answer)
Now, Case: What must the period of rotation be so that the centripetal acceleration has a magnitude of 10 g ?
Substituting the values in eqn.2 again:
a = 4π2R / t2
=> 10*9.8 = 4π2*6.5 / t2
=> t2 = 4π2*6.5 / 10*9.8
=> t = 1.617 seconds (Answer)
Thanks!!!
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