In a book I saw that the time period of a pendulum inside a elevator moving up is, T=2π√Lg+a I was curious as to why we use (g+a) as we know inside an elevator,
Fnet=Fn−mg
or,manet=Fn−mg
or,Fn=m(anet+g)
So my question is shouldn't we use anet instead of the acceleration due to the normal force?
Answer
The net force on the pendulum is:
→Fnet=−m→g−→Fn
so
m→anet=−m→g−m→an
dividing both sides by m:
→anet=−→g−→an
where both →g and →an point downwards. You state instead that (and I think that this is the source of confusion) →Fn, and thus →an points upwards, which is the case for the lift, but the normal reaction force (which the pendulum experiences), which is equal in magnitude to the acceleration of the lift →a is pointing downwards. So the magnitude of the net acceleration is g+an, pointing downwards, which we obviously can't use as an.
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