How to find the period of a simple pendulum in an elevator going up with an acceleration of $a$.
Don't just say, $T=2 \pi$ $\sqrt{ \frac l {g+a}}$
I want to know how the above equation is formed.
$\begingroup$
$\endgroup$
3
-
2$\begingroup$ What do you think? $\endgroup$– CuriousOneCommented Jun 2, 2015 at 2:59
-
1$\begingroup$ I downvoted this because the answer is on this site and one 10 second search found it. $\endgroup$– user81619Commented Jun 2, 2015 at 3:11
-
$\begingroup$ I searched you know but couldn't find anything helpful $\endgroup$– jessijCommented Jun 2, 2015 at 3:14
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
Einstein's Equivalence Principle (also derivable I believe from Newton's laws) states that being in an accelerating frame of reference is indistinguishable from being under a gravitational force.
In particular, the mechanical laws in an accelerating frame of reference are the same as if a gravitational field of equivalent magnitude were added in the opposite direction to that of the acceleration.
So in your frame of reference accelerating upward at a in a standard gravitational field of g downward, we see that this is equivalent to a gravitational field of (g+a) downward.
So we can take any equation involving the local gravitational field g which applies in an inertial frame, and change g to (g+a), and this new version will apply in your accelerating frame.
-
$\begingroup$ Can you please, help me in deriving this using Newton's laws? $\endgroup$ Commented Sep 22, 2017 at 8:42