Pendulum

[Ehwic]

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The question asked if the pendulum used to calculate the local value of g were not placed in an evacuated chamber, then how would the results vary form one that was?

The purpose of the chamber was to eliminate air resistance.

The correct answer was: The measured period would be longer; the calculated value for g would be too low.

I chose: The measured period would be shorter; the calculated value for g would be too high.

I approached this problem as an conservation of energy problem where with drag, some of the kinetic energy would be lost and thus, would not be able to achieve its original height when it swings to the other side and this in return, would decrease the period. as a result, knowing that period= 2pi sqrt(length/gravity), shorter period would mean greater g constant. Why is this wrong?

Also, why does greater resistance mean longer periods, I keep thinking it would cause shorter periods. That is probably why I got that question wrong.

 

[Balantidiumcoli]

The formula for a pendulum's period is given by:T= 2pi* (L/g) ^ 1/2.

As g -> 0, T -> infinity.

In the air resistance pendulum the acceleration of gravity is slightly decreased due to the friction caused by air resistance. F = ma, with a friction constant F=maK. K<1 so you can think of it as reducing the acceleration to reduce the total force in one direction -> F=m*(a/x) where x>1.

 

[YouNeverKnow22]

easier way to look at it is that in a vacuum there would be less gravity (0 to be exact)

the equation for period is T= sqrt (L/g), decreasing G increases T.

 

[Balantidiumcoli]

easier way to look at it is that in a vacuum there would be less gravity (0 to be exact)

I think OP's question assumes that the evacuated chamber isn't in orbit.

The bottom part of your post is sound though.

Another way to think about it OP is to imagine if the pendulum was placed in water where the resistance goes up considerably. There's the mathematical way to think about it but the resistance would clearly reduce the amount of time it takes to complete a period, Obviously, it wouldn't even complete an entire swing to its original height if you tried this in real life but the principle is the same.

 

[YouNeverKnow22]

I think OP's question assumes that the evacuated chamber isn't in orbit.

The bottom part of your post is sound though.

Another way to think about it OP is to imagine if the pendulum was placed in water where the resistance goes up considerably. There's the mathematical way to think about it but the resistance would clearly reduce the amount of time it takes to complete a period, Obviously, it wouldn't even complete an entire swing to its original height if you tried this in real life but the principle is the same.

ah ok! another way is to realize that friction will decrease frequency, thereby increasing the period.