Problem

$\bullet$ A 1.35 $\mathrm{kg}$ object is attached…

01:59

Problem 49 Hard Difficulty

$\bullet$ $\bullet($ a) If a pendulum has period $T$ and you double its length, what is its new period in terms of $T ?$ (b) If a pendulum has a length $L$ and you want to triple its frequency, what should be its length in terms of $L ?(\mathrm{c})$ Suppose a pendulum has a length $L$ and period $T$ on earth. If you take it to a planet where the acceleration of freely falling objects is ten times what it is on earth, what should you do the length to keep the period the same as on earth? (d) If you do not change the pendulum's length in part (c), what is its period on that planet in terms of $T ?(\mathrm{e})$ If a pendulum has a period $T$ and you triple the mass of its bob, what happens to the period (in terms of $T ) ?$

Answer

a) $\sqrt{2} \mathrm{T}$
b) $\frac{L}{9}$
c) 10 $\mathrm{L}$
d) $\frac{T}{\sqrt{10}}$
e) $T^{\prime}=T$

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Physics 101 Mechanics

College Physics

Chapter 11

Elasticity and Periodic Motion

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Video Transcript

our guy says, Take a look at the question. The question I was asking us will happen to the period if the last is double. Okay, so we know the formula actually going to pipe tens square Oolong. Well, if the lances double, which means that T prying is equal to buy. Swear room to our G. And this will give us two pi square org. Times Square is who Okay, remember, This whole thing's was equal t. Okay, So t prime was just simply able to square room two times. T So that's what happens to the time period. Okay, question be was asking us if the frequency was triple What happened to the land off a pencil? Well, same question to you. Go to two pi times square room L O G. And we know the frequencies. Wow, words. He good. So is equal to one over too high Times square. Well, org. So in this case, after trying which is equal to 3/2 snow become this Okay, well, in the if we triple times the frequency with triple times the equation, we just want over to buy Times Square ol o gy. And this is also Can you go to one over? Want there times to buy Times Square Well, over G. Okay, because one thing I wonder is multiplied by three. Okay, so if we plug in a wander here back into the square root, we'll get 1/2 pi times square root one overnight because square of long When I iss wonder Ok, times l over G which means that one over to buy Times Square. Oh, one overnight l over G Hope you know what I mean. Jump to the next page then. So you give us to buy me one over to buy square one over now while Renai l over ji he's equal to three year which is you go to F crime which is equal to one over to buy times square root l A pry over G you see here is in this should be match, which means that O brien is equal to one over night l which is Oh, and I. So if you triple the frequency in a lance off a pencil and should decrease nine times okay, and you see no question See, it was asking us if the gravitational constant was 10 times as many original gravitational constant. What happens with left off a pendulum? While we know the questions to your words? T go to troop I times. Uh oh, gee, the square root. Okay, so in his case, you want to keep the same period if you increase the gravitational constant, which will give us the san Tonalities. So it's ah, crime over 10 g. Because Geep Ryan's he Siegel's attention okay, means that is have to equal do 10 l over 10 g, right, Because we're trying to keep the same period. So if we increase the gravitational constant about 10 times, that means the lands need to increase about 10 times as well, so they can cancel out eventually and still get it. The original equation here. Okay, so l prime has to be equal to hang out in order to match the same period. Okay, for ah, next question was asking us still, if the gravitational constant was 10 times the original one. What happened to a time period of time? Okay, so remember t 0 to 2 pi square allergy. So now T Prime Siegel two pi square with our over G crime, would you see with the two pi school l over 10 g. If we take it out the wall of a tan, we'll get to buy times. Oh, through L o g times square root 1/10. Okay, remember this? This whole thing is evil t so t prime, we'll be able to square 1/10 times T, which is t over square overtime. So those T price is equal to t over square routine. Okay, for the last question, it was asking us if the mass was increased three times. What happened to the to the period? Well, remember, the pure is equal to pi Times Square L O G. So teas is owned depending on the lands off pendulum and the gravitational constant. Okay, so it's not dependence on the mass. So no matter how you change the mass, the time here want change. Which means that t prime we couldn t sees mass while effect the time period. Okay, It is my answer for a question. Thank you.

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