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If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?

$l_{2}=1.0001157 \cdot l_{1}$

Physics 101 Mechanics

Physics 103

Chapter 16

Oscillatory Motion and Waves

Periodic Motion

Wave Optics

University of Michigan - Ann Arbor

Hope College

University of Sheffield

McMaster University

Lectures

02:51

In physics, wave optics is…

10:02

Interference is a phenomen…

05:32

Clocks The speed at which …

01:28

Pendulum How must the leng…

06:03

Suppose the length of a cl…

10:13

03:09

Pendulum clocks are made t…

02:18

(a) What is the effect on …

01:51

A simple pendulum is swing…

00:50

What is the length of a pe…

02:53

The period of a pendulum (…

03:58

(II) Your grandfather cloc…

04:33

A clock is constructed so …

00:56

The pendulum on a cuckoo c…

01:32

Law of the Pendulum The pe…

02:07

Pendulums. The time it tak…

05:52

Your grandfather clock…

05:09

(III) The pendulum in a gr…

01:53

02:42

If a grandfather clock is …

A pendulum with a string l…

08:32

you know that the period the equation would be to pi multiplied by the length of the pendulum al, divided by G, the acceleration due to gravity. And so we can then say that the period is directly proportional to the square root of the length of the pendulum. And so we can say that here, we're going to say that Tisa bow, which would essentially be t long divide by teeth of s, would be equaling the square root of the length long length short. And so we can then say that here one minus length, it's a pal over at length. Some s, uh this would be essentially equaling. This would be the period long. So there are 86,400 seconds in one day, and then it is always five seconds late. This would be divided by the length some short or this would be the length correct. Essentially. And this would be 86,400 seconds quantity squared. And so we can then say that here this would be equaling one minus l over l. Whether we can say l sub divided by Alsup s, this is equaling one minus 1.16 And so we can say that here, the answer would be we'd have to increase the length by a factor. Ah, 0.116 And so we can say that where we can increase the length by a percentage of 0.116 percent. And so this would be our final answer. That is the end of the solution. Thank you for one.

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