Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.5, Problem 52E

To determine

To calculate the value of dT .

Expert Solution

Answer to Problem 52E

dT=−π(Lg3)12dg

Explanation of Solution

Given information:

The relation of T , g , L is given by T=2π(Lg)12

Calculation:

Obtain derive of T in terms of g .

T=2π(Lg)12dTdg=2πL12(−12g−32)dT=−πL12g−32dgdT=−π(Lg3)12dg

To determine

To explain that if g increases, will T increase or decrease, will a pendulum clock speed up or slow down.

Expert Solution

Answer to Problem 52E

If g increases then T decreases and as T decreases the pendulum will speed up.

Explanation of Solution

Given information:

The relation of T , g , L is given by T=2π(Lg)12

According to part (a) you have dT=−π(Lg3)12dg , where (Lg3)12 is always positive because it is a root. Hence, the value of dT will be negative if dg is positive and will be positive if dg is negative. If g increased, dg is positive. Hence dT is negative, therefore T is decreased.

Since the time period T is the time it takes to complete a swing. The more is the period the less is the speed. As T decreased pendulum will speed up.

To determine

To find dg and estimate the value of g at the new location.

Expert Solution

Answer to Problem 52E

The value of dg is −0.977 cm/sec2 and the value of g is 979.023 cm/sec2

Explanation of Solution

Given information:

A clock with 100 cm pendulum is moved from a location where g=980 cm/sec2 to a new location. This increases the time period by dT=0.001 sec .

Calculation:

According to part (a) you have dT=−π(Lg3)12dg ,

Now substitute the values in the above equation

dT=−π(Lg3)12dg0.001=−π(1009803)12dgdg=−0.977

For g ,

g=980+dgg=980−0.977g=979.023

Therefore,

The value of dg is −0.977 cm/sec2 and the value of g is 979.023 cm/sec2

Chapter 5.5, Problem 51E

Chapter 5.5, Problem 53E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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