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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 3.3 - Problem 5e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 3.3 - Problem 5e

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# Solved: The period T of a simple pendulum is given by ISBN: 9780073401331 38

## Solution for problem 5E Chapter 3.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 5E

Problem 5E

The period T of a simple pendulum is given by where L is the length of the pendulum and g is the acceleration due to gravity.

a. Assume g = 9.80 m/s2 exactly, and that L= 0.742 ± 0.005 m. Estimate T, and find the uncertainty in the estimate.

b. Assume L = 0.742 m exactly, and that T = 1.73 ± 0.01 s. Estimate g, and find the uncertainty in the estimate.

Step-by-Step Solution:
Step 1 of 3

Solution 5E

Step1 of 3:

Let T be the period of of a simple pendulum and it is given by Where,

L = length of the pendulum

g = acceleration due to gravity

Here our goal is:

a).We need to Estimate T, and find the uncertainty in the estimate by Assuming g = 9.80 exactly, and that L = 0.742 0.005m

b).We need to Estimate g, and find the uncertainty in the estimate by Assuming L = 0.742 m exactly, and that T = 1.73 0.01 s.

Step2 of 3:

a).

From the given information we have g = 9.80, L = 0.742, Here  mathematical constant and its value is 3.14 = = 6.28 = 6.28(0.2751)

= 1.7280

Hence, 1.7280.

Consider, Differentiate above equation with respect to “L” we get Let u = L/g

du = 1/g

Apply chain rule to above equation to get a differential equation and it is given by = = Substitute “u” value in above equation we get

= = = = = = 1.1645

Hence, = 1.1645.

Now,

The estimate of uncertainty is given by = (1.1645)(0.005)

= 0.005822

Hence, = 0.005822

Therefore, The estimate of uncertainty is T = 1.7280 0.0058 s.

Step3 of 3:

b).

From the given information we have  T = 1.73, L = 0.742, Here = T = Square above equation on both side we get = g = Now,

g = = 4(9.8596)(0.742)(0.3341)

= 9.7775

Hence, g = 9.7775.

Consider,

g = Differentiate above equation with respect to “T” we get = = = = -8 = -8(9.8596)(0.742)(0.1931)

= - 11.3035

Hence, = -11.3035.

Now,

The estimate of uncertainty is given by = = (11.3035)(0.01)

= 0.1130

Hence, = 0.1130

Therefore, The estimate of uncertainty is g = 9.7775 0.1130 Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

This full solution covers the following key subjects: estimate, assume, Pendulum, uncertainty, exactly. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 5E from chapter: 3.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “The period T of a simple pendulum is given by where L is the length of the pendulum and g is the acceleration due to gravity.a. Assume g = 9.80 m/s2 exactly, and that L= 0.742 ± 0.005 m. Estimate T, and find the uncertainty in the estimate.________________b. Assume L = 0.742 m exactly, and that T = 1.73 ± 0.01 s. Estimate g, and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 71 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 5E from 3.3 chapter was answered, more than 391 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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