×
Log in to StudySoup
Get Full Access to University Physics - 13 Edition - Chapter 1 - Problem 98cp
Join StudySoup for FREE
Get Full Access to University Physics - 13 Edition - Chapter 1 - Problem 98cp

Already have an account? Login here
×
Reset your password

The length of a rectangle is given as L ± l and its width

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 98CP Chapter 1

University Physics | 13th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

4 5 1 382 Reviews
24
2
Problem 98CP

The length of a rectangle is given as ?L ± ?l and its width as ?W ± ?w?. (a) Show that the uncertainty in its area ?A is ?a = ?Lw + ?lW?. Assume that the uncertainties ?l and ?w are small, so that the product ?lw is very small and you can ignore it. (b) Show that the fractional uncertainty in the area is equal to the sum of the fractional uncertainty in length and the fractional uncertainty in width. (c) A rectangular solid has dimensions ?L ± ?l?, ?W ± ?w?, and ?H ± ?h?. Find the fractional uncertainty in the volume, and show that it equals the sum of the fractional uncertainties in the length, width, and height.

Step-by-Step Solution:
Step 1 of 3

Solution 98CP a) The length of the rectangle is L ± l. The width is W ± w As we know the formula for the area of a rectangle, area = length × width = ( L ± l) × (W ± w) = LW ± Lw ± lW + lw = LW + lw ± (Lw + lW) As the uncertainties w and l are very small, we can ignore lw term. The uncertainty in area is ± (Lw + lW) . b) The fractional uncertainty or the relative uncertainty is defined as, uncertainty / measured value. The uncertainty in area is (Lw + lW). Measured value of the area is LW . Fractional uncertainty in area = (Lw + lW) / LW ----------------(1) Now the uncertainty in length is l. Measured value of the length is L. Uncertainty in width is w Measured value of width is W . Fractional uncertainty in length is l/L. Fractional uncertainty in width is w/W . The sum of fractional uncertainties in length and width is , lW+Lw l/L + w/W = LW ------------------(2) From equation (1) and (2) it is clear that, Fractional error in area = sum of fractional errors in length and width (proved) c) The same is true for volume too. There 1 more term will be added which is the height H. The error in height say ± h. The calculation is same as part b) calculation and trivial.

Step 2 of 3

Chapter 1, Problem 98CP is Solved
Step 3 of 3

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

The length of a rectangle is given as L ± l and its width