Workbook to Accompany Physics for Students of Science and Engineering

265 Pages·1985·18.24 MB·English

by  J. Tanner (Auth.)

Workbook
to accompany
Physics for Students
of Science and Engineering
A. L. Stanford and J. M. Tanner
Georgia Institute of Technology
Academic Press
(Harcourt Brace Jovanovich, Publishers)
Orlando San Diego San Francisco New York London
Toronto Montreal Sydney Tokyo Sao Paulo
Copyright ® 1985, by Academic Press, Inc.
All rights reserved.
No part of this publication may be reproduced or transmitted
in any form or by any means, electronic or mechanical,
including photocopy, recording, or any information storage
and retrieval system, without permission in writing from the
publisher.
Academic Press, Inc.
Orlando, Florida 32887
United Kingdom Edition published by
Academic Press, Inc. (London) Ltd. 24/28 Oval Road,
London NW1 7DX
ISBN: 0-12-663382-7
Printed in the United States of America
PREFACE
This workbook is designed to accompany the textbook, PHYSICS FOR STUDENTS
OF SCIENCE AND ENGINEERING, by A. L. Stanford and J. M. Tanner. The workbook
consists of a collection of questions and problems that are representative of
the topics covered in that textbook. The purpose of the workbook is to provide
the student
(1) an opportunity to practice and test the student's problem-solving
skills using questions and problems representative of the material from
each chapter of the textbook.
(2) a comparison of the student's results with illustrated solutions
obtained using the problem-solving strategy stressed in the text.
(3) practice in the use of a disciplined format in the solution of
problems, including the checking of results.
The format of the workbook is based on individual chapters of the textbook.
The questions and problems associated with each chapter begin with a one-page
review of the definitions, units, and simple relationships appropriate to that
chapter. Each review, in the form of questions and one-step problems, is
followed by more comprehensive problems, formatted one to a page. Each problem
is stated at the top of a page, and the student is provided space to execute
each element of the problem-solving procedure. A detailed solution to each
problem is presented in the same form, i.e., in the format of the problem-
solving procedure, on the reverse side of the page. The solution page often
includes comments and suggestions appropriate to the specific type of problem
being considered.
It will be noted that many of the problems in the workbook are similar to
those in the text. Some problems from the text, of necessity, appear in the
workbook in abbreviated form.
A. L. Stanford
J. M. Tanner
Georgia Institute of Technology
Atlanta, GA 30332
CHAPTER 1: INTRODUCTION 1-Ra
REVIEW
1. Complete the following:
1 km = m = cm
1 ug = g = kg
1 mm m = cm
1 ms s = us
1 ns = s = ms
1 Mm = m = km
1 ps = s = ms
1 in = m = cm
1 ft = m = cm
1 m = in
Complete the following if
a = 8 /40° b = 61 + 8j d = 6i - 8j
a = a
where b = b /B
x
c where d = d /D
Write the appropriate relationship between a, b, and c under
each of the vector diagrams shown.
en
4. If A = 9i +12j + 20k and B = 12i - 3j - 4k, then
A* A = A =
B-B = B =
A-B = A x B =
Cosine of the angle between A and B =
Angle between A and B =
1-Rb CHAPTER 1: INTRODUCTION
REVIEW
1. Complete the following:
3 5
1 km 10 m = 10 cm
6 9
1 yg io- g = IO" kg
3 1
1 mm = ID' m = 10" cm
3 3
1 ms IO" s = 10 ys
9 6
1 ns io" s = IO" ms
6
3J
1 Mm 10 m = km
12 109
1 ps = 10" s = IO" ms
1 in = 0.0254 m = 2.54 cm
1 ft = 0.3048 m = 30.48 cm
1 m = 39.4 in
Complete the following if
a = 8 /40° b = 6i + 8j d = 6i - 8j
a =
6.1 y 5.1 53° where b = b /B
c =
8.7 5.0 307° where d = d /D
y
b + d = 12i a + c = 15 i + 10j 2b = 12i + 16j
3c = 26i + 15j d - b = -16j a + b = 12i + 13j
b-d = _ -28 a*c = 79
a x c = •14k b x d = -96k
3. Write the appropriate relationship between a, b, and c under
each of the vector diagrams shown.
a + b a + b + c = 0 a = b + c
4. If A = 9i +12j + 20k and B = 12i - 3j - 4k, then
A* A = 625 A = 25
B-B = 169 B = 13
A-B = -8 A x B = 12i + 276j - 171k
Cosine of the angle between A and B = -0.0246
Angle between A and B = 91°
1-la
PROBLEM: Determine the sum of the vector, A = 20 /50", and the
vector, B = 35 7120°.
GIVEN: FIGURE:
FIND:
RELATIONSHIPS:
SOLUTION FOR UNKNOWN QUANTITIES:
RESULTS:
CHECKS:
1-lb
PROBLEM: Determine the sum of the vector, A = 20 /J30 , and the
vector, B = 35 7120°.
GIVEN: A 20 FIGURE:
B 35
FIND: C = A + B
2 2 2
RELATIONSHIPS: C = A + B - 2AB cosa (Law of cosines)
sinr sina
(Law of sines)
B ~~C
C = C /r+50°
SOLUTION FOR UNKNOWN QUANTITIES:
From the figure, we see that
a = 60° + 50° = 110°
Then, using the law of cosines, we get
2 2
C = / 20 + 35 - 2-20-35-cosll0° = 45.9
sinr = B-(sina)/C = 35-(sinll0°)/45.9 = 0.717
_ 1
r = sin (0.717) = 45.8°
C = 46 /46°+50° = 46 796°
RESULTS:
The sum of the vectors A and B is the vector C = 46 /96°
CHECKS:
To check C and 2r, us2e the 2law of cosines to calculate B:
B2 = A 2+ C - 22AC cosr
B = 20 + 45.9 - 2-20-45.9-cos45.8° = 1227
B = 35 (CHECK!)
COMMENT
You may have elected to solve this problem by resolving the given vectors into
rectangular components, adding these components to get the sum, and then
determining the magnitude and direction of this sum. This gives:
A = 12.91 + 15.3j B = -17.5i + 30.3j
C = A + B = -4.6i + 45.6j = 45.8 /95.8° = 46 /96°
PROBLEM: Calculate the angle between the two vectors
r = -2.4i + 1.8j + 4.0k
s = 2.0i + 6.0j + 1.5k
if these two vectors are drawn starting from one point.
GIVEN: FI6URE:
FIND:
RELATIONSHIPS:
SOLUTION FOR UNKNOWN QUANTITIES:
RESULTS:
CHECKS:
l-2b
PROBLEM: Calculate the angle between the two vectors
r = -2.4 i + 1.8j + 4.0k
s = 2.0i + 6.0j + 1.5k
if these two vectors are drawn starting from one point.
GIVEN: r and s FIGURE:
FIND: The angle a shown in the figure.
RELATIONSHIPS:
-*-
r*s = rs cosa
SOLUTION FOR UNKNOWN QUANTITIES:
f-s = r s + r s + r s = (-2.4)(2.0) + (1.8)(6.0) + (4.0)(1.5) = 12
x x y y z z
2 2 2 2
= f.f = (-2.4) + (1.8) + (4.0) =25 r = 5.0
r 2 2 2
s = s-s = (2.0) + (6.of + (1.5) = 42.25 s = 6.5
-*»
r* s 12
cosa = = _ _ = 0.369
w
rs (5.0)(6.5)
a = c o s " ^ ^^ = 68.3°
RESULTS:
The angle a between the two vectors is 68°.
CHECKS:
An alternative method for determining the angle a may be used to verify the
result obtained for this angle. To do so, recall that the magnitude of the
cross (vector) product of two vectors is related to the sine of the angle
between these two vectors by
|r x s| = rs sina
A direct evaluation of the cross product of r and s gives
f x s = -21.31 + 11.6j - 18.0k
|r x s| = 30.2
sina = , 1°'* = 0.929
c x c
(5.0)(6.5)
1
a = sin" (0.929) = 68.3°
l-3a
PROBLEM: The sum of two vectors, a and b, is equal to the vector, c = 15 /50°.
If b is subtracted from a, the vector, d = 25 7140°, results.
Determine the two vectors, a and b.
GIVEN: FIGURE:
FIND:
RELATIONSHIPS:
SOLUTION FOR UNKNOWN QUANTITIES:
RESULTS:
CHECKS: