Transcript Eg. 2

Fundamentals of Physics I
PHYSICS 1501
CRN # 23140
SPRING 2010
8:00 am – 8:50 am
Instructor: Dr. Tom N. Oder
Office: WBSH 1016
E-mail: [email protected], phone (330) 941-7111
Office Hours: M, T, W, F 1:00 pm – 2:00 pm.
Research: (Wide Band Gap) Semiconductors.
Website: www.ysu.edu/physics/tnoder
Class website:
www.ysu.edu/physics/tnoder/S10-PHYS1501/index.html
Requirements
(a) Passing grade in Algebra/Trig (Math
1504 or YSU Math Placement Test).
(b) Text: College Physics, By A. Giambattista
et al., 2nd Edition
(c) A “ResponseCard RF” from Turning
Technology (available at the Bookstore).
Hard Cover version
YSU Customized version
Vol. 1
Regular/Punctual Class attendance encouraged.
Homework: In the Syllabus, will not be graded.
For your practice
Quizzes and Worksheets:
• Short in-class Quizzes
• Worksheets – group exercises.
• No make-ups.
• Least four scores will be dropped.
Exams
No make-ups will be given.
Midterm 1: on Fri. Feb 5th.
Midterm 2: on Fri. March 5th.
Midterm 3: on Fri. April 16th.
Finals: Ch.1-8, 10-12 Mon. May 3rd, 8:00 –10:00am
Exam questions will be developed from questions
in the Homework/Quizzes/Worksheets/Class notes.
Grading:
Quizzes/Worksheets :100 points
Midterms (100 points each): 300 points
Final Exams: 200 points.
Final Grade:
540 – 600 points (90% - 100%) = A
480 – 539 points (80% - 89%) = B
420 – 479 points (70% - 79%) = C
360 – 419 points (60% - 69%) = D
0 – 359 points (0% - 59%) = F
No bonus points, no grade-curving
Cell Phones:
• Cell phones must be muted or
turned off during class and exam
sessions.
•A student whose cell phone audibly
goes on during any exam will lose
5% of his/her points in that exam.
Chapter 1: INTRODUCTION
• Physics: branch of physical science that deals
with energy, matter, space and time.
• Developed from effort to explain the behavior
of the physical environment.
• Summary: laws of Physics, Formula, graphs.
• Basis of rocket/space travel, modern
electronics, lasers, medical science etc.
• Major goal: reasoning critically (as a
physicist), sound conclusions, applying the
principles learnt.
• We will use carefully defined words, e.g.
velocity, speed, acceleration, work, etc.
§ 1.3: The Use of Mathematics
• Factor (or ratio) – number by which a
quantity is multiplied or divided when
changed from one value to another.
• Eg. The volume of a cylinder of radius r and
height h is V = r2h. If r is tripled, by what
factor will V change?
• Vold = r2h, Vnew = (3r)2h = 9. r2h, Vnew/Vold
= 9. V will increase by a factor of 9.
(a) Decreasing the number 120 by 30% gives ---(b)Increasing the number 120 by 30% gives -----
Proportion
• If two quantities change by the
same factor, they are directly
proportional to each other.
• A  B – means if A is doubled, B
will also double.
• S  r2 – means if S is decreased by
factor 1/3, r2 (not r!) will also
decrease by the same factor.
Inverse Proportion
• If A is inversely proportional to B – means
if A is increased by a certain factor, B will
decrease by the same factor.
• K inversely proportional to r [K 1/r] –
means if r is increased by factor 3, K will
decrease by the same factor.
• The area of a circle is A = r2.
(a)If r is doubled, by what factor will A
change?
(b)If A is doubled, by what factor will r
change?
An expression is written as
2 f 2L
K 3
Pr
From this expression, we can conclude that:
(A)K is directly proportional to f
(B)K is directly proportional to f2
(C)K is inversely proportional to P
(D)K is inversely proportional to 1/P3
An expression is written as
2
2f L
K 3
Pr
From this expression, we can conclude that:
A. K is directly
proportional to f
B. K is directly
proportional to f2
C. K is inversely
proportional to P
D. K is inversely
proportional to 1/P3
Examples
The area of a circle is A = r2.
(a)If r is doubled, by what factor will A
change?
(b)If A is doubled, by what factor will r
change?
§ 1.4: Scientific notation:
• Rewriting a number as a product of a number
between 1 and 10 and a whole number power
of ten.
• Helps eliminate using too many zeros.
• Helps to correctly locate the decimal place
when reporting a quantity.
• Eg: Radius of earth = 6,380,000 m
= 6.38 x 106 m
Radius of a hydrogen atom
= 0.000 000 000 053 m = 5.3 x 10-11 m.
Precision/Accuracy in Scientific
Measurements
• In reporting a scientific
measurement, it is important to
indicate the degree of precision and
the accuracy of your measurement.
• This can be done using absolute (or
percentage) error, significant figures
and order of magnitude, etc.
What is the difference between
accuracy and precision?
Precision:
• Reproducibility or uniformity of a result.
• Indication of quality of method by which a set of
results is obtained.
• A more precise instrument is the one which gives
very nearly the same result each time it is used.
• A precise data may be inaccurate!!
Accuracy:
• How close the result is to the accepted value.
• Indication of quality of the result.
• A more accurate instrument is the one which gives a
measurement closer to the accepted value.
Precise/Accurate
Precise/Not Accurate
Not Precise/Accurate
Not Precise/Not Accurate
(a)Absolute/Percentage error:
Eg. Length of a notebook = 27.9 ± 0.2 cm
 Actual length is somewhere between 27.9
– 0.2 and 27.9+0.2, ie 27.7 and 28.1 cm
 ± 0.2 is the estimated uncertainty (error).
 0.2 is the absolute uncertainty (error).
 27.9 is the central value
 27.7 and 28.1 are called extreme values.
Percentage Uncertainty
Absolute Error
x 100
Percentage uncertainty =
Central Value
Eg. Length of a notebook = 27.9 ± 0.2 cm
% Uncertainty = 0.2
x 100  0.7%
27.9
AbsoluteError
Fractional Error 
CentralValue
0 .2

27.9
Examples
• The length of a table was found to
be 1.5 m with 8% error. What was
the absolute error (uncertainty) of
this measurement?
• The mass of a bag was found to be
12.5 0.6 kg. What was the percent
error in this measurement?
Error Propagation in Addition/Subtraction
The absolute error in the sum or difference of
two or more numbers is the SUM of the
absolute errors of the numbers.
x  x and y  y
Sum  ( x  y )  (x  y )
Difference  ( x  y )  (x  y )
Eg. 8.5  0.2 cm and 6.9  0.3 cm
Sum = 15.4  0.5 cm
Difference = 1.6  0.5 cm
Error Propagation in Multiplication/Division
The fractional error in the product or quotient of two
numbers is the SUM of the fractional errors of the
numbers.
x  x  x and y  y  y
x
y
Fractional errors : in x is
and in yis
x
y
Pr oduct  P  P  P  x. y
P
x y
Fractional error in P is
which is (  )
P
x
y
x
Quotient  Q  Q  Q 
y
Q
x y
Fractional error Q is
which is (  )
Q
x
y
Error Propagation in Multiplication/Division
Eg. x = 8.5  0.2 cm and y = 6.9  0.3 cm
Fractional errors:
0 .3
0
.
2
in y =
=
in x =
=
6 .9
8 .5
Find the product, P = x.y and its
absolute uncertainty (P).
(b) Significant Figures:
Number of reliably known digits in a
measurement. Includes one “doubtful” or
estimated digit written as last digit.
Eg. 2586
[6 is the last digit. It is the doubtful digit].
Eg. 25.68
[8 is the last digit. It is the doubtful digit].
Significant Figures contd:
• All nonzero digits are significant.
• Zeros in between significant figures are
significant.[2,508]
• Ending zeros written to the right of the decimal point
are significant. [0.047100]
• Zeros written immediately on either sides of decimal
point for identifying place value are not significant.
[0.0258, 0.258]
• Zeros written as final digits are ambiguous.[25800] To
remove ambiguity, rewrite using scientific notation.
• Eg. (i) 58.63 – 4 sf, (ii) 0.0623 – 3 sf, (iii) 5.690 x 105 – 4
sf. (iv) 25800 – 2.58x 104 = 3 sf, 2.580x 104 = 4 sf,
2.5800x 104 = 5 sf.
Significant Figures in Addition/Subtraction
The sum/difference can not be more precise
than the least precise quantities involved.
ie, the sum/difference can have only as many
decimal places as the quantity with the least
number of decimal places.
Eg: 1) 50.2861 m + 1832.5 m + 0.893 m =
2) 77.8 kg – 39.45 kg =
“keep the least number of decimal places”
Significant Figures in Multiplication/Division
The product/quotient can have only as many
sf as the number with the least amount of sf.
Eg: 1) What is the product of 50.2861 m
and 1832.5 m?
2) What is 568 m divided by 2.5 s?
“keep the least number of significant figures”
(c) Order of Magnitude
– (roughly what power of ten?) To determine
the order of magnitude of a number:
• Write the number purely as a power of ten.
• Numbers < 5 are rounded to 100
• Numbers  5 are rounded to101
• Eg. 754 =7.54 x 102 ~101 x 102 = 103. The
order of magnitude of 754 is 3.
• 403,179 = 4.03179 x 105 ~100 x 105 = 105 =
5 O/M
• 0.00587 ~ orders of magnitude = - 2 (how?).
§ 1.5: Units
We will use the SI system of units
which is an international system of
units adapted in 1960 by the General
Council of Weights and Measures.
• In SI system:
Length is measured in meters (m).
Mass is measured in kilograms (kg).
Time is measured in seconds (s).
• Other fundamental quantities and
their units in the SI system includes
Temperature (in Kelvin, K),
Electric current (in Amperes, A)
Amount of substance (in mole, mol) and
Luminosity (in Candela, cd).
• The SI system is part of the metric
system which is based on the power of
ten.
Converting Between Units
Eg. Convert 65 miles/hour to SI units.
1 mile = 1.609 km = 1609 m.
1 hour = 3,600 seconds
65 miles 65 x 1609m

 29.1 m / s
1 hour
1 x 3600s
§ 1.6: Dimensional Analysis
Dimensions – Units of basic
(Fundamental) quantities:
Mass [M], Length [L], Time [T]
We can only add, subtract or equate
quantities with the same dimensions.
Eg. 1 Check if the expression v = d2/t is correct,
where v = speed (in m/s), d is the distance (in
m) and t is time (in s).
Quantity Dimension
[ L]
V
[T ]
d2
T
v = d2/t
[L]2
[T]
[ L] [ L]2

[T ] [T ]
Hence eqn is
not correct
Eg. 2: If the equation was now
correctly written as v = kd2/t, what
must be the units of k?
2
[ L]
[ L]
1
k
k
[T ]
[T ]
[ L]
The units of k must be m-1
§ 1.7-1.9: Reading Assignment
1. The SI units of length and mass are
meter and pound
meter and kilogram
meter and second
kilometer and kilogram
centimeter and gram
50% 50%
ce
an
d
ki
nt
lo
im
gr
am
et
er
an
d
gr
am
nd
co
lo
m
et
er
ki
m
et
er
an
d
an
et
er
d
ki
se
lo
g
un
d
po
d
an
m
et
er
0% 0%
ra
m
0%
m
A.
B.
C.
D.
E.
3
m
2
10
8
2.
5
x
3.
25
75
3.
25
m
3
m
3
m
3
.6
23
24
m
3
2. A rectangular container has sides of
dimensions 14.5 m by 2.8 m by 6.25 m. The
volume of this container, keeping the correct
50% 50%
significant figures is
A. 24 m3
B. 23.6 m3
C. 253.75 m3
D. 253.8 m3
0% 0% 0%
E. 2.5 x 102 m3
3. The mass of a watermelon was measured to be
12.6 kg. If the percent uncertainty in this
measurement was 12.0 %, what was the absolute
uncertainty in the measurement?
100%
0.
95
2
kg
0%
0
10
51
kg
0.
0.
60
0
kg
.0
12
0%
kg
0%
kg
0%
1.
(A)12.0 kg
(B)0.600 kg
(C)1.51 kg
(D)0.100 kg
(E)0.952 kg
4. What is the order of magnitude of the
number 680,835?
50%
0%
7
0%
4
5
0%
8
50%
6
(A)6
(B)5
(C)4
(D)7
(E)8
5. The area of a circle is increased by 40%. By what
percent has its radius increased? [Area of a circle of
radius r is given by the formula r2]
50%
%
85
%
0%
18
%
0.
18
%
0%
20
6.
30
%
0%
0%
%
50%
80
(A)6.3%
(B) 20%
(C) 0.18%
(D) 18%
(E) 85%
(F) 80%
6. How many significant figures will the
sum of 15.3 + 26.20 + 198.071 contain?
0%
3.
6
4
0%
3
0%
50%
29
50%
6
1
3
4
6
293.6
1
A.
B.
C.
D.
E.
The radius (r) of a circle is quadrupled. By
what factor will its area change? [Area = pr2]
1.
2.
3.
4.
5.
16
8
4
¼
1/16
What is the order of magnitude of
the number 89,792?
1.
2.
3.
4.
5.
6
5
9
7
9x104
What is 36.18/2.2 when the rule of
significant figures is followed?
1.
2.
3.
4.
16
16.4
16.44
16.445
The length of a room was measured and found
to be 4.9 ± 0.2 m. What is the percentage
error in this measurement?
1.
2.
3.
4.
5.
0.04%
24.5%
4%
4.9%
0.98%