General Physics
•
•
•
•
Dr. Nathan J. Dawson
[email protected]
http://www.nathandawson.org
Office: Far right office in T30
Initial topics to cover
•
•
•
•
•
Some course goals
Course procedures
Web resources and requirements
Coverage
Math Survey
Physiology of Learning*.
• Learning requires cycles.
–
–
–
–
Experience (sensory cortex)
Reflection (back integrative cortex)
Abstraction/hypotheses (front integrative cortex)
Active testing of ideas (motor cortexsensory cortex)
*J. E. Zull, The Art of Changing the Brain (Stylus, Sterling VA, 2002).
The brain
Neuronal networks are knowledge.
Where is your locus of control?
•
•
•
•
What are your goals for this course?
What do you expect class time to do for you?
What do you expect the book to do for you?
What time commitment will you be able to put
into the course?
Some Goals:
• To show that physics is interesting and useful.
• To dispel the notion that physics is just a
collection of equations used to solve obscure
problems.
• To challenge you to improve your ability to
reason, think critically, and solve problems.
• To help you gain a conceptual understanding of
physics and how physics builds models of the
relationships between concepts and the world.
Read the course syllabus/ outline!!!
•
•
•
•
Grading policies
Homework
Tests
Academic honesty
Look for patterns, practice.
• Read ahead, check for extra homework
assignments.
• Ask questions, talk about physics in class
• Reread, but look for logic and focus on what
you don’t understand.
• Do physics (homework, workbook, additional
exercises)
• Work together outside of class to teach each
other.
Four Types of Motion We’ll Study
Quiz: Sometimes problems are simply
the process of proportional reasoning:
1. If r varies directly as s2, and if r=48 when s=4,
find r when s=8.
2. If p varies directly as q , and if p=8 when q=16,
find q when p=24.
3. If c varies inversely as d, and if c=4 when d=9,
find c when d=21.
4. If y varies inversely as the square of z, and if
y=16 when z=½ , find z when y=½.
5. If y varies inversely as the square root of w, and
if y=3 when w=4, find w when y=4.
6. If p varies inversely as q, and if p=6 when q=3, find p when
q=36.
7. A varies directly as s2 and inversely as r. If s2 = 4s1 and r2 =
r1/4, determine A2/A1.
8. H varies directly as the square root of A and inversely as the
square of L. If A2 =16A1 and L2=L1/2, find H2/H1.
9. The acceleration of an object moving in a circle at constant
speed varies directly as the square of the speed of the object
and inversely as the radius of the circle. By what factor does
the acceleration increase if the speed is doubled while the
radius is halved?
10. A flurp varies directly as a quarp and inversely as the square
of a phlar. If a quarp and a phlar are both doubled, by what
factor does a flurp change?
Extremely useful geometric theorem
• Pythagorean Theorem: c2 = a2 + b2
(for right triangles only)
c
a
b
Mathematics knowledge/preference
Do you prefer letters or numbers?
For a straight line, which character is the independent variable?
The quadratic equation…
There are 2 roots in the right graph.
What are roots?
How do we solve for them?
Slope of a curved line
The slope of a curved line is NOT constant.
A linear approximation can be used between two close points on a curved line.
Models and theories
In physics, a model is a simplified system that helps to
understand more complicated phenomena that we
observe from experiments.
A theory is a more general explanation of related
phenomena that are observed by scientists.
A law is an experimentally verified relationship between
physical parameters that holds for a broad range of cases.
Dimensional analysis
In physics, the word dimension means the physical nature of a quantity.
For constant acceleration from rest, we have the equation
We find that this equation is dimensionally consistent, where
Equations must be dimensionally consistent, but just being dimensionally
consistent does not necessarily mean an equation is correct.
International System of Units (SI)
Measurement
Unit
Length
meter
Mass
kilogram
Time
second
Charge
Coulomb
SI Units from meters-kilograms-seconds (mks)
(Just a few of many that we will learn in the college physics courses)
Measurement
Unit
mks
Force
Newton
1 N = 1 kg∙m/s2
Energy
Joule
1 J = 1 kg∙m2/s2
Power
Watt
1 W = 1 kg∙m2/s3
What is 1 W/N equivalent to in mks units?
Unit Conversion Examples
Time
60 s = 1 min
60 min = 1 hr
24 hr = 1 day
Length
1 ft = 0.3048 m
1 in = 2.54 cm
Force
1 lb ≈ 4.448 N
1 mi ≈ 1.609 km
Significant figures and measurements
During a measurement, a number is
significant when the last digit is 1 digit past
the last mark on the scale.
The last digit given for any measurement is
the uncertain digit.
Rules for Operations with Significant Figures
Addition and Subtraction
Significant Digits.
Multiplication & Division
Significant Digits.
• Perform the operation.
• Perform the operation.
• Round off to the least
precise value involved, the
position of the last digit in
the least precise
measurement.
• Round off to the number of
digits in the least precise
factor of the problem
Significant Figures
(Precision)
34.57 has four significant figures
2400 has two significant figures.
Q. Why?
A. The rightmost zeros that are still left of the decimal point
don’t contribute.
1001 has four significant figures.
1000.0 and 3.0000 both have five significant figures.
Q. Why?
A. The rightmost zeros that are right of the decimal point
contribute to the significant digits.
Q. How do we write 2400 with three significant figures?
A. We use Scientific Notation, and write 2.40×103.
Propagation of significant figures
When multiplying two measured quantities, the product has the lowest of the significant
figures of either of those two quantities.
3.4 × 1.35 = 4.6 (4.59 if both these numbers are exact and not measured)
When adding two measured quantities, the total sum is only as precise as the least
precise number in the summation.
120 + 1.35 + 34.9 = 160 (156.25 if both these numbers are exact and not measured)
Note that this only pertains to the entire calculation, where “round-off error” can occur if
rounding at each step.
0.4 + 1.34 = 1.7 and 2.12 + 1.4 = 3.5 Adding those results gives 1.7 + 3.5 = 5.2
Adding all measurements together before rounding gives 0.4 + 1.34 + 2.12 + 1.4 = 5.3
The quantity 0.120 x 104 m/s has how many
significant figures?
A. 1
B. 2
C. 3
D. 4
E.
5
Compute 33.24 m + 0.532 m to the
correct number of significant figures:
1.
2.
3.
4.
33.7 m
33.77 m
33.772 m
33.7720 m
3.999 x 103 + 2.5 x 10-5 =
A. 3.999 x 103
B. 3.9 x 103
C. 4.0 x 103
D. 4.002 x 10-2
E. None of the above
Propagation of uncertainty
We will later learn that the magnitude of force is equal to the mass
multiplied by the magnitude of acceleration.
Suppose we measure the mass to be 1.45 kg with an uncertainty of 0.08 kg.
Also, we measured the force to be 14.1 N with an uncertainty of 0.9 N.
The minimum acceleration is
The maximum acceleration is
The average acceleration is
The uncertainty follows as
Thus, the acceleration of the system is