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AP Physics B August 17 to 27, 2010 Ch. 1: Introduction and Mathematical Concepts.
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Plans for the Week and Assignments:
1. Tuesday(08/17): Introduction to Physics, Class Expectations.
HW: Work on Website Assignment #1, and get your materials for class
(3-ring binder, notebook paper, calculator, lab money $10, pens, and pencils).
2. Wednesday(08/18): Scientific Notation, Significant Digits, Order of
Magnitude, and Isolating Unknowns in Equations. HW: Complete Website
Assignment #1, and get materials for class.
3. Thursday(08/19): LAB Experiment on Measurement. HW: Process lab
data.
4. Friday(08/20): Textbook pick-up and Post-Lab discussion.
HW: Complete lab report and write Abstract (due Tuesday).
5. Monday(08/23): Mathematics of Vectors. HW: Begin work on Website
Assignment #2, and get materials for class.
6. Tuesday(08/24): REVIEW I for Test on Ch.1. HW: Finish Review Handout
started in class and study all materials for Test.
7. Wednesday(08/25): REVIEW II for Test on Ch.1. HW: Finish
Review Handout.
8. Thursday(08/26): REVIEW III for Test on Ch.1. HW: Finish all
handout assignments and study for Test.
9. Friday(08/27): TEST on Ch.1
- Introduction to Physics.HW: Go to web site for notes on Ch.2 - Kinematics in One Dimension.
Very Important: If you have any questions or were absent from class,
see me before school (8:00 - 8:30 AM), during Lunch, 7th period,
or after school. Best to send an email to rpersin@fau.edu.
Website Notes for Ch. 1 - The Mathematics of Physics.
1. The scientific method is probably the most efficient problem-solving tool
ever devised. There are 6 steps in the scientific method: (I) Define the
problem, (II) Gather information, (III) State your hypothesis, (IV) Test
the hypothesis, (V) Form your conclusion, (VI) Publish the results. The
scientific method is the process by which scientists, collectively and over
time, endeavor to construct an accurate (that is, reliable, consistent and
non-arbitrary) representation of the natural world.
2. The Metric System (Systeme International, SI) was first introduced by
the French Academy of Science in 1795 as an attempt to unify existing
systems. The SI contains the basic units for length (meter, m), mass
(kilogram, kg), and time (second, s), with speed (m/s), volume (m3),
and density (kg/m3) as some derived units.
3. All calculations must be done observing significant digits and scientific
notation. When a number is expressed in scientific notation, the number
of significant figures is the number of digits needed to express the number
to within the uncertainty of measurement. We always round to the least
precise measurement. Here is an example problem, if you have to
multiply 2.5 cm x 1.23 cm the result is 3.1 cm2 .
4. The number of significant figures of a product or quotient of two or
more quantities is equal to the smallest number of significant figures for
the quantities involved. For example, if you multiply 5.2 x 3.751 x 6.43,
your answer must be written using only two significant digits as 130.
For addition or subtraction, the number of significant figures is determined
with the smallest significant figure of all the quantities involved. For
example, the sum 10.234 + 5.2 + 100.3234 is 115.7574, but should be
written 115.8 (with rounding), since the quantity 5.2 is significant only
to ± 0.1.
5. Order of magnitude (power of 10) calculations provide quick estimates
for answers to certain questions. An order of magnitude calculation is an
estimate to determine if a more precise calculation is necessary. We round
off or guess at various inputs to obtain a result that is usually reliable to
within a factor of 10. Specifically, to get the order of magnitude of a given
quantity, we round off to the closest power of 10 (example: 75 kg is
expressed as 102 kg). Another example, the average distance from the
Earth to the Sun is 93,000,000 miles. In scientific notation this is
9.3x107 miles. But since 9.3 is closest to 101, we would express the order
of
magnitude as 108 miles.
6. A frame of reference is a coordinate system for specifying
the precise location of objects in space. Maybe you have heard the
expression, "It depends on your frame of reference."
7. Accuracy refers to the agreement of a measured value with an accepted
value. Percent error measures accuracy.
8. Precision is the agreement of a set of measured values with each other.
It can be measured by average deviation.
9. All graphs are plotted with the independent (control) variable on the
x-axis, and the dependent (measured) variable on the y-axis.
10. Graphs can show direct (linear), inverse (hyperbolic), periodic
(sinusoidal), quadratic (parabolic), or chaotic relationships.
11. All equations must be dimensionally correct. We use dimensional
analysis (factor labeling) to determine if equations are correct.
12. The number of atoms in one mole of any element or compound is
6.02x1023 , Avogadro's number.
13. The density of a substance is defined as its mass per unit volume. We
use the Greek letter rho, ρ, for density and the equation is ρ = m / V.
14. Some equations that you may remember from Mathematics are
A = πr2, C = 2πr, A = 4πr2, V = πr2h, V = 4/3 πr3, and d = vt. Notice that
variables in Physics are case sensitive. For example, A is area, but a
is acceleration. Another example, T is temperature, but t is time.
15. We also need to remember SOHCAHTOA to compute the value of
unknown sides and angles of right triangles.
16. We need these steps to solve any problem in Physics:
(i) read the problem and identify the given variables
(ii) determine what you are asked to solve for
(iii) find the correct formula to use
(iv) isolate the unknown
(v) substitute-in the given information and simplify.
Website Homework Assignment #1.
Copy the problem and show all work on your paper.
1. Write a paragraph that illustrates how a student would use the scientific
method to determine what college to attend.
2. Find an English-to-Metric System of Measurement conversion table. Then
use it to make the following conversions:
(a) 6.75 inches = ______ centimeters
(b) 3.0 miles = _____ kilometers
(c) 400 cubic inches = ______ Liters
(d) 100 lbs = ______ kilograms
3. How many significant digits are in each of the following measurements:
(a) 12.375 cm ____ (b) 3.000 m _____
(c) .00075 s _____ (d) 6.0075 in. _____
(e) 93,000,000 mi. ____ (f) 25,000 km ______
4. Express all the measurements given in #3 in scientific notation.
5. Perform the following calculations and express your answers in scientific
notation with the correct amount of significant digits:
(a) 2500 m x 2.75 m = ___________
(b) 4.3 cm + 1.75 cm + .041 cm = ___________
(c) 2.4x107 cm / 1.45 cm = ________
(d) (6.3x108 m x 4x109 m) / 7.11x10-5 m = _______
6. Express each answer in #5 as an order of magnitude.
7. Solve for the variable in red. Show all of your steps.
(a) F = mv2/r ________ (b) E = mc2 ________
(c) T = 2π√(L ⁄ g) _______ (d) d = ½ at2 _______
(e) 1/p + 1/q = 1/f _______ (f) F = (G m1·m2)/r2 _______
(g) Combine these equations E = mc2 , c = f·λ , E = hf to get
an equation for λ that does not involve E or f .
Website Notes for Scalars and Vectors:
I. Vectors.
Vectors are used to describe multi-dimensional quantities. Multi-dimensional
quantities are those which require more than one number to completely
describe them. Vectors, unlike scalars, have two characteristics, magnitude
and direction. A vector is indicated by an uppercase letter either in boldface
or with an arrow over the top. For example, A or  . Examples of vector
quantities are: position in a plane, position in space, velocity, acceleration,
and force.
II. Scalars.
Scalars are used to describe one-dimensional quantities, that is, quantities
which require only one number to completely describe them. They have
magnitude only. Direction does not apply. There are cases where scalars can
be combined mathematically, but we will save that for later. Some examples
of scalar quantities are: temperature, mass, time, volume, density, length,
area, and energy.
III. Vector Diagram.
Any vector can be resolved into perpendicular component vectors using sine
and cosine functions. Actually, for all vector problems just remember
SOHCAHTOA.
IV. Some Properties of Vectors.
Two vectors are equal only if they have the same magnitude and
direction. To find the opposite of a given vector just keep the same
magnitude but point it in the opposite direction. ex. A - B = A + (-B)
Vectors can also be expressed using polar coordinates (r , θ) specifying
the length of the radius vector r , and the angle of rotation, Ø ("Phi"),
from the positive x-axis.
Additionally, in a two-dimensional coordinate system, vectors can be
denoted using the unit vectors î and ĵ. Each unit vector has magnitude
equal to 1, and they point in the x and y directions, respectively. We
can easily add the third dimension, or z direction using unit vector k.
V. Addition of Vectors
Vectors can be added graphically using the head-to-tail method. You
begin by drawing the first vector in a coordinate system, and then
drawing the second vector from the endpoint of the first, and so on.
Then you draw a single vector from the origin to the head of the last
vector.
VI. Vector Subtraction.
The vector difference works the same as vector addition except that
we multiply the vector we are subtracting by -1. It is much like
subtracting two numbers: A - B = A + (-B). The diagram below
illustrates vector subtraction in the tip-to-tail style. The original B
vector is shown as a dotted line.
VII. Multiplication of a Vector by a Scalar.
A vector may be multiplied by a scalar by multiplying each of its
components by that number. Notice that the vector does not change
direction, only length. If A = (1,2) then 3A = (3,6). This is shown
pictorially below.
Click Here to View a Vector Presentation
Website Homework Assignment #2.
Solve These Vector Problems and Show All Work.
1. Find the x and y components of the following vectors:
a. 240 km at 330º
b. 34 m/s at 210º
c. 15 m at 12º
d. 20 m/s2 at 90º
2. From the x and y components given, find the direction and magnitude
of the resultant.
a. Fy = 120 N, Fx = 345 N
b. vy = 31 m/s, vx = 8 m/s
c. ax = -15 m/s2, ay = 12 m/s2
3. Add the three vectors below. Use the graphical method to show a
picture of the addition of the vectors. Use the mathematical method to
obtain the magnitude and direction of the resultant vector.
A = 450 N at 20º, B = 250 N at 270º, C = 100 N at 70º
4. A soccerball is kicked with a horizontal velocity of 11.3 m/s and a vertical
velocity of 3.5 m/s. What is the magnitude and direction of the resultant
velocity of the ball?
5. A pole-vaulter applies a force of 415 N to the pole at an angle of 37º.
What are the horizontal and vertical components of this force?
For some extra help on the above problems, click here.
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And Remember... "From Newtonian Mechanics, Through Quantum Theory, Without Physics, Life Would Be Dreary." |
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