1. The scientific method could be the most efficient problemsolving 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
nonarbitrary) 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 (m^{3}),
and density (kg/m^{3}) 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 cm^{2}. 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.
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 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 (ex: 75 kg is expressed as 10^{2} kg). Another ex., the average distance from the Earth to the Sun is 93,000,000 miles. In scientific notation it is 9.3x10^{7} miles. But since 9.3 is closest to 10^{1},
we would express the order of magnitude as 10^{8} miles. 6. A frame of reference is a coordinate system for specifying the precise location of objects in space. You make a convenient choice for the origin of the system. 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. Precision is the agreement of a set
of measured values with each other. It can be measured by average deviation. 8. Each instrument has an inherent amount of uncertainty in its measurement. Even the most precise measuring device cannot give the actual value because
to do so would require an infinitely precise instrument.
9. A measure of the precision of an instrument is given by its uncertainty. As a good rule of thumb, the uncertainty of a measuring device is 20% of the least count. Recall that the least count is the smallest subdivision given on the measuring device. The uncertainty of the measurement should be given
with the actual measurement, for example, 41.64 ± 0.02cm.
10. Here are some typical uncertainties of various laboratory
instruments:
Here's an example. The uncertainty of all measurements made with a meter stick whose smallest division (least count) is one millimeter is 20% of 1mm or 0.02 cm. Say you use the meter stick to measure a metal rod and find that the rod is between 10.2 cm and 10.3 cm. You may think that the rod is closer to 10.2 cm than it is to 10.3 cm, so you make your best guess that the rod is 10.23 cm in length. Since the uncertainty in the measurement is 0.02cm, you report the length of the rod as 10.23 ± 0.02 cm (0.1023 ± 0.0002 m). When a quantity is graphed, it is common for the uncertainty of that quantity
to be represented by error bars. 11. Graphs are plotted with the independent (control) variable on the xaxis,
and the dependent (measured) variable on the yaxis. 12. Graphs can show direct (linear), inverse (hyperbolic), periodic (sinusoidal),
quadratic (parabolic), or chaotic relationships. 13. All equations must be dimensionally correct. We use dimensional analysis
(factor labeling) to determine if equations are correct. 14. The number of atoms in one mole of any element or compound is 6.02x10^{23}
which we know as Avogadro's number. 15. 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. 16. Some equations that you may remember from Mathematics are A = πr^{2}, C = 2πr, A = 4πr^{2}, V = πr^{2}h, V = 4/3 πr^{3}, 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. 17. We also need to remember SOHCAHTOA to compute the value of unknown
sides
and angles of right triangles.
18. 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) substitutein the given information and simplify.
Very Important: If you have any questions or were absent from class, see me before school (7:30  8:00 AM), during Lunch, or after school (4:00 – 5:00 PM).
Best to send an email to
rpersin@fau.edu.
Website Homework Assignment #1.
Show all work. 1. Write a paragraph that illustrates how a student would use the scientific
method to determine what college to attend. 2. Find an EnglishtoMetric 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) 2.4x10^{7} cm / 1.45 cm = __________
(c) 4.3 cm + 1.75 cm + .041 cm = ___________
(d) (6.3x10^{8} m x 4x10^{9} 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 = mv^{2}/r ________
(b) E = mc^{2 }________
(c) T = 2π√(L ⁄ g) _______ (d) d = ½
at^{2} _______
(e) 1/p + 1/q = 1/f _______ (f) F = (G m_{1}·m_{2})/r^{2}
_______
(g) Combine these equations
E = mc^{2} , 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 multidimensional quantities. Multidimensional 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 Â . Examples of vector quantities are: position in a plane, position in space, velocity, acceleration,
and force.
II. Scalars. Scalars are used to describe onedimensional 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. This allows us to find the x and y components of any vector. For the horizontal, or xcomponent of a vector A, we have, A·(cos F ). Then to find the ycomponent we use A·(sin F). This can easily be proven
with
the Pythagorean Theorem.
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, F ("Phi"), from the positive
xaxis. Additionally, in a twodimensional 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 headtotail 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 can draw a single vector from the
origin to the
head of the last vector.
The vector difference works the same as vector addition except that we multiply the vector we are subtracting by 1. In other
words, to subtract a vector, just add the opposite.
It is much like subtracting two numbers: A  B = A + (B). This diagram illustrates vector subtraction in the tiptotail style.
The original B vector is shown
as a dashed 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 above, that the vector does not change direction,
only
length.
If A = (1,2) then 3A = (3,6).
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 2. From the x and y components given, find the direction and magnitude
of
the resultant.
a. F_{y} = 120 N, F_{x} = 345 N
b. v_{y} = 31 m/s, v_{x} = 8 m/s 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 polevaulter applies a force of 415 N to the pole at an angle of 37º.
What are the horizontal and vertical components of this force?  

