measurement and time - washingtonville central school … · measurement and time i. units ... -...
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Name:_____________________ Date:________
Regents Physics Mr. Morgante
UNIT 1
Measurement, Time, and Math Review
2
Measurement and Time I. Units
Definition- a unit is a standard quantity with which other similar quantities can
be compared.
Ex. The distance between 2 cities is 26 miles.
- Miles is the unit.
He was traveling at a speed of 40 miles/hour.
-Miles/hour is the unit.
II. SI System (System Internacionale “French”) or MKS
- Provides standardized units (base units) for scientific measurements
- In Physics we deal with the Meters (m)
Kilograms (Kg)
Seconds (s)
III. Dimensional Analysis
- Analyzing units helps to solve problems.
- Units on the left side of an equation must always equal units on the right side of an
equation.
- Quantities can only be added or subtracted if they have the same units.
Ex. If I am solving for the speed of an object, I know the answer must be in units of
miles/hr, or meters/seconds, etc
IV. Measuring Length
In the MKS System, we always take length measurements in meters (m).
- However, it is easier to measure with a ruler in centimeters sometimes. We can convert
to meters as follows.
55 cm= ? m When 100cam = 1 m [100cm/1m] or [1m/100cm]
1. Create a proportion: 55cm x 1m/100cm= 0.55m
and solve
Typical metric units and equivalent standard unit for length
1000mm=1m
100cm=1m See ref. Table for additional prefixes mm=millimeter
10dm=1m cm=centimeter
1000m=1km dm=decimeter
m= meter
V Measuring Mass
Mass- the amount of matter contained in an object, or the amount of space an
object occupies
-You can use a triple beam balance to measure an objects mass.
Typical metric units for mass, eq. standard Unit
1000g=1kg g=grams
1000mg=1g kg kilograms
mg=milligrams
How many mg are there in 1 kg?
By now you have noticed all conversion are multiples of 10 for metric units.
3
VI. Measuring Force
Force- a push or pull on a mass. Forces are measured with a spring scale. The units for
force are kgm/s2 or Newtons. We will use Newtons (N) for now.
VII. Significant Figures
A. Rules
1. 0’s that appear before a nonzero digit are not significant
ex 0.002 has 1 sig fig
0.13 has 2 sig figs
2. 0’s that appear between nonzero digits are significant only if:
a. followed by a decimal point
Ex. 40s has only 1 sig fig
b. they appear to the right of the decimal point
Ex.37.0 cm has 3 sig figs
4.100m has 4 sig figs
How many sig figs does 0.040900kg have?
Note: you should review/ remember from previous math how to add subtract, divide, multiply,
sig fig numbers.
VIII. Scientific Notation
Follows the General Form Ax10n
1x103m= ?km
? mg= 1x 10-3
g etc, etc
Solve the problems above
A. Addition an Subtraction
- They can be added and subtracted only if they are expressed in the same units and to the
same power of ten
- You can first change the power of 10 and then add/ subtract
Ex. 3.2x102m + 4.73x 10
3 m=
0.32x103m + 4.73 x 10
3m = 5.05x10
3m
B. Multiplication and Division
General rules
(Ax10n)(Bx10
m)= (AxB)(10
n+m)
and
(Ax10n) = A x 10n-m
(Bx10m) B
Ex. (1.3x105m)(3.47x10
2m)= 4.5x10
7m
2
(8.4x105m)/(2.10x10
2m)=4x10
3m
C. Estimation and Orders of Magnitude
1x103 => Order of magnitude=103 or 1000
7x103 => Order of magnitude = 104 or 10,000
<5, order may go up to next order!
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GRAPHING
Once you know how to play a game and are sure of all of the rules, most games are fun to
play. If you don’t know how to play, and you don’t know the rules very well, any game can be a
pain. Graphing data is like this too. Once you know the rules and how to do it, believe it or not,
you might even enjoy it!
Here are a few of the rules for graphing:
1. Begin by using a ruler and a pen to draw a line up and down (the vertical or y-axis). Then
draw a line from side to side (the horizontal or x-axis).
2. Decide which one of the columns of the data table you controlled in your experiment. This
data is called your independent variable and it is plotted on the x-axis.
3. The other column of data is called the dependent variable and it is plotted on the y-axis. Did
you forget which is “x” and which is “y”?
Check this out………
4. Choose a set of numbers from zero up to some number which is larger than your largest
experimental number. Your set should be 0, 5, 10, 15 etc., or 2, 4, 6, etc., or 10, 20, 30, etc. Nice
numbers like these, never numbers like 0, 7, 14, 21, etc., which are difficult to divide by 2 more
than once. Arrange these numbers in ink and evenly along the axis so that your highest number
falls about two thirds or three quarters of the way along the axis. The numbers you choose for
your two axes do not have to be the same. They must fill the data which you have to plot, so your
largest number falls at the least half way along each axis.
5. Next, in ink, print the titles from your data table along the axes; just below or to the left of the
numbers you printed on the axes.
6. Now, in pencil, plot your data with small dots, like this . and put a circle around each dot, like
this:
. Note: this is done in pencil, not pen.
7. Next, in pencil a1so, draw a straight line or curve, so as to go through as many points as
possib1e and still keep the curve smooth or the straight line straight. This is done in pencil, not
pen.
8. Finally, in ink, print a title for your whole graph. To do this, copy the title you have printed on
the y-axis, followed by the word “as it depends on” or “as it is related to” and the title which you
printed on the x-axis in 5 above.
Note: Everything is drawn in ink, except the dot, circles and graph line. All straight lines are
drawn using a ruler.
5
Now dive in and try to graph the following data:
A cart is allowed to run down a ramp with a load of bricks in it. The speed of the cart is
measured at the end of the ramp. The data below shows how the speed of the cart varies with the
height of the upper part of the ramp.
Here is the data which you are to plot:
------------------------------------------------------------------------------------
Height of the Ramp Speed of the Cart at Bottom of
in cm. Ramp in cm/sec
------------------------------------------------------------------------------------
10 3.0
15 8.0
20 16.6
25 20.0
30 24.2
------------------------------------------------------------------------------------
1. Which is the independent variable? (i.e. you control this variable)
2. What is your title for the x-axis?
3. What is your title for the y-axis?
4. What is the main title for your graph?
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Graphing Math Relationships
Direct Linear Proportions
Math Eqs.: follows y=mx+b format (y=2x, y=4x+2, etc.) as shown in graph below.
As x value goes up, the y value goes up in a direct linear fashion. POSITIVE SLOPE.
A few Reference Table Eqs. that look like this if graphed: Ff =µFn, p=mv, Fs=kx, W=Fd,
v=fλ
+y
+x
Indirect Linear Proportions
Math Eqs.: follows y=mx+b format (y=-2x, y=-4x+2, etc.) as shown in graph below.
As x value goes up, the y value goes down in an indirect linear fashion. NEGATIVE SLOPE.
+y
+x
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Inverse Indirect Proportions
Math Eqs.: follows y=1/x format (y=1/2x, y=-1/4x+2, etc.) as shown in graph below.
As x value goes up, the y value goes down in an indirect nonlinear fashion. NEGATIVE
SLOPE.
A few Reference Table Eqs. that look like this if graphed: v =d/t, a=Δv/t, T=1/f, n=c/v,
R=V/I
+y
Note: Slope is not as steep as direct or indirect square
graph.
+x
Direct Square Proportions
Math Eqs.: follows y=mx2 +b format (y=2x
2, y=-1/4x
2+2, etc.) as shown in graph below.
As x value goes up, the y value goes up in an exponential (hence x2 term) fashion. POSITIVE
SLOPE.
A few Reference Table Eqs. that look like this if graphed: PEs = ½ kx2, KE = ½ mv
2, E=mc
2
+y
+x
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Indirect Square Proportions
Math Eqs.: follows y=1/x2 format (y=1/2x
2, y=-1/4x
2, etc.) as shown in graph below.
As x value goes up, the y value goes down in an exponential (hence 1/x2 term) fashion.
NEGATIVE SLOPE.
A few Reference Table Eqs. that look like this if graphed: Fe = kq1q2/r2, Fg=Gm1m2/r
2
+y
+x
Constant Proportions
Math Eqs.: follows y=1 format (y=5, y=-7, etc.) as shown in graph below.
Straight line parallel to x axis at the height of the y value. NO SLOPE.
+y
y=5
+x
y=-7
-y
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GENERAL ITEMS TO KNOW
Test Taking Strategies & Study Tips for Regents Physics
Solve all of the problems you are comfortable with first. Only when this is done should
you go back and solve the problems that you had trouble with.
Make sure you answer all questions, show all equations and all substitutions with units.
No units, no substitution, no equation means no credit.
If you are spending more than 3 minutes per problem, chances are you are doing
something wrong. The problem solutions are usually straight forward and don’t require
more than 3 minutes.
Find a Study Buddy! Sit next to someone in class who can help you in your studies, not
negatively affect you. This can go a long way in obtaining an understanding of the
material.
If you don’t pay attention in class and participate, and you don’t reinforce the material
learned every night with homework and study YOU WILL NOT DO WELL IN THIS
CLASS.
How to Use Exponential Functions on Your Calculator
A. Texas Instruments Calculators (TI-83 Plus example but applies to most Ti calculators):
Use the steps below to calculate (-3.0x104) ∙ (4.5x10
-7)
1. Type the negative sign first that is in brackets (-) DO NOT USE THE MINUS OR
SUBTARCTION SIGN
2. Type the number 3.0
3. Press the 2nd
function, then press the EE button
4. Then type the number 4 for the exponent.
5. Press the multiplication sign, then type 4.5
6. Press the 2nd
function, then press the EE button
7. Type the negative sign first that is in brackets (-) DO NOT USE THE MINUS OR
SUBTARCTION SIGN
8. Then type the number 7 for the exponent.
B. Casio Calculators:
Use the steps below to calculate (-3.0x104) ∙ (4.5x10
-7)
1. Type the negative sign first that is in brackets (-).Some older models also have a +/-
button you should use otherwise. DO NOT USE THE MINUS OR SUBTARCTION
SIGN.
2. Type the number 3.0 then press the EXP button
3. Then type the number 4 for the exponent.
4. Press the multiplication sign, then type 4.5
5. Press the EXP button
6. Type the negative sign first that is in brackets (-).Some older models also have a +/-
button you should use. DO NOT USE THE MINUS OR SUBTARCTION SIGN.
7. Then type the number 7 for the exponent.
10
Remember, you can also estimate what the answer should be by just multiplying the coefficients
and adding or subtracting exponents as discussed earlier in the this note packet.
Example
Step 1: -3.0 x 4.5 = -13.5
Step 2: 4 + (-7) = -3
Step 3: Final Answer is -13.5 x 10-3
OR -1.35 x 10-2
YOU SHOULD BE ABLE TO GET AN IDEA IF YOU ARE CORRECT BY CHECKING THE
ORDER OF MAGNITUDE WHICH CAN BE DONE IN YOU HEALD USING SIMPLE
MULTIPLICATION AND ADDITION IN THE EXAMPLE ABOVE.
11
Name:_______________________ Date:________
Regents Physics Graphing Exercises Mr. Morgante
1. For a bug running down a sidewalk, the distance traveled depends on time based on the
information shown below.
Time (s) 2.5 5.0 7.5 10.0 12.5 15.0
Distance
(m)
0.075 0.165 0.23 0.33 0.39 0.49
a. Plot the graph, determine the slope, and write the equation expressing the distance as
a function of time.
b. How long would it take the bug to travel a distance of 0.2m? Compare your value
calculated from the equation to the value read from your graph.
OVER
12
2. Water is pumped into a large tank. The water in the tank is measured at various times
x (cm3) 0.0 2.0 5.0 8.0 10.0 13.0
y (s) 0.0 175 470 770 1000 1400
a. Plot a graph showing how the remaining volume depends on time. Calculate the
slope and write the equation.
b. How much water is in the tank after 90 minutes?
13
Name:_______________________ Date:________
Regents Physics Units Conversion Worksheet #1 Mr. Morgante
1. Perform the following unit conversions:
a. 64000 nm = __________ mm
b. 52km = __________ cm
c. 5.3xl0-5
mm =_______ um
d. 0.63 kg = __________ g
e. 0.49 hours = ________ ms
f. 9.8 x 105 minutes =_________ days
g. 1.000 days =__________ weeks
h. l.0xl06 s = ____________ years
3. Convert the following to SI base units:
a. 0.03 km/h
b. 5.6 g/cm3
c. 7800 cm3
d. 7800 km3
e. 3.250 kg/L (note: 1 mL = 1 cm3)
f. 0.30 Mm2
g. 7800 km2
h. 0.059 kg/cm3
14
Name:_______________________ Date:________
Regents Physics Units Conversion Worksheet #2 Mr. Morgante
1. Perform the following unit conversions:
a. 4200 km = __________ nm
b. 94 cm = __________ um
c. 2.2xl0-5
um =_______ km
d. 0.31 dg = __________ kg
2. Convert the following to SI base units:
a. 0.07 cm/min
b. 4.9 g/cm3
c. 200 cm3
d. 45 km3
e. 0.72 Gm2
f. 234 Mm2
g. 0.125 mg/cm3
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Name:_____________________ Date:__________
Regents Physics Unit Conversion/Scientific Notation Mr. Morgante
1. Calculate the following, and put your answer in base units (MKS) SHOW ALL WORK:
a. Find the volume and surface area of a cube whose sides are 1.05 cm long.
b. Find the area of a right triangle whose perpendicular sides are 2.35 cm and 4.2 cm long.
2. Convert the following to SI base units (MKS). Show ALL WORK!!!!!!!
a. 23 mm
b. 23 mm2
OVER
c. 23 mm3
16
d. 6 km/day
e. 23 g
f. 0.38 g/cm3
3. Change the following numbers from scientific notation to decimal notation:
a. 3.26 × 103 _______________________________ c. 5.09 × 10
5 _____________________
b. 4.0 × 10-8
________________________________ d. 2.0 × 102 ______________________
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Name:_______________ Date:_______
Regents Physics Algebra Practice #1 Mr. Morgante
1. The equation is d = vit + ½ at2. Solve for t in the space below if vi = 0.
2. The equation is PEs = ½ kx2. Solve for x in the space below.
3. The equation is vf2 = vi
2 + 2ad. Solve for d in the space below.
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Name:_________________ Date:__________
Regents Physics Trigonometry Practice#1 Mr. Morgante
SHOW ALL WORK!!!!
1. B a
6.4 a A
B
A
4
10
2. A
A ______
6
B c B ______
c ______
3. 9
a ______
60o
B ______
c a c ______
B
OVER
19
4.
A ______
B ______
A
c ______
4 c
B
3.5
5.
A ______ B ______ c________
B c
A
4
2.5
6.
A A_______ c__________
1.25 c
50o
1
20
Name:_______________________ Date:________
Regents Physics Order of Magnitude Worksheet Mr. Morgante
1. The thickness of a dollar bill is closest to
a. 10-4
m
b. 10-2
m
c. 10-1
m
d. 101 m
2. What is the approximate diameter of a dinner plate?
a. 0.0025 m
b. 0.025 m
c. 0.25 m
d. 2.5 m
3. The height of a doorknob above the floor is approximately
a. 1x102 m
b. 1x101 m
c. 1x100 m
d. 1x10-2
m
4. What is the approximate mass of a chicken egg?
a. 1x101 kg
b. 1x102 kg
c. 1x10-1
kg
d. 1x10-4
kg
5. Which measurement of an average classroom door is closest to 1 meter?
a. thickness
b. width
c. height
d. surface area
6. The mass of a physics textbook is closest to
a. 103 kg
b. 101 kg
c. 100 kg
d. 10-2
kg
7. The length of a high school physics classroom is probably closest to
a. 10-2
m
b. 10-1
m
c. 101 m
d. 104 m
8. The approximate mass of a nickel is
a. 0.0005 kg
b. 0.005 kg
c. 0.5 kg
d. 5 kg
9. The approximate mass of an average high school student is
a. 7.5x10-1
kg
b. 7.5x102 kg
c. 7.5x101 kg
d. 7.5x104 kg
10. The height of an average high school student is closest to
a. 1x102 m
b. 1x10-1
m
c. 1x100 m
d. 1x10-2
m
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Name:_____________________ Date:_____________
Regents Physics Mr. Morgante
Order of Magnitude/Scientific Notation/Graphing/Unit Conversion Worksheet
Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.
____ 1. Calculate the following, and express the answer in scientific notation: 10.5 8.8 3.14
a. 2.9 102 c. 290.1
b. 290.136 d. 290
____ 2. Calculate the following, and express the answer in scientific: (0.82 + 0.042 ) (4.4 103)
a. 3.8 103 c. 3.784 10
3
b. 3.78 103 d. 3784
____ 3. Which of the following equations best describes the graph below (next page?
a. y = 2x c. y = x2
b. y = x d. y = x
OVER
22
____ 4. Which of the following equations best describes the graph above?
a. y = x2 + 1 c. y = –x
2 + 1
b. y = x2 – 1 d. y = –x
2 – 1
____ 5. What are the basic SI units?
a. meters, kilograms, hours c. meters, kilograms, seconds
b. feet, pounds, seconds d. feet, kilograms, seconds
____ 6. Estimate the order of magnitude of the length of a football field.
a. 10–1
m c. 104 m
b. 102 m d. 10
6 m
____ 7. Estimate the order of magnitude of your age, measured in units of months.
a. 10–1
months c. 102 months
b. 101
month d. 103 months
8. Convert 92 103 km to decimeters using scientific notation using the space below.
23
Speedometer reading
(km/h)
Time for 100 km trip (h)
20.0 5.00
30.0 3.33
40.0 2.50
50.0 2.00
60.0 1.67
70.0 1.43
80.0 1.25
90.0 1.11
100.0 1.00
9. Using the table above, construct a graph of the time required to make a trip of 100 km measured
at various speeds.
10. Convert 1 m to meters using scientific notation.
11. Convert 5.52 108 g to kilograms using scientific notation.
12. Convert 8.66 10–9
m to millimeters using scientific notation.
13.Calculate the following, expressing the answer in scientific notation:
(8.86 + 1.0 10–3
) 3.610 10–3
Z:\PHYSICS\REGENTS PHYSICS\CLASS MATERIAL\UNIT 1 (MEASUREMENT AND TIME) 1-5-10.DOC