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!

4

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?

6

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

7

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

8

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

9

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

15

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 ______________________

17

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.

18

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

21

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