Introduction to Summer Work For AP Physics C: These worksheets

118 Pages·2013·5.56 MB·English

by  William D. Smith

AP Physics C - Summer Work

Introduction to Summer Work For AP Physics C:
The summer work for AP Physics C is contained in four separate worksheets. If you have already taken a
college-prep science course most of this material will be a review of topics you have already mastered.
If this is your first encounter with this material there are several resources included in this package to
help you learn the material.
The Worksheets appear in the following order:
Worksheet No. Page(s)
WS-1: Review of Metric System and Scientific Notation 2
WS-2: Significant Figures and Uncertainty in Calculations 3 - 7
WS-3: Metric Conversions and Consistent Units 8 - 10
WS-4: Unit Analysis. 11 - 14

In addition to the worksheets you will find the following resources
Resource
1. Text Chapter 1
2. Power Point Presentation on the Metric System
3. Calculations involving Significant Figures

Each of the worksheets has examples with solutions. However you may find the text materials and the
optional power-point presentations helpful.
These worksheets will be due the first day of class at which time you
should be prepared to take an exam covering this material.

If you have any problems with these materials pleae do not hesitate to contact me via e-mail:
[email protected]

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AP Physics C - Summer Work

WS-1: Review of Metric System and Scientific Notation

(a) Complete the table for units of length, mass or time in the metric system.
Name of Measurement Abbreviation Decimal value Power of 10
Example: kilosecond ks 1,000 s 103s
Gigameter
dg
10-9s
1,000 m
Ts
centigram
Mm
micrometer 0.001m
10-6s

(b) Complete the table
Number and
metric
Number Scientific Notation abbreviation that
requires no
exponent
Example: 0.000 000 0042 s 4.2 x 10-9 s 4.2 ns
9,080,000 m
0.000,0023 g
0.010 m
84,40 s
0.003077 g
6,700 m
0.000 000 000 0054 s
0.23 g
0.000 000 000 00134 m
0.0035 s

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WS-2: Uncertainty in Measurement and Calculations:
1. Exact Numbers:
Counted numbers and definitions do not involve any measurement and are considered as exact
numbers
Definitions: 1 week = 7 days.
1 mile = 5,280 feet
1 yard = 3 feet

Counted: 5 Players on the basketball court.
23 students in a room
25 pennies used by a class in an experiment.
5 rocks

2. Measured Numbers:

a. All measured numbers have some degree of uncertainty.

b. In recording measurements we record only the significant figures. Record your
measurement to include one decimal estimate beyond the smallest increment on the measuring
device. Examples:
Smallest increment = 1m recorded measurement must include 0.1m (3.1m)
Smallest increment = 0.1m recorded measurement must include 0.01m (5.67.1m)
Smallest increment = 0.01m recorded measurement must include 0.001m (12.675m)
c. Unless otherwise stated the uncertainty in the last significant figure
(the uncertain digit) is assumed to be 1 unit. Modern digital instruments and many types of
volumetric glassware will state the degree of uncertainty.

3. Rules for counting Significant Figures.
a.Non-Zero Numbers: Non-zero numbers are always significant.
b. Zeros:
1: Leading zeros that precede the first non-zero numbers are never
counted as significant numbers
2. Captive zeros (sandwich zeros) that fall between two non-zero digits are always
significant.
3. Ending zeros that appear after the last non zero digit are significant only when a
decimal point appears somewhere in the number.
c. Scientific Notation: Significant figures are recorded in the mantissa (number 1  x < 10)
Example: 3.0 x 103 has 2 significant figures
5.998 x 105 has 4 significant figures
6.00000 x 10-23 has 6 significant figures
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4. Rules for Using Significant Figures in Calculations
(a) Multiplication, Division, Powers and Roots: - “LEAST SIG.FIG RULE”
1. The number of significant figures in the result is reported as equal to the same number having
the least number of significant figures.
2. The focus is on the number of significant figures in each of the measured numbers!

Example1:
2.3 5.78Calculatorreturns13.294
2.3 has 2 sig.fig
5.78 has 3 sig.fig.
2.35.7813 The answer must be rounded to show 2 sig.fig

Ex ample2.
1.6 7x1050.00045calculatorreturns2.505000000x1024
2x1023

1.67x105 has 3 sig.figs

0.00045has 2 sig.figs
2x10-23has 1 sig.fig
1.6 7x1050.00045
3x1024(roundedto1sig.fig)
2x1023

Example3

2.3calculatorreturns1.516575089

2.3has2sig.figs

2 .31.5 round answerto2sig.figs

(b) Addition and Subtraction: “LEAST PRECISE DECIMAL RULE”
1. The answer will be reported with the same decimal precision as the number having the
uncertain digit in the least precise decimal place
2. The focus is on the decimal precision in each of the measured numbers!

Example4:ac
a. 123cm5.35cm128cm(roundedto100)
b. 1.0001m0.0003m1.0004m(roundedto104)
c. 1.002s0.998s0.004s(roundedto103)

Ex ample5:Watch fornumbersending withzero!
10 0.0110calculatorreturns10.0110
10:theuncertaindigitappearsinthe101 place
0.0110:theuncertaindigitappearsinthe104 place
10 0.011010 round answer to the 101 place

Rationale:The uncertainty in the measured number 10 is ±1. The uncertainty alone
in the first number (10) is greater than the entire second number (0.0110).
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(c) Addition/Subtraction combined with Multiplication/Division
– Always perform the addition portion of the calculation 1st to determine the correct decimal
precision of the sum. (least precise decimal rule)
– Once the precision of the sum has been determined you can count the number of significant
figures in the sum to apply the “least sig.fig rule” in performing the multiplication.
– Do not round until the final calculation has been completed.

Example6:

(34.00.56)(3.2x103)
calculator returns1.827211896x1014
1.345x1010

lst:Perform addition and determine least precise decimal

3: uncertain digit appears in 100

4.0:uncertain digit appears in 10-1

0.56:uncertain digit appears in 10-2

(34.00.56)7.568(rounded to100 thesu mwill have1sig.fig)
2nd:determine the number with the least sig.figs
8 (sum): 1 sig.fig
3.2x103:2sig.fig
1.345x1010:4sig.fig

(34.00.56)(3.2x103)
2x1014 (rounded to1sig.fig)

1.345x1010

(d) Scientific Notation with different powers of 10:

Example7:
1.38x1047.98x1056.89x103 calculatorreturns8.18690x105
1st:Change all numbers to have the same power of 10
7.98x105:multiply the mantissa by 101 and the power of ten by 10-1=79.8x104
6.89x103: multiply the mantissa by 10-1 and the power of ten by 101=0.698x104
8.18690x105:multiply the mantissa by 101 and the power of ten by 10-1=81.8690x104
2nd:Comparethe precisionof thedecimal places
1.38x104:unceratin digit appears in the 10-2 of the mantissa
79.8x104:unceratin digit appears in the 10-1 of the mantissa
0.698x104:unceratin digit appears in the 10-3 of the mantissa
1.38x10479.8x1040.698x104 81.9x104 (roundedto10-1inthemantissa)
3rd:Returntostandard scientificnotation
81.9x104:multiply mantissa by 10-1and the power of ten by 101 = 8.19x105
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Problems

How many significant figures in the following numbers:

1. ______ 1,245m 2. _______ 0.030m

3. _______ 10,000m 4._______ 1.340 x 1023m

5. _______ 3.02003 x 1014m 6. _______ 0.0000001m

7. _______ 1,000. 8. _______ 0.10000010

9. Complete the following table: (Assume standard uncertainty unless otherwise specified.)
Measurement Smallest # Uncertainty Maximum Minimum
increment s.f  Value Value
3.030 m
100 m
3.606g Digital 0.003g

10: Convert the following numbers into standard scientific notation:

a. 96.3 x 104 ____________________

b. 0.05 x 1023 ____________________

c. 123 x 10-7 ____________________

Problems 9 – 13: Perform the following Calculations and record your answers in the proper
number of significant figures.

11. 0.3030 + 0.42 =

12. 2.1m + 0.3889m – 123.22m =

13. 3.1567 x 102 + 9.212 x 104 - 4.677 x 106 =
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14. 31.33x105 

0.303
15. 
1.0x103

1.25x103
16. 
(3.2104.9)(1.3x106)

17. Calculate the average height of the starting line of the following Basketball team. Record your
answer in the correct number of significant figures. (Hint: The counted number “5” will be an exact number.
The sum of the heights will require the application of the sum rule)

Player No. Height
1 2 m
2 1.995 m
3 2.2m
4 2.4333m
5 1.98m

18. Calculate the volume of a box that has a height of 3.233m, a width of 4.33m and a length of 1.2 x
10m. Report your answer in the correct number of significant figures. (Hint: volume equals length x width x
height)

19. Three atoms are measured and found to have the following radii: 1.47x10-14m,
1.5 x 10-15m and 1.4978 x 10-15m. Find the average radius.
(Hint: Begin by changing all three into the same power of ten …watch out for the negative exponent). Next add the
mantissas together and round to the “least precise decimal”. Then divide by 3 which is a counted “exact number”.)

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WS-3 Simple Metric Conversions and Consistent Units

Section 1: Metric Conversions
One of the major benefits of using the metric system is the ability to move from a large unit of measure
to a smaller unit of measure simply by moving the decimal point or changing the exponent. For
example, 0.003 km is easily changed to 3.00m and 4.50 x 102nm is easily changed to 4.50 x 10-7m by
applying a few simple rules.

Step 1: Determine the number of decimal places between the units involved in the conversion.
3 0 -2 -3 -6 -9
km = 103m m = 100m cm = 10-2m mm = 10-3m m = 10-6m nm = 10-9

Step 2 for Standard Numbers:
If you are converting from a large unit to a smaller unit the number will get bigger and the decimal
place will move to the right. If you are converting from a smaller unit to a larger unit the number will
get smaller and the decimal place will be moved to the left. An easy way to remember the direction of
the decimal shift is to use the following rule of thumb:
Large  Small  Large and Small  Large  Small

Example: Convert 0.003km to cm.
Step 1: There are 5 decimals between km and cm. (3-(-2)) = 5
Step 2: km is larger than cm so the number must become larger. The
decimal must be moved to the right by a total of 5 decimal places.
Large  Small  Large
Therefore 0.003km = 300cm

Scientific Notation: If you are converting from a large unit to a smaller unit the number becomes larger
which means the exponent must increase. If you are converting from a smaller unit to a larger unit the
number will become smaller and the exponent will decrease. An easy way to remember the direction of
the decimal shift is to use the previously stated rule of thumb:

Example: Convert 3.0 x 10-3 m to cm.
Step 1: There are 4 decimals between m and cm. (-6(-2)) = -4
Step 2: m is smaller than cm which means the number must become smaller!
Small  Large  Small
The exponent must be decreased by 4.

Therefore 3.00 x 10-3 m = 3.00 x 10-7 cm

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Section 2: Using Consistent Units in Calculations:

When performing calculations, it is important to verify that all of the basic units of measurement
(length, mass, time, etc) are measured in the same metric prefix.

Example: An ant was observed to travel 3.00m south, turn to the west and move an
additional 50.1cm, and finally turn to the north and travel an additional 0.0110km. Determine
the total distance in meters traveled by the ant.

Solution: The first step is to recognize that the three distances have been given to you in
different units of length. Before you can perform the addition you will need to convert all of the
measurements to the same unit of length. In this case the most convenient choice is the meter.
Make certain to preserve the correct number of significant figures as you make the conversions.

3.00m = 3.00m (3 sf) 50.1cm = 0.501m (3 sf) 0.0110km=11.0 m (3 sf)

We can now proceed with the addition: (3.00m + 0.501m + 11.0m) = 14.501m
Next use the addition rule (least precise decimal) and round to 10-1: Reported Answer: 14.5m

Problems

Part (a): Make the following conversions – preserve the number of significant figures in the answer!

1. 450nm _________________ mm
2. 34km __________________cm
3. 43 000mm __________________m
4. 4.0 x 106nm __________________m
5. 3.98 x 10-3km __________________m
6. 456mm __________________km
7. 136 000m __________________km
8. 4.89 x 1012 mm __________________km
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9. 2.68 x 106m __________________km
10. 456 000m __________________mm
11. 450mm __________________m
12. 23cm __________________mm
13. 234m __________________cm
14. 2.34 x 104cm __________________m
15. 4.56 x 10-7cm __________________nm

Part (b): Solve the following problems. Record your answer in the designated unit with the correct
number of significant figures.

16. The crew of the Apollo 9 collected moon rocks to bring back to earth. Three of the rocks were
massed to be 9.60g, 0.00345kg and 195mg. What was the total mass of these rocks reported in grams.

17. The length of a warehouse is measured to be 95.00m. The height of the roof is measured to be
1,350.00cm. The width is measured to be 0.0015km. Calculate the volume of the warehouse in cubic
meters (m3).

18. A triathelete completed the swim portion of the triathalon in 3.5 x 103s, the bike portion was
completed in 2.6ks and the marathon was completed in 3.6 x 106ms. Calculate the total time to
complete the marathon in seconds.

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