)
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)
Date
_
Period
I '
_
c __.,
Name
...............9
Physics Skills
.i'.... i.
, ii' ,;,il! 111'
Name
_
Use with Chapter 2.
Significant Digits
Any measurement
is inaccurate to some degree. The inaccuracy stems from several factors. The precision
of any measuring device is limited. The person doing the measurement
may introduce error. The experimental technique may be faulty. Because a measurement
contains some degree of inaccuracy, the
number of digits that are valid for the measurement
are also limited.
There are four basic rules that can be used to determine
surement.
1.
2.
3.
4.
the number
of significant
13. Complete
4.
2.
1843.02 L
7.
six
3.65 kg
5.
km
six
8.7Dl'C
three
four
3. 365 kg
6. 2000.12
three
six
8.
9.
14.
a.
these addition
3.414 s
+
10.02 s
b.
58.325 s
seven
1884 kg
a.
15.
as a least precise measurement.
4.301 kg .,. 1.9 cm '
An experiment calls for 16.156 g of substance
and 9.44 g of substance D.
a.
How many significant
A.
five
B.
A, 28.2 g of substance
B, 0.0058
g of substance
C,
digits are there in each measurement?
three
C.
b. What is the total mass of substances
two
D.
three
in this experiment?
53.B g
0.000 98 s
c. How many significant
digits are there in the answer to part b?
three
+
0.94 kg
+
1.0 kg
+
9.778 kg
16. Your lab partner has measured 16.50 mL of water. You accidentally tip over the graduated cylinder
and spill some of the water. You stand the cylinder up and determine that there are 8.0 mL of
water left.
these subtraction
2104.1 m - 463.09
problems.
Write the difference
as a least precise measurement.
a. Which measurement
m
1641.0 m
b.
Write the quotient
Because the least precise measurement
is 45.0 kmjh, the answer can be precise only to the nearest
one-tenth. Thus the correct answer, rounded off, is 46.7 km/h. Answer the following questions.
h
1896 kg
12. Complete
problems.
2.4 s
45.0 + 48.21 + 47.024 = 140.234
140.234 .,. 3 = 46.74466
71.76 s
b.
-i-
Averages follow the same rule. Suppose a car travels around a track three times. Your measurements
for
the three trials are 45.0 km/h, 48.21 km/h, and 47.024 km/h. Determine the average speed of the car.
10. 0.000 101 045 0 s
Write the sum as a least precise measurement.
+
these division
80.23 m
2.3 g/cm3
three
problems.
+
em X 0.0159 an
33 mls
When you perform mathematical
calculations, the result of your calculations can never be more precise than the least precise measurement
Add the following quantities: 44.1 kg + 8.002 kg + 0.93 kg =
53.032. The least precise measurement,
44.1 kg, is precise only to the nearest one-tenth. The sum of the
masses, therefore, must be rounded off to the nearest one-tenth. So, the answer is 53.0 kg.
11. Complete
140.01 cm X 26.042
Complete
a.
0.5 mL
704000
as a least precise measurement.
58.0 cm3
onE!
mm
Write the product
0.13 m2
b.
2.00012
problems.
digits in a mea-
Suppose an observer measures the speed of an object and determines that it is moving at 6.13 m/s.
The speed of a second object is determined to be 5.02 m/s. Which digits are significant in these two
measurements?
According to rules 1 and 3, all the digits are significant
Using the rules given above,
determine the number of significant digits in each of the following measurements.
four
these multiplication
a. 10.19 m X O.Ol3·m
Nonzero digits are always significant.
All final zeros after the decimal point are significant.
Zeros between two other significant digits are always significant
Zeros used only for spacing the decimal point are not significant
1. 23.30 cm
Physics Skills
Multiplying and dividing are a little different. In these kinds of calculations, the product or quotient
has the same number of significant digits as the least precise number. If you multiply 21.3 an by
9.80 em, the answer is 209, not 208.74. Because the less precise measurement,
21.3 em, has only three
significant digits, the product has three significant digits.
.}I.}I}I "
Determining
_
b.
2.326 h - 0.104 08 h
or yoursl
Explain.
one-
8.5mL
2.222 h
Physics: Principles and Problems
is more precise, your lab partner's
The lab partner's measurement
is more precise because it is measured
to the nearest
hundredth
of a milliliter.
How much water did you lose when you tipped over the graduated cylinderl
Physics Skills
23
24
Physics Skills
Physics: Principles and Problems
.z;....
2
Dimensional Analysis
Name~,--,Y,-
_
Period
_
Dimensional Analysis
Exercising Problem Solving Skills
1. The record long jump is 349.5 in. Convert this to meters. There are 2.54 em
344.S
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c""
ill
an inch.
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2. A car is traveling 55.0 miles per hour. Convert this to meters per second. One mile is equal to
1.61 km,
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3. How many mg are there in a 5.00 grain aspirin tablet?
There are 16.0 ozflb.
1 grain
= 0.00229 oz. There are 454 g/lb.
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4. Mercury has a mass density of 13.54 g/ml..
d~ •.•.
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=-
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How ma~lYmilliliters would 100. grams occupy?
'vOl4}1\e:=
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=
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5. In 1980, the US produced 18.4 billion (109) pounds 0rphosphorlc acid to be used in the manufacture
of fertilizer. The average cost of the acid is $318/tol (1 ton == 2000 Ib) What was the total value of
the phosphoric acid produced?
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Laying the Foundation
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;11
Chemistry
Dimensional Analysis
2
6. On planet Zizzag, city Astric is 35.0 digs from city Betrek. The latest in teenage transportation is a
Zeka which can travel a maximum of 115 millidigs/zip. On Zizzag the planet turns once on its axis
each dyne. Their time system divides each dyne into 25.0 zips. How many dynes will it take Pezzi
to get from Astric to Betrek to see his girlfriend? There is no telephone communication on Zizzag.
Do you think this relationship will last?
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7. While prospecting in the North Woods, Joe found a gold nugget which had a mass density of
19.2 g/cm'. When he dropped it into water in a graduated cylinder, the water level increased by
15.0 mL. How many grams of gold did Joe have?
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8. Light travels at a speed of3.00 x 1010 cm/s. What is the speed of light in kmlh?
10
3.00
x ~o
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c""-
:::
9. A cheetah has been clocked at 112 kmlh over a 100-m distance.
What is this speed in m/s?
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10. An electric current of 10.0 amperes is passed througha solution of gold(IlI) chloride for a period of
0.500 hours. After this period of time, how much gold has plated out on the cathode? There are
96,500 coulombs/mol of electrons. A mol of gold has a mass of 197 g/mol. An ampere is equal to
1 coulomb/second.
It is necessary to transfer 3.00 mol electron/mol gold.
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in Chemistry
277
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,
Foundation Lesson JJJ
Name-----+-K~(~y~·
_
Period
_
Literal Equations
Manipulating Variables and Constants
EXERCISES
Directions: For each of the following equations, solve for the variable in bold print. Be sure to show
each step you take to solve the equation for the bold variable.
1. v
=
V
a. ;::
at
t
F
2. p=A
-3. A
r-
:;:
p
h
=-
p
4. F(Llt)
=
mLlv
.0
t -
M!
VV\
"l).
-
G6. C
=
9
3
8. Kavg = -kB T
2
-
---
5
-(F-32)
2
Laying the Foundation in Physics
(VI '2.
q C
s
T-
32-
T -
1
9. K = -mv2
~V
-t='
v
=J~::
73
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Foundation Lesson III
10. vnns
=
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2
=
1
v =
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