PHYSICS
Chapter 1 and Appendix A and B
Overview
Mathematics is one of the most important tools available to the physicist. In this first unit you will review
your basic mathematical skills including significant digits , powers of ten, scientific notation
unit conversions, and algebraic operations. Since most of the problems that you will encounter in the
textbook are word problems a “problem solving method” which stresses the importance of how an
answer is achieved and communicated on paper will be introduced.
Objectives
-. To review many of the mathematical skills you will need to solve physics problems.
-. To review the importance of unit conversion, significant digits and precision measurement.
-. To introduce the problem solving method which will be used throughout this course.
Problems: Mathematical Review
1. What is a significant figure in a measurement? It is all the measured values you are certain of
plus one that you are reasonably certain of. It indicates the precision / reproducibility of the
measurement.
2. How many significant figures are in each of the following measurements?
a) A car’s mass is 809 kg 3 sig figs - zeroes between non-zero digits are measured
b) A person runs the 800 m in 108.0 seconds 4 sig figs - zeroes after the decimal point and
after a non-zero digit are significant
c) The length of a soccer field is measured as .110 km. 3 sig figs - zeroes after the decimal
point and after a non-zero digit are significant
d) The width of the soccer field is measured as .075 km. 2 sig figs – zeros that come before
non- zero digits after the decimal point are place holders and are not significant ( not
measured)
e) A ball bearing in a roller blade has a mass of .0049090 kg 5 sig figs
f) A person runs the 5000 m in 1200 seconds Undetermined – the value should be written in
scientific notation.
g) A person runs the 10000 meters in 2.500 x 103 seconds 4 sig figs
3. Calculate the following
a) What is the perimeter of a field hockey field with a length of .102 km and width of .059 km?
.322 Km Since both measurements are to the thousandth of a Km, rounding is not necessary
b) What is the area of the field hockey field?
= .006018 km2 and should be rounded to .0060 km2 When rounded values that are
multiplied or divided round to the least number of significant figures found in your original
measurement
4. Unit conversions - You must show the factor label method on a separate piece of paper.
a) Convert 20.2 cm to inches. (2.54 cm = 1 in)
20.2 cm ( 1 in
) = 7.95 in
( 2.54 cm)
b) Convert .0143 kg to 1 mg
(1000 mg = 1 g) ( 1000 g = 1 kg )
.0143 kg ( 1000 g) (1000 mg)= 1.43x104 kg
( 1 kg ) ( 1 g
)
c) Convert 2.44 km to cm
( 1 cm = .01 m ) ( 1 m = .001 km )
2.44 km ( 1000 m) ( 100 cm)= 2.44x105 cm
(1m ) ( 1m )
d) Convert 17.0 yr to sec ( 1 day = 24 hr ) ( 60 min = 1 hr ) ( 1 min =60 s) ( 1 yr = 365 day s )
17.0yr ( 365 day) ( 24 hr) ( 60 min) ( 60 s ) = 5.38x108s
( 1 yr ) ( 1 day) ( 1 hr ) ( 1 min)
e) Convert 250 cm3 to m3 ( 1 m = 100 cm )
250 cm3 ( 1 m )3 = .000000250 m3 2.5 x10-7 m3
(100 cm)3
f) Convert 1.0 g
to
kg
(1000 g = 1 kg )
(1000 ml = 1 L)
----------ml
L
1.0 g ( 1 kg ) ( 1000 mL ) = 1 kg
mL ( 1000g) ( 1 L
)
L
g) Convert 55 mi
---hr
to
m
---s
(1 mi = 1.61 Km )
(1 hr = 60 min ) ( 1 min = 60 s )
( 1000 m = 1 km )
55 mi ( 1.61 km ) ( 1000 m ) ( 1 hr ) ( 1 min ) = 25.6 m/s
hr( 1 mi
) ( 1 km ) ( 60min) ( 60 s )
5. What power of ten is each of the following common prefixes equal to?
Abbreviation
e) Mega
10?=106
f) Kilo
10?=103
g) centi
10?=10-2
h) milli
10?=10-3
i) micro
10?=10-6
j) nano
10?=10-9
Powers of Ten: Calculate each of the following
a) What is the perimeter of a piece of paper with a length of 2.8 x 10-4 km and
a width of 2.16 x 10-4 km?
6.048 x 10-8 km2  6.0 x 10 -8 km2
b) What is the area of this piece of paper rounded to the correct number of significant
figures?
6.048 x 10-8 km2  6.0 x 10 -8 km2
7. Algebraic Operations: Show your work on a separate piece of paper.
a. Rearrange or solve the equation for the variable t:
vs = d
---t
t= d
vs
b. Rearrange or solve the equation for the variable x:
v =x
---t
c. Rearrange or solve the equation for the variable vo:
v = vo + a t
tv=x
v – at = vo
d. Rearrange or solve the equation for the variable a:
v = vo + a t
v – vo = at
v – vo = a
t
e. Rearrange or solve the equation for the variable t:
v = vo + a t
v – vo = at
v – vo = t
a
f. Rearrange or solve the equation for the variable xo:
x = xo + vo t + 1/2 a t 2
x - vo t - 1/2 a t 2= xo
g. Rearrange or solve the equation for the variable vo:
x = xo + vo t + 1/2 a t 2
x - xo - 1/2 a t 2 = vo t
x - xo - 1/2 a t 2 = vo
t
h. Rearrange or solve the equation for the variable a:
x = xo + vo t + 1/2 a t 2
x - xo - vo t = 1/2 a t 2
( x - xo - vo t ) =
½ t2
a
i. Rearrange or solve the equation for the variable v:
2( x - xo - vo t ) =
t2
v2 = vo2
v =
j. Rearrange or solve the equation for the variable vo:
a
+
vo 2
2 a ( x - xo )
+
v2 = vo2
2 a ( x - xo )
2a x
+
v2 - 2 a ( x - xo ) = vo2
v2 - 2 a ( x - xo ) = vo
k. Rearrange or solve the equation for the variable a:
v2 = vo2
+
v2 - vo2
=
v2 - vo2
=
2( x - xo )
l.
Rearrange or solve the equation for the variable  x :
2 a ( x - xo )
2 a ( x - xo )
a
v2 = vo2 +
2ax
v2 - vo2
=
2ax
v2 - vo2
2a
=
x
8.
a) What are the SI units of length? meters m
b) What are the SI units of time? seconds
s
c) What are the SI units of mass? kilograms kg
d) What are the units of speed? meters per second m/s
e) What are the SI units of velocity? meters per second m/s
f) What are the SI units of acceleration? meters per second per second m/s2