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Chapter 1
Branches of Physics
Measuring = units
MASS
[kg]
LENGTH/DISTANCE
[m]
TIME
[s]
What do these have in
common?
Odd one out???
LBS vs. KG
Weight is measured in pounds (USA)
Mass is measured in kilograms
1 kg = 2.20462262 pounds
1 kg = 2.2 lbs
1 lb = 454 g
MASS
50 – 75 kg
MASS
Bumblebee bat – 1.5g – 2.0 g
MASS
Blue whales:
Newborn –
2.5 tons
Avg. 100 – 120
tons
Biggest – 190 tons
CONVERT
1) your weight in lbs to mass in
kg (1 kg = 2.2 lbs)
2) 190 tons to pounds
1 mile = 1.609344 kilometers
1 mile = 1.6 km
1 yard = 0.9144 m
1 foot = 0.3408 m
1m = 3.2808 ft
Football field in meters?
What is the length of a football field in meters?
120 yards
1 yard = 0.9144 m
mph – km / h – m/s
65 mph = 104 km/h
104 km / h
to m/s
104 km = 140,000 m; 1 h = 3600 s
65 mph = 29m/s
km / h – m/s
é km ù 1000 é m ù 10 é m ù
êë h úû = 3600 êë s úû = 36 êë s úû
[km / h]
= [m / s]
3.6
75 km/h =
25 m/s =
120 km/h =
12 m/s =
Scale of the Universe
 A super cool applet
SN you need to remember:
-9
nano
n
-6
micro
m
-3
milli
m
-2
centi
c
10
3
kilo
k
10
6
mega
M
10
10
10
10
Convert, use Scientific Notation
+
BIG ® SMALL Þ BIG(10 )
-
SMALL ® BIG Þ SMALL(10 )
Examples
[cm] ® [m]
-
SMALL ® BIG Þ (10 )
45cm ® ...[m]
-2
-1
45cm = 45 ×10 m = 4.5 ×10 m
Examples
[m] ® [cm]
+
BIG ® SMALL Þ (10 )
45m ® ...[cm]
45m = 45 ×10 cm = 4.5 ×10 cm
2
3
Examples
[ mm] ® [m]
-
SMALL ® BIG Þ (10 )
200 mm ® ...[m]
200 mm = 200 ×10 m = 2 ×10 m
-6
-4
Examples
[m] ® [ mm]
+
BIG ® SMALL Þ (10 )
200m ® ...[ mm]
200m = 200 ×10 mm = 2 ×10 mm
6
8
Practice 1
2.5 days to seconds ________________________________________
3.5 km to mm ______________________________________________
43 cm to km _______________________________________________
22 mg to kg _______________________________________________
671 kg to µg _______________________________________________
8.76 x 107 mW to GW _______________________________________
1.753 x 10-13 s to ps _________________________________________
Practice
The mass of the parasitic
wasp Caraphractus cintus
can be as small as 5x10-6 kg.
What is the mass in
a)g
b)mg
c) µg
PRACTICE
2 dm - … mm
2h 10 min - … s
16 g - … micrograms
0.75 km - … cm
0.675 mg - …g
462 µm - … cm
35 km/h - … m/s
Precision & Sig. Dig.
LAB on Precision
 1) Use the solid 1 m stick and measure the length of the
lab table
 2) Use the 1 m stick marked with dm
 3) Use the 1 m stick marked with cm
 4) Use the actual meter stick to measure the length of
your desk.
 Write down the results to the maximum precision in each
case.
SIG FIGS MADE SIMPLE
Sig. Fig.
100 000
100. 00
202 000
0.0050
340 505
0.00505
How many Sig.Figs?
300 000 000 m/s
3.00 ×108 m/s
25.030 °C
0.006 070°C
1.004 J
1.305 20 MHz
Practice
The value of the speed of light is
now known to be 2.997 924 58
×108m/s.Express the speed of
light in the following ways:
a) 3 SF
b) 5 SF
c) 7 SF
Adding and Subtracting
# of digits 0.______ (after the
decimal point) = the least
precise
3345.28 + 0.2 = 3345.48 = 3345.5
57.8 – 0.567 = 52.233 = 52.2
Multiplying and Dividing
#SF (result) = the least #SF (A*B)
1.34 x 2300 = 3082 = 3.1103
#SF (result) = the least #SF (A/B)
23967 / 45 = 532.6 =5.3102
Practice
Bicyclists in the Tour de France
reach speeds of 34.0 miles per hour
(mi/h) on flat sections of the road.
What is this speed in a) km/h and b)
m/s - ?
1 mile = 1.61 km
Practice
a) find the sum of 756 g,
37.2 g, 0.83 g, and 2.5 g
b) the quotient 3.2 m/ 3.563 s
c) the product of 5.67 mm ×π
d) 27.54 s - 3.8 s
Density lab
Trig Review
c = a2 + b2
b = csin a
a = ccosa
a = csin b
b = ccos b
æ bö
a = tan ç ÷
è aø
æ aö
b = tan ç ÷
è bø
-1
a
b
c
=
=
sin a sin b sin g
-1
c2 = a2 + b2 - 2ab cos l
Physics Quantities
SCALARS –
magnitude
only
VECTORS –
magnitude
and
direction
Vector vs. Scalar
Velocity
vs.
Displacement
v – scalar;
vs.
Speed
Distance
v - vector
v – vector;
(typed text)
a)
b)
c)
d)
Comparing vectors
Which vectors have the same magnitude?
Which vectors have the same direction?
Which arrows, if any, represent the same vector?
Adding vectors
a
b
a+b
a+b
b+a
b+a
Subtracting vectors (+ negative)
a
a-b
a-b
b
b-a
b-a
Subtracting vectors (“fork”)
a
a-b
b
a-b
b-a
b-a
Check your understanding
Construct and label a diagram that shows the
vector sum 2A + B. Construct and label a
second diagram that shows B + 2A.
Construct and label a diagram that shows the vector
sum A – B/2. Construct and label a second diagram that
shows B/2 - A.
Adding ^ vectors
R = 1600 + 400 = 44.7(km)
-1 æ 40.0 ö
q v = tan ç
= 63.4
÷
è 20.0 ø
R
qv
qv
20.0km
qh
40.0km
æ 20.0 ö
q h = tan ç
= 26.6
÷
è 40.0 ø
-1
Practice (p. 24, #24)
 Vector A has a magnitude of 63 units and
points due west, while vector B has the same
magnitude and points due south. Find the
magnitude and direction of
 (a) A+B and
 (b) A-B .
 Specify the directions relative to due west.
Practice (p. 24, #25)
 (a) Two workers are trying to move a heavy crate. One
pushes on the crate with a force A , which has a magnitude
of 445 newtons and is directed due west. The other pushes
with a force B, which has a magnitude of 325 newtons and
is directed due north. What are the magnitude and
direction of the resultant force A+B applied to the crate?

(b) Suppose that the second worker applies a force - B
instead of . What then are the magnitude and direction of
the resultant force A-B applied to the crate?
 In both cases express the direction relative to due west.
Adding vectors that are not
 To add vectors that are not
perpendicular to each other, we
will use components.
 Each vector has vertical and
horizontal components, for
example a has ax and ay
^
Components
3.0km 30 WN
bx
y
2.5km 30 NE
b
by
a
ay
bx = -3.0sin 30 = -1.5(km)
by = 3.0 cos 30 = 2.6(km)
ax
x
ax = 2.5 cos 30 = 2.2(km)
ay = 2.5sin 30 = 1.25(km)
Adding vectors
y
b
R
a
x
To find the resultant…
Rx
Ry
R
We need the components
Finding Rx and Ry
y
Rx - ?
Rx = ax + bx
b
Ry - ?
Ry = ay + by
R
R = Rx2 + Ry2
a
x
To find the resultant…
Rx
Rx = ax + bx = 2.2 - 1.5 = 0.7(km)
Ry = ay + by = 1.25 + 2.6 = 3.85(km)
Ry
qv
R
R = Rx2 + Ry2 = 0.49 + 14.8 = 3.9(km)
Direction?
qh
æ Ry ö
q h = tan ç ÷
èR ø
-1
x
Answer : 3.9km 80 NE
æ Rx ö
q v = tan ç ÷
è Ry ø
-1
or 3.9km
20 EN

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