Transcript Power Point
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) 2) your weight in lbs to mass in kg (1 kg = 2.2 lbs) 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
éé
h
é éé = 1000 3600 é
m
éé
s
é éé = 10 36 é
m
é éé
s
éé [
km
/
h
] = [
m
/
s
] 3.6
75 km/h = 120 km/h = 25 m/s = 12 m/s =
Scale of the Universe A super cool applet
SN you need to remember: 10 9
nano n
10 6
micro
m 10 3
milli m
10 2
centi c
10 3
kilo k
10 6
mega M
Convert, use Scientific Notation
BIG
®
SMALL
Þ
SMALL
®
BIG
Þ
BIG
(10 + )
SMALL
(10 )
Examples [
cm
] ® [
m
]
SMALL
®
BIG
Þ (10 ) 45
cm
® ...[
m
] 45
cm
= 45 × 10 2
m
= 4.5
× 10 1
m
Examples [
m
] ® [
cm
]
BIG
®
SMALL
Þ (10 + ) 45
m
® ...[
cm
] 45
m
= 45 × 10 2
cm
= 4.5
× 10 3
cm
Examples [ m
m
] ® [
m
]
SMALL
®
BIG
200 m
m
® Þ (10 ) ...[
m
] 200 m
m
= 200 × 10 6
m
= 2 × 10 4
m
Examples [
m
] ® [ m
m
]
BIG
®
SMALL
200
m
® Þ (10 + ) ...[ m
m
] 200
m
= 200 × 10 6 m
m
= 2 × 10 8 m
m
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 10 7 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 ×10 8 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 ×10 8 m/s.Express the speed of light in the following ways: a) b) c) 3 SF 5 SF 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
10 3
#SF (result) = the least #SF (A/B) 23967 / 45 = 532.6 =5.3
10 2
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
b
=
c
sin a
a
=
c
sin b a = tan 1 æ ææ
b a
æ ææ
a
sin a =
b
sin b =
c
sin g Trig Review
c
=
a
2 +
b
2
a
=
c
cos a
b
=
c
cos b b = tan 1 æ ææ
a b
æ ææ
c
2 =
a
2 +
b
2 2
ab
cos l
Physics Quantities SCALARS – magnitude only VECTORS – magnitude and direction
Vector vs. Scalar
Velocity vs. Speed Displacement vs. Distance
v – scalar;
v –
vector;
(typed text)
v
- vector
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 b
+
a b
+
a a
+
b
Subtracting vectors (+ negative)
a
-
b a b a
-
b b
-
a b
-
a
Subtracting vectors (“fork”)
a b a
-
b b
-
a a
-
b 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.
R
= q
v
= 1600 + 400 = tan 1 æ ææ 40.0
20.0
æ ææ= 44.7(
km
) 63.4
R
q
v
20.0
km
q
v
q
h
40.0
km
q
h
= tan 1 æ ææ 20.0
40.0
æ ææ= 26.6
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.
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 a x and a y
Components
b x y
3.0
km
30
WN
2.5
km
30
NE b b x
= 3.0 sin 30 = 1.5(
km
)
b y
= 3.0 cos 30 = 2.6(
km
)
b y a a y a x x a x
= 2.5 cos 30
a y
= 2.5 sin 30 = 2.2(
km
) = 1.25(
km
)
y
Adding vectors
R a b x
To find the resultant…
R x R y R
We need the components
Finding R x and R y
y R b R x
?
R x
=
a x
+
b x R y
?
R y
=
a y
+
b y R
=
R
2
x
+
R y
2
a x
To find the resultant…
R x R x
=
a x
+
b x
= 2.2
1.5
= 0.7(
km
)
R y
=
a y
+
b y
= 1.25
+ 2.6
= 3.85(
km
)
R y
q
v R
q
h R
=
R x
2 +
R y
2 = 0.49
+ 14.8
= 3.9(
km
) q
h
= Direction?
tan 1 æ
R y
ææ
R x
æ ææ q
v
= tan 1 æ æ
R x R y
æ æ
Answer
: 3.9
km
80
NE or
3.9
km
20
EN