Physics Profile Sheet • What questions do you have
about physics? • Where does the universe come
from, does it have boundaries, will it end?
• How fast are we expanding from the Big Bang?
• How is everything made of stardust?
• Can we travel at light speed? • How does … work?
• Boomerangs, no fly zones, medical physics, structural engineering, lamps, gravity,
Paper tower challenge
• Goal: build the tallest free standing tower, using:
• -one sheet of paper
• -30 cm tape
• -up to 3 brains
• Not a lab, just an “activity”
Paper bridge challenge
• Goal: build a free standing bridge that supports its own weight over the longest flat span, using:
• -one sheet of paper
• -30 cm tape
• -up to 3 brains
• Not a lab, just an “activity”
Marshmallow challenge
• Goal: build the tallest free standing tower out of 50 stands of spaghetti, 30 cm string, and 30 cm tape, supporting a single marshmallow
• Winning tower suspends the marshmallow at the highest point above the table
• Not a lab, just an “activity”
Measurement
• Physicists (and physicists in training) need to excel at taking measurements
• Ex 1: what is the width of your table (in meters)?
• The most accurate and precise value wins :)
Measurement
• Physicists (and physicists in training) need to excel at taking measurements
• Ex 1: what is the width of your table?
1.524m
Precision & Accuracy
• Accuracy refers to the correctness of a measurement
• Precision is how well you define the value
• If the accepted value was 1.467 m,
– a measurement of 1.5 m would be accurate but
not very precise
– a measurement of 1.33425 m would be precise
but not accurate
Units
• In physics we typically use “mks” units:
– meters
– kilograms
– seconds
• All other units are derived from these:
– Velocity: m/s
– Force: 1N 1kgm/s2
• When doing calculations, we always carry the units through to help check our answer
Prefixes
• These are another way to simplify large or small values:
– deci
– centi
– milli
– micro ()
– nano
– pico
• To convert we fill in the appropriate factor
of 10 for the prefix: e.g. 23 ms = 23 10-3 s
Unit Conversions
• We often want to convert to “mks” base units:
– sometimes we can replace a prefix with its equivalent
– Ex 1: convert to base units
km5.5 m)10(5.5 3 m5500
cm193 m)10(193 2 m93.1
Unit Conversions
• We often want to convert to “mks” units:
– sometimes we multiply by a scale factor
• this is a fraction equivalent to 1
• you must choose one that will cancel out the unwanted units!
– Ex 2: convert to m/s
h
km100
km
m
1
1000
s
h
3600
1
s
m28
What is a golfer’s favorite number?
• 5.2 m has a possible error of…0.05 m
– Draw a line from the G to H through to U
If you've got a dollar and you
spend twenty-nine cents on a
loaf of bread, you've got
seventy-one cents left. But if
you've got seventeen grand
and you spend twenty-nine
cents on a loaf of bread,
you've still got seventeen
grand. There's a math lesson
for you.
-- Steve Martin
Comedian and writer.
Operations using Place Value
• The least precise measurement dominates calculations
• When adding or subtracting, we use place value
– ex 1:
45.34
2.2
25.32
4.34
• When multiplying or dividing, we use sig figs
– ex 2:
Operations with Prefixes
• We often want to convert to similar units first:
– ex 1: 230 mg + 0.000 42 kg
• 230 10-3 g + 0.000 42 103 g
• 0.23 g + 0.42 g
• 0.65 g
• 650 mg?
Significant Figures
• A number should indicate the precision of the measurement
– e.g. t=5.2 s implies the time is known to the nearest tenth of a second: 2 sig figs.
– 5.21 s =>3 sf
– A number such as 550 kg : use “cannot be determined”
• To clarify, we follow these rules:
– Any non-zero digits are significant: 223.4
– Place holding zeroes are not: 0.003 m
– Sandwiched zeroes are: 900 023
– Trailing zeroes after the decimal are: 2.30 m
– Scientific notation: ALL digits are significant
• When multiplying or dividing, we use sig figs
– ex 1:
• When multiplying or dividing, we use sig figs
– ex 2:
95.702.225.32
71
Practice Problems
• #1-5 p. 16
• Worksheet: note “placeholding zeros” like for 8300kg go into NUMBER CANNOT BE DETERMINED category
Scientific Notation • We can express very small numbers and
very large numbers in more compact form:
– The mass of a proton mp=
• 0.000 000 000 000 000 000 000 000 001 67 kg
• or 1.67 10-27 kg
– The mass of the Sun ms=
• 1 980 000 000 000 000 000 000 000 000 000 kg
• or 1.98 1030 kg
• The value is written as a decimal number x (where 1x<10) multiplied by a factor of 10
Calculations with Sci. Not.
• We can save work by dealing with each part separately:
• We can add or subtract numbers if they have the same exponent
– ex 1: 1.67 10-27 kg + 1.70 10-27 kg
• (1.67 + 1.70) 10-27 kg
• 3.37 10-27 kg
• We can multiply or divide using exponent rules:
– ex 2: 1.5 10-2 m 4.0 104 m
• 1.5 4.0 10-2 m 104 m
• 6.0 102 m2
Conclusion: Summarize your results (what did you learn?). What were
the sources or error? What improvements could you make?
Exercises
• #1-5 p. 18
Gravitational acceleration Name(s)
Date
Block
Partner Purpose: to test gravitational acceleration in room 107
at NorKam
Procedure: : Refer to text p. 24, but use iPad camera
Observations:
Lab Prep
Displacement/
m Time /s Velocity/s
0.10
0.15
0.20
0.25
0.30
0.35
Pendulum Lab Name
Date
Block
Partner Purpose: to test Galileo's clock idea
Procedure: refer to text, p. 5 but with the following
changes: …
Observations:
Lab Prep
l/m/angle/d Time (50) /s Period /s Period^2
0.10
0.15
0.20
0.25
0.30
0.35
• What does the graph tell us?
• Since g
lT 2
slopeT
lg
2
2
2 44
• First do questions #1-2, then write a conclusion comparing your result to gravitational field g=9.8 m/s2
The Perfect Graph!
• Title
• Labelled axes
• Appropriate scale
• Best fit line (do not connect the dots)
• Slope calculations
• Correctly chosen dependent/ independent variables
Displacement vs. time
Disp
lacemen
t (m)
Time (s)
12
12
xx
yy
x
ym
Ex 1: Graph vs t
• Graph the velocity of a Tesla roadster as a function of time given:
time (s) velocity (m/s)
0 0
1 8
2 15
3 22
4 28
5 34
Velocity of a Tesla as a function of time
Velo
city (m
/s)
Time (s) 0 1 2 3 4 5
10
20
30
40
ss
smsm
xx
yy
x
ym
14
626
12
12
s
smm
3
20
27.6s
mm
Acceleration activity
• Who is NorKam’s best athlete?
• Use your velocity graph from the iPad to calculate your acceleration
t
va
Rearranging Formulae
• Basic rules for rearranging equations:
– We can do anything as long as we do the same to the other side of the equation
– To move a variable or term to the other side, perform the opposite operation
– To isolate a buried variable, work from the outside in: SAMDEB!!!
• Ex 1: solve for a
atuv
atuv t
uv
t
at
t
uva
Ex 3: rearrange to find v
2
2
1
1
cv
2
2
2
1
1
cv
11 22
2
c
v
22
2 11
cv
1122
2
c
v
22
2 11
cv
22
2 11
cv
2
11
c
v
2
11cv
2100
11 cv
cv %995.99
Dimensional Analysis
• We can carry units through to check our work
• We can even use units to check if a formula is correct
• Ex 1: which is the correct formula for time?
dvt 2dvt v
dt dvt
smmt 2
smmt
sm
mt
m
sm
t smt
2
2
3
s
mt st s
t 1 1 st
Work on:
• Start Scientific Notation 1-5 p. 18
• Ex: 0.00572kg
• Three jumps to get the decimal after the first non-zero digit
• 5.72x10-3 kg