Physics 11

•Intro: Measurement

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

Metric System

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

How can we remember?

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?

Practice Problems

• #1-6 p. 15

• Ex 1: 12.678mm+0.25mm

• 12.928mm

• Round off to 12.93mm

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

F o r

m u l a e

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

2

2

1atuts

2

2

1atuts

2)(2 atuts

at

uts

2

)(2

• Ex 2: solve for a

Ex 3: rearrange to find v

2

2

1

1

cv

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

Work on:

• Start Chapter Review p. 19 #3-7