Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics... · Physical quantities. Units. Kinematics. Velcity. ... Example 1: 0.24630 1sf

Lecture 1Lecture 1

Physical quantities. Units. Kinematics. Velcity.

Welcome to Physics 111Welcome to Physics 111

About myself● Mohamad Al-Saqer● Office: 209 Phyics Hall● Phone: 294-9361● Office Hours:

● MWRT 1:15 PM-2:15 PM.● Or by appointment.

● Research:Theoretical Physics in NanomagneticMolecules and computation.

The Physics 111 Instructor TeamThe Physics 111 Instructor Team● Lecturer:

● Dr. Mohamad Al-Saqer 12:10-1:10

● Course secretary:● Deb Schmidt. Room 12 Physics.

● Lab supervisor:● Dr. Paula Herrera-Siklody. Room 15 Physics.

● Recitation and Lab TAs: Separate sheet are provided in the course website.

The syllabus● Linked from Physics course web page:

http://course.physastro.iastate.edu/phys111● and in Canvas course page.● Contains all the information needed for the course:

● Contact info.● Lecture and course timeline.● Homework, recitation and grading policy info.● Lab info (more about lab in a separate Canvas page.)● etc.

Zeroth! Homework Assignment:Read the Syllabus carefully.

Exams:

● 3 mid-semester exams at lecture time:

➔Final exam

Monday, June 25 12:10pm – 1:10pmMonday, July 9 12:10pm – 1:10pmMonday, July 23 12:10pm – 1:10pm

Friday, Aug 3 11:00am – 1:00pm

Make no other plans for these times

Recitations & Homework

● Tue Wed Thur Fri (60 minutes)

● Quizzes: Last 15 minutes of Wed and Fri recitations. Except first week (only Friday) and last week (Only Wednesday)

● Online homework will be linked from Canvas.● There is an introductory to MasteringPhysics assignment

(optional for no credit) to get you familiarized with the interface.

● First homework is due Tuesday 6/12 midnight.

Labs● 14 two-hour labs● Each section meets every week.● Prelab must be completed before corresponding lab.● Check lab schedule for dates and time of your session.● Detailed lab info on Canvas separate page.● For questions regarding labs, e-mail Paula Herrera (

siklody@iastate.edu).Questions based on material covered in recitations and labs will be on the final exam!

How to succeed in Physics 111Physics can only be learned by doing it(just like swimming, bike riding or becoming a mechanic)

● Lectures● Prepare for lecture.

● Read the indicated assignments before class ● Attend actively.

● Ask questions, participate in interactive problems● Homework

● Do all problems● Review the HW solutions● Understand and learn from your mistakes.● Reflect on the problems you've done right.

How does Physics work?How does Physics work?

Observe and

measure

Build a model

Make a prediction

math

math

math

math

math math

check

units

SI UnitsSI Units

Length: The meter (1 m = 3.281 ft)

Mass: The kilogram (1 kg = 0.06585 slug)Not the same as weight!

on Earth 1 kg weighs 2.205 lbon the Moon 1 kg weighs 0.368 lb

Time: The second (s)

Standard International Units are used by scientific and engineering communities and almost everywhere in the world.

The British System is used in the USA

Combinations:Unit of speed m/s Unit of force (Newton) is 1 N =1 kg m/s²

Other systems: mks (meter-kilogram-second)cgs (centimeter-gram-secos)

Multiples of UnitsMultiples of Units10-24 yocto- y10-21 zepto- z10-18 atto- a10-15 femto- f10-12 pico- p10-9 nano- n10-6 micro-

10-3 milli- m10-2 centi- c103 kilo- k106 mega- M109 giga- G1012 tera- T1015 peta- P1018 exa- E1021 zetta- Z1024 yotta- Y

Formal conversion of units:

•Multiply by the appropriate representation of 1 to cancel the unwanted units away:

•eg. convert 10 mph into m/s

10 mile 1 h

= 10 mile 1 h

×1 h

3600 s×

1609 m mile

= 4.47 m/s

Consistency of EquationsConsistency of Equations

If A=B then A and B must have the same combination of units (dimensionality).

• For example (distance)=(speed)(time) [m] = ([m]/[s]) [s]

ACT: Dimensional AnalysisACT: Dimensional Analysis The period T of a swinging pendulum depends only

on the length of the pendulum d and the acceleration of gravity, g. Which of the following formulas could be correct?

A.

C. 2 dT gp=

d

Note: [Acceleration] = m/s2

T = 2π (dg )2 T = 2π(dg )

2

B.

D.T = 2π√ gd

ACT: Converting AreaACT: Converting AreaAn area of 3.0 ft2 in System international is:

note (1 m = 3.281 ft)

A. 280 m2

C. 0.028 m2

B. 2800 m2

D. 0.28 m2

Significant figures

When we measure something, there’s a limited accuracy: result error (or accuracy, or uncertainty)

Example 1: 2.35 0.01

Example 2: Imagine I write: 2.35 0.1 . Does this make sense? No!Wrong: 2.35 0.1Correct: 2.4 0.1

Example 1: 0.24630

1sf 0.22sf 0.253sf 0.2464sf 0.24635sf 0.24630

Example 2: Not so clear in some cases: 200 (1,2,3 ?)

Scientific notation is crystal clear: 2 102 (or 0.2 103) 1sf2.0 102 (or 0.20 103) 2sf2.00 102 (or 0.200 103) 3sf

Measurement and uncertaintyMeasurement and uncertainty

Significant figures ...continuedSignificant figures ...continued

A distance measured with a ruler with millimeter markings cannot be 1.047543 m

The last three digits are meaningless

Keep track of that in calculationsEg. Find the distance covered by a car moving at 31.6 mph for 35 minutes.

Correct value is 1.047 m (4 significant figures)

1 h35 min 0.583 h

60 minLast digit is meaningless, but you can keep it until last step…

Correct answer is 18 miles (only 2 significant figures given for time)

distance = 31.6miles

h×0.583h = 18.4miles

Scientific notation and significant figuresScientific notation and significant figures

Number Significant figures

3.4 2

3.40 / 3.45 3

0.3 / 3 / 0.0003 1

30 1 or 2?

3101 1

3.0101 2

3.00101 3

Order of magnitudeOrder of magnitude

• Intuition: A coin is dropped from 2 m. How long does it take to reach the ground?

→ About 1 s. (not 10 s, not 0.1 s)

• Estimation:

Example: The roof in room 5 is a 10 m x 20 m flat surface. If the drains get clogged and 1 cm of water accumulates on it, this is an extra

How “strong” should a roof be?

Not 200 kg, not 20,000 kg

200 m2 × 0.01 m × (1000 kg1 m3 ) = 2000 kg (4410 lb)

An overview of Mechanics An overview of Mechanics

Mechanics: study of the motion of objects. 1. Kinematics: How do objects move?

2. Dynamics: Why do objects move?

4. Some special cases:•Rigid body motion

•Simple harmonic motion

•Gravitational forces, Hooke’s law…

3. Conservation laws:•Work-energy

•Momentum (linear and angular)

For some problems, the math is easier to handle with

The Simplest Case: The Simplest Case: 1D Motion along a Straight Line1D Motion along a Straight Line

Position: A single + or – number (coordinate) describes the location of an object relative to a reference point (origin).

Description of motion: position x as a function of time t:

An equation x(t)A graphA table of data

Time (t)

Position (x)

tA

xA

tB

xB

tE

xE

tD

xD ,

tC

xC

Displacement: Change in position  ΔxAB = xB − xA

Displacement over a fixed time period only tells us about the “result” of the motion (not the path).

ΔxAB > 0ΔxBD < 0ΔxAD = 0 !!!

Time (t)

Position (x)

tA

xA

tB

xB

tD

xD ,

VelocityVelocity

= rate of change of position

txv

=

Simplest idea: For displacement of Δx over a time Δt :

Average velocity

Unit: m/s

xvt

=

!!!

Not a very good description of what really happened!Problem: Our time intervals are too large and too many things are happening in between.

t

x

AB

D

For Δ t = tB−tA → v > 0For Δ t = tD−tB → v < 0For Δ t = tD−tA → v = 0

E

t

x

A

C

D

B

It is the slope of

the x(t) curve.

Instantaneous VelocityInstantaneous Velocity

vC = 0

Solution: take limit Δt 0.→

vA > 0

vB > 0 ( |vB|>|vA| )

vD < 0

vE < 0

v = limΔ t → 0

Δ x

Δ T

Motion with Constant velocity: Motion with Constant velocity: GraphicsGraphics

v =Δ x

Δ t

Example: Graph of motion: Speed vs. TimeExample: Graph of motion: Speed vs. Time

v =Δ x

Δ t

va =24 m−12 m

10 s−4 s= 2 m/s

vb =24 m−24 m

20 s−10 s=

0

10 s=0

vc =4 m−24 m

30 s−20 s=

−20 m

10 s=−2 m/s

3- What speed we are reading on the speedometer: average or instantaneous?

Velocity versus speedVelocity versus speed

Velocity = vector (value including sign, in 1D)

Speed = magnitude of velocity (always positive)

The speedometer of the truck #1 moving to the east reads 90 km/h. It passes another truck, #2, that moves to the west at 90 km/h.1- Do both trucks have the same velocity? NO2- Do both trucks have the same speed? Yes

Instantaneous

Velocity versus speedVelocity versus speed

A car traveled 0.5 h from Ames to Des Moines. Then it traveled 0.5 h from Des Moines to Ames. The distance traveled in each direction is 50 km. Find the average speed and velocity.

Velocity versus speedVelocity versus speed

A car traveled 0.5 h from Ames to Des Moines. Then it traveled 0.5 h from Des Moines to Ames. The distance traveled in each direction is 50 km. Find the average speed and velocity.

|vAmes to Des Moines|=50 km

0.5 h=100 km/h

|vDes Moines to Ames|=50 km

0.5 h=100 km/h

vAmes to Des Moines back to Ames=50 km+(−50 km)

0.5 h+0.5 h=

0

1 h=0 km/hRound trip

velocity:

|vAmes to Des Moines back to Ames|=50 km+50 km

0.5 h+0.5 h=100 km/hRound trip

speed: