Newtonian Mechanics 8.01

W01D2

Why Study Physics

Textbook

Authors: Young and Freedman

University Physics 13th Edition Volume 1

In-Class Active Participation

Students are expected to complete daily reading assignments and hand in answers before the class

Active Participation:

Concept Questions using Turning Point Clickers

Short Group/Table Problems with student presentation of work at boards

Mini-experiments and quantitative experiments

Weekly Schedule

Mon/Tue: In-Class (2 hr): Hand in Answers to Mon/Tues Reading Question, Presentations, Concept Tests, Table Problems.

Tue Night: Hand Written Problem Set due 9 pm, Math Review Nights 9-11 pm.

Wed/Thurs: In-Class (2 hr): Hand in Answers to Wed/Thur Reading Questions, Presentation, Concept Tests, Table Problems, Experiments

Fri In-Class (1 hr): Hand in Answers to Fri Reading Questions, Group Problem Solving, Mini-experiments.

Sun: Tutoring Center Help Sessions from 1-5 pm in 26-152

Office Hours: Faculty and TA office hours throughout the week

Problem SolvingA MIT Education requires solving 10,000 Problems

Measure understanding in technical and scientific courses

Regular practice

Expert Problem Solvers:

Problem solving requires factual and procedural knowledge, knowledge of numerous models, plus skill in overall problem solving.

Problems should not ‘lead students by the nose” but integrate synthetic and analytic understanding

Problem Solving/Exams

In-Class Concept Questions and Table Problems

In-Class Group Problems (Friday)

Weekly Problem Sets 1. Multi-concept analytic problems2. Pre-class Reading Questions3. Pre-lab questions and analyze data from experiments

Online “Mastering Physics” Practice Assignments: 1. One practice assignment per week with hints and tutorials2. Review problems for exams

Exams: Three Evening Exams and Final Exam

8

Guidelines for CollaborationProblem Sets:

Please work together BUT

Submit your own, uncopied work

In Class Assignments:

Must sign your own name to submitted work

Signing another’s name is prohibited

In Class Concept Questions:

Use only your clicker

Using another’s clicker is prohibited

Exam DatesExam 1: Thurs Sept 22, 7:30 pm -9:30 pmConflict Exam 1: Fri Sept 23, 9:00 am - noon

Exam 2: Thurs Oct 27, 7:30 pm -9:30 pmConflict Exam 2: Friday Oct 28, 9:00 am - noon

Exam 3: Tues Nov 22, 7:30 pm -9:30 pm (Thanksgiving week)

Conflict Exam 3: Wed Nov 23, 9:00 am - noon

Final Exam: Date/time to be announced by Registrar

Please do not buy plane tickets home without consulting these dates, especially for the Thanksgiving holiday.

Grading Policy 3 Exams + Final Exam =   15%+15%+15%

+25% = 70%  (Individual Work)

You must pass the exam portion in order to pass the course.

Problem Sets 10% (Individual Work) Reading Questions 5% (Individual Work) Concept Questions 5% (Group Work) In Class Work 10%: Experiments (Group

Work) and Friday Problem Solving (Group Work)

Registering “Mastering Physics”

(See instructions at mastering physics sign up info) Go to http://www.masteringphysics.com Register with the access code in the front of the

access kit in your new text, or pay with a credit card if you bought a used book.

WRITE DOWN YOUR NAME AND PASSWORD Log on to masteringphysics.com with your new

name and password. The MIT zip code is 02139 The Course ID: MPDOURMASHKIN40470

Website: web.mit.edu/8.01t/www1. Course Information/Announcements2. Daily Class Schedule3. Presentations4. Concept Questions and Solutions5. Group Problems and Solutions 6. Experiments Write-ups7. Problem Set Assignments and Solutions8. Course Notes9. Math Review Night Presentations 10. Exam Prep 11. Office and Tutoring Hours

Stellar Site for Course Gradebook

8.01, 8.012, or 8.01L: which course is best suited for me?

Reasons for Working in Groups

Develop collaborative learning skills

Develop communication skills in Core Sciences

Create an environment conducive to learning and teaching for everyone in the class

Opportunity to ask teachers and peers more questions

Research labs or work places depend on group interactions

Coordinate Systems

Cartesian Coordinate System

1. An origin as the reference point

2. A set of coordinate axes with scales and labels

3. Choice of positive direction for each axis

Coordinate system: used to describe the position of a point in space and consists of

Cartesian Coordinate System

Vectors

Vector Reading Assignment:

Young and Freedman: University Physics

13th edition: 1.7-1.9

12th edition: 1.7-1.9

Vector

A vector is a quantity that has both direction and magnitude.

The magnitude of

is denoted by

| A≡A |r

Ar

Application of Vectors

(1) Vectors can exist at any point P in space.

(2) Vectors have direction and magnitude.

(3) Vector equality: Any two vectors that have the same direction and magnitude are equal no matter where in space they are located.

Vector Addition

Ar

Br

Let and be two vectors. Define a new vector , the “vector addition” of and , by the geometric construction shown in either figure

= +C A Br r r

Ar

Br

“head-to-tail” “parallelogram”

Vector DecompositionChoose a coordinate system with an origin and axes. We can decompose a vector into component vectors along each coordinate axis, for example along the x, y, and z-axes of a Cartesian coordinate system. A vector at P can be decomposed into the vector sum:

x y z= + +A A A Ar r r r

Unit Vectors and ComponentsThe idea of multiplication by real numbers allows us to define a set of unit vectors at each point in space with

Then vector decomposition becomes with components vectors:and components:Thus

( )ˆ ˆ ˆ, ,i j k 1, 1, 1ˆ ˆ ˆ| | | | | |= = =i j k

x x y y z zˆ ˆ ˆA , A , A= = =A i A j A k

r r r

x y zˆ ˆ ˆA A A= + +A i j k

r( )x y zA , A , A=A

r

rA =

rA x +

rA y +

rA z

Vector Decomposition in Two Dimensions

Consider a vector

x- and y components:

Magnitude:

Direction:

( 0)x yA ,A ,=Ar

Ax =Acos(θ), Ay =Asin(θ)

A = Ax

2 + Ay2

Ay

Ax

=Asin(θ)Acos(θ)

=tan(θ)

θ =tan−1(Ay / Ax)

Vector Addition

Vector Sum:

Components

rA =Acos(θA) i + Asin(θA) j

rB =Bcos(θB) i + Bsin(θB) j

= +C A Br r r

C

x=Ax + Bx, Cy =Ay + By

Cx =Ccos(θC ) =Acos(θA)+ Bcos(θB)Cy =Csin(θC ) =Asin(θA) + Bsin(θB)

ˆ ˆ ˆ ˆ( ) ( ) cos( ) sin( )x x y y C CA B A B C Cθ θ= + + + = +C i j i jr

Worked Examples and Table Problems: Vectors

Given two vectors,

find:

(a)

(b)

(c)

(d)

(e) a unit vector pointing in the direction of

(f) a unit vector pointing in the direction of

rA =2 i + −3 j + 7 k

rB =5i + j + 2k

rB

rA

rA +

rB

rA −

rB

rA A

B rB

Table Problem: Vector Decomposition

Two horizontal ropes are attached to a post that is stuck in the ground. The ropes pull the post producing the vector forces and as shown in the figure. Find the direction and magnitude of the horizontal component of a third force on the post that will make the vector sum of forces on the post equal to zero.

rA =70 N i + 20 N j

rB =−30 N i + 40 N j

Preview: Vector Description of Motion

1. Position

2. Displacement

3. Velocity

4. Acceleration

ˆ ˆ( ) ( ) ( )t x t y t= +r i jr

( ) ( )ˆ ˆ ˆ ˆ( ) ( ) ( )x y

dx t dy tt v t v t

dt dt= + ≡ +v i j i j

r

( )( ) ˆ ˆ ˆ ˆ( ) ( ) ( )yxx y

dv tdv tt a t a t

dt dt= + ≡ +a i j i j

r

ˆ ˆ( ) ( ) ( )t x t y tΔ =Δ +Δr i jr

Table Problem: Displacement Vector

At 2 am one morning, a person runs 250 m along the Infinite Corridor at MIT from Mass Ave to the end of Building 8, turns right at the end of the corridor and runs 178 m to the end of Building 2, and then turns right and runs 30 m down the hall.

What is the direction and magnitude of the displacement vector between start and finish?

Things to Do For W01D3

• Buy a Textbook (12th ed., or 13th ed.)

• Get “Mastering Physics” (comes with new textbook or purchase separately) and register

• Buy Clicker at MIT Coop

• Reading Assignment: Young and Freedman Sections 1.7-1.9, 2.1-2.6

• Answer Reading Questions Posted on Friday’s webpage to be handed in before class on friday