As you come in…

  Pick up graded homework from front   Turn in homework in the box

LECTURE 3 CONTINUING CHAPTER 2 Professor Cassandra Paul

How I graded homework   I was thorough and lenient!

 A’s (4.0) were given if it was complete, and thought was given to every question

 C’s (2.0) were given if a number of problems were not completed, or no work was included (or late)

 F’s (zeros) were only given if you turned nothing in  Pay attention to comments, and if I suggest you come to

office hours, please do!

  Common issues:  Polar coordinates  Free fall  Velocity/acceleration confusion

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If you are not officially added yet, your name might not be listed here even though I have not received homework from you.

Before we start

  Get in small groups (lets try 3)   Discuss any issues you had with the

homework   Help your group-mates with their difficulties   (5 minutes)

Any further Issues:

  See me in office hours   Make an appointment with me   Set up a time to meet with some classmates   Ask your workshop facilitator for help   Physics Club?   Peer connections (drop in tutoring): http://peerconnections.sjsu.edu/

Groups of 5

  Name tags up   White boards, markers, erasers   Clickers

Last time: Multiple choice

  An object with a positive velocity (+3m/s for example) indicates the object must: A.  Be speeding up B.  Be traveling in a positive direction C.  Have a positive acceleration D.  Have a positive displacement E.  Both A & B

Multiple choice

  An object with a positive velocity (+3m/s for example) indicates the object must: A.  Be speeding up B.  Be traveling in a positive direction C.  Have a positive acceleration D.  Have a positive displacement E.  Both A & B

v=Δx/t t is always positive therefore if v is positive Δx is also positive

Multiple choice

  An object with a positive velocity (+3m/s for example) indicates the object must: A.  Be speeding up B.  Be traveling in a positive direction C.  Have a positive acceleration D.  Have a positive final distance E.  Both A & B

Unit Conversion

Convert 20 inches to centimeters: *Remember multiplying by 1 gives us the same quantity back! 5 x 1 = 5 20.0 inches x 2.54 centimeters

1 inch = 20.0 x 2.54 = 50.8 centimeters

Learn this!

Updated since class: correct values and sig figs

You try:

Convert 100 miles/hour into meters/second 1 mile ~ 1610 meters 100 miles x 1 hour x 1 min x 1610 meters hour 60 min 60 sec 1 mile = 44.72 meters second

Position, Velocity & Acceleration vs. Time graphs

Δx = xf – xi v = Δx/Δt a = Δv/Δt = = = − −

Case 1: A student walking across campus to class at a constant speed.

t

x

tf

Distance changing at a constant rate.

t

v

tf

Velocity is constant and positive.

tf t

a

Acceleration is zero because velocity is not changing.

Case 2: Dr. Paul bicycling down San Fernando.

t

v

tf t

a

tf t

x

t4

Check-In Clicker question

A. I am very confident in my understanding of these graphs and ability to produce them

B. I think I might need to study a bit more, but I feel ok with them

C. I will need to seek help to learn these

D. I am completely lost

Velocity

v = Δx/Δt Average Velocity v = lim Δx/Δt Instantaneous velocity

− =

− Δt 0

Review on Limits

Δx/Δt = rise/run = slope

(t1, x1)

(t2, x2)

x

t

Review on Limits

Δx/Δt = rise/run = slope

(t1, x1)

(t2, x2)

x

t

Review on Limits

Δx/Δt = rise/run = slope

(t1, x1)

(t2, x2)

x

t

Review on Limits

v = lim Δs/Δt (or v=dx/dt in calculus) Δt 0

x

t the line tangent to the position vs. time graph is defined to be the instantaneous velocity at that time

v = lim Δx/Δt (or v=dx/dt)

t

x

tf t

x

tf

Δt 0

the line tangent to the position vs. time graph is defined to be the instantaneous velocity at that time

t

x

tf t

x

tf

This is why why we often calculate average velocity and not instantaneous velocity.

When you are asked to find instantaneous velocity what do you do?

t

x

t1 t

x

t2

Graphical Instantaneous Velocity

  Average velocities are the blue lines

  The green line (tangent) is the instantaneous velocity

Section 2.2

Instantaneous Velocity

  The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero

  The instantaneous velocity indicates what is happening at every point of time  The magnitude of the instantaneous velocity is what

you read on a car’s speedometer

Section 2.2

Acceleration

Average Acceleration

Instantaneous Acceleration

a = lim Δv/Δt Δt 0 =

You try:

In groups of 5 use your white boards to graphically represent Be as accurate as possible!

Free Fall

  A freely falling object is any object moving freely under the influence of gravity alone  Free fall does not depend on the object’s original

motion

  All objects falling near the earth’s surface fall with a constant acceleration

  The acceleration is called the acceleration due to gravity, and indicated by g

Section 2.6

Free Fall

g = acceleration due to gravity g x mass = weight = force of the earth pulling on you Convention: The direction of the pull of the earth is downwards, therefore a = -g = -9.81. (in the –y direction)

Common Confusions

  Pg 43 : The value of g decreases with increasing altitude…. at Earth’s surface g is equal to 9.81m/s

  G varies for VERY large distances, it’s negligible at Earth’s surface

Gravity

San Jose State, Elevation: 85ft g = 9.81

University of Wyoming, Elevation: 7200 ft g = 9.79

Clicker Question

  Which of the following is true?   For a freely falling object:

A.  Acceleration is always downwards B.  Acceleration is downwards only when the

object is traveling downwards (past max height)

C.  Acceleration is zero at max height D.  Acceleration is constant E.  Both A and D

Homework:

  Chapter 2 “problems”: 6, 20, 24, 35, 45, 47, 51   Read Chapter 3: take notes, work examples   Chapter 3: “Conceptual Questions”: 1, 3, 4, 7,

10, 11