Physics 1B3-summer Lecture 11 PHYSICS 1B03- MECHANICS Dr. Waldemar Okoń Office: ABB-150 e-mail: [email protected] Office Hours: T,R 1:00-2:00pm

Physics 1B3-summer Lecture 1 1

PHYSICS 1B03- MECHANICS

Dr. Waldemar Okoń

Office: ABB-150

e-mail: [email protected]

Office Hours: T,R 1:00-2:00pm

Course web page:

http://physwww.mcmaster.ca/~okon/1b03s/1b03s.html


Grade Calculation:

-Term work: 12.5% of the final grade - 7.5% will be for the CAPA problem sets - 7.5% will be for class quizzes.

- Labs: 12.5% of the final grade. If you did the labs before, get an exemption from the Physics Office (ABB-241)

-Two Midterm tests: 30% of the final grade.

- Final exam: 45% of the final grade.


WebCT

Login page: http://webct.mcmaster.ca/

We are using the WebCT system as the main source of information related to the course. Your term marks will be posted regularly. A “discussion area” allows you to seek help with assignment or other questions from other students in the course.

WebCT will be used for access to the CAPA assignment problems, so all students will need to use it. The WebCT login page explains how to get your login account working. Start trying now! If you have a problem, it may require a few days to get it fixed by CIS.


Homework Using CAPA

Web page: http://capa.physics.mcmaster.ca/

• There will be an assignment each week. Answers are entered into the computer. The CAPA system tells you immediately whether the answer is correct, and allows you to try again. You can log in and out many times without having to complete the entire assignment in one session. You’ll have 10 tires for each question.

• You can access the CAPA assignments directly from WebCT.

• You should try to complete the CAPA assignments a day before the final deadline. You may use the student computer labs on campus. If you work from home, finish the assignments well in advance, to avoid being caught by internet malfunctions.

•Read the CAPA help page before you start! (help on units etc…)


Labs• You will need a lab manual and a black lab notebook ($2 in the lab) with bound-in graph paper. The lab notebook will remain in the lab between sessions.

• Labs begin with “Session 1: Kinematics in one Dimension”. Prepare for the lab by reading Appendix C in the Lab Manual (Introduction to Data Studio). This first lab period will begin with an introduction to the measuring equipment and Data Studio software. Check in WebCT to see which lab section you are in.

• You will also need to read the instructions for the lab itself (“Session 1”), and complete the pre-lab exercise to hand inwhen you arrive.

Labs start this Thursday !!! (BSB – B115)


Lectures

• Introduce the important concepts and principles, with the aid of demonstrations. Examples with solutions.

• Partial lecture slides will be posted on the web page or WebCT before the lecture. The slides are not the whole lecture! Take notes as we work things out on the blackboard – print the slides out!

• Lectures will include short “concept quizzes” after each main idea.

•You should read the relevant sections of the text before the lecture, ask questions in class and discuss topics among yourselves from time to time.


i-clicker quizzes

• During the lectures we will have multiple choice quizzes

• For these quizzes we will use the i-clickers

• 7.5% of the course mark will be based on these. If you are not in class, you will not get these marks! • Quizzes for marks will start on Thursday

• You must register your i-clicker (see link on the course site) at some time before the final exam (late registration will result in a mark of zero for the quizzes).


Concept Quiz

a) Increases with time, starting from zerob) Is large as soon as the elevator starts, then

decreases with timec) Is constant after the elevator starts to move.

A 2000-kg elevator starts from rest and moves upwardswith a constant acceleration of 1.0 m/s2. The power required from the motor

Example:


Doing well in Physics 1B03

• Keep up with the course! Expect to spend 10 hours every week on the course, in addition to time in the lectures and labs. Come to the lectures. Read the text! Solve many, many problems, but, not blindly! Make sure you understand them.

• Discuss questions and problems with other students. Explaining something helps you clarify your ideas.

• Extra problems are posted on the website for extra practice.


Homework • Read the course outline and find the course web page. Read everything…

• Log in to WebCT and find Physics 1B03.

• Get the lab manual. If the bookstore is out of stock, put in an order right away. Get the black lab book.

• Buy the text – you’ll find it useful for the next few years !!! Read the first two chapters of the text (review).

• Books – it does not matter which version of the book you have (there are no assignments for marks from the book). You should use Knight, but Serway or Serway and Jewett texts are OK too.


10 min break


Kinematics in One DimensionKinematics in One Dimension

• Displacement, velocity, acceleration• Graphs• A special case: constant acceleration• Bodies in free fall

Knight: Chapters 1, 2


• Kinematics : the description of motion in terms of space and time

– ignores the agents that cause the motion (dynamics)

• One dimension : motion along a straight line (e.g., the x-axis)

Examples - sprinter running 100 meters in a straight line

- ball falling straight down, and bouncing back up


Motion: the change of object position with time

Position: measure of where an object is, relative to some pre-defined point, often the origin, x=0.

Displacement: change in position

Distance: the distance between two positions


1-D motion can be described by scalars (real numbers with units) as functions of time:

• The sign (positive or negative) keeps track of direction.

• Algebraic relations involving position, velocity, and acceleration come from calculus.

• The same relations can be seen from graphs of position, velocity, and acceleration as functions of time.

Position x(t) (displacement from the origin)

Velocity v(t) (rate of change of position)

Acceleration a(t) (rate of change of velocity)


position x as a function of time t

Average velocity : (slope of the secant line)txv /

x

t

x1

x2

t1 t2 t

x

12 xxx Displacement :


Instantaneous velocity is the average over an ‘infinitesimal’ time interval :

vdtdx

tx

ttt and 0 , 12

v is the slope of the tangent to the x vs. t graph. Physically, v is the rate of change of x, hence dx/dt.

t t

x


Acceleration is the rate of change of velocity:

dt

dva

tt

vv

t

va

:onAccelerati ousInstantane

:onAccelerati Average 12

12


Concept Quiz

A particle (in one dimension) is initially moving. A few seconds later it has stopped (not moving).

During that time interval:

a) The particle’s average acceleration is positive

b) The particle’s average acceleration is negative

c) Not enough information to tell


position x

time

Graphs of x(t), v(t), a(t)


x

v

a

t

t

t

Graphs of x(t), v(t), a(t)

Notice the kinks and discontinuities – they rarely happen in the real world…


acceleration a

position x

time

velocity v

There are more likely graphs of x(t), v(t), a(t)


Concept Quiz

A rubber ball is dropped and bounces twice from the floor before it is caught. (Take x to be upwards, and x=0 at the floor.)

At the highest point of the first bounce, v and a are:

a) both nonzero

b) one is zero, one is not zero

c) both zero

d) other (explain)

Suggestion: Sketch graphs of x, v, a vs. time.


Exercise: eliminate t or a to show that

002

21

0

)(

)(

constant

xtvtatx

vattv

a

vtxxvv

xxavv

00

02

02

2

)(2

Caution: These assume acceleration is constant.

These are sometimes convenient. They are valid only for constant acceleration.

Using the definitions we can derive

A Special Case: Constant Acceleration

dtdx

vdtdv

a ,


All objects in free fall move with constant downward acceleration:

This was demonstrated by Galileo around 1600 A.D.

The constant “g” is called the “acceleration due to gravity”.

“g” is NOT gravity, and it is not a force !!!

Example: Free Fall.

(“Free fall” means the only force is gravity; the motion can be in any direction).

][downwards s/m 80.9 2ga


The free-fall acceleration is the same for all objects; size and composition don’t matter.

But:

• g varies slightly with location and height, about 0.03 m/s2 over the surface of the Earth, and up to a few kilometers above

• if air resistance is significant, we don’t really have “free fall”.

Demo


Concept Quiz

A block is dropped from rest. It takes a time t1 to fall the first third of the distance. How long does it take to fall the entire distance?

a) t1

b) 3t1

c) 9t1

d) None of the above

3


10 min break


Kinematics in One DimensionKinematics in One Dimension

• Displacement, velocity, acceleration, free fall• Examples

Knight: Chapters 1, 2


1-D motion can be described by scalars (real numbers with units) as functions of time:

Position x(t) (displacement from the origin)

Velocity v(t)=dx/dt (rate of change of position)

Acceleration a(t)=dv/dt (rate of change of velocity)


2 2

1)(

)(

constant

tatvtx

atvtv

a

o

o

advv 221

22

Caution: These assume acceleration is constant.

Using the definitions we can derive

A Special Case: Constant Acceleration

dtdx

vdtdv

a ,

From the above you can get:


Example 1

A particle’s position is given by the function:

x(t)=(-t3+4t) m

a) what is the velocity at t=3 s ?

b) what is the acceleration at 3 s ?

c) make a sketch of the motion


An object if thrown straight up with a velocity of 5m/s. What will the velocity be when it comes back to its original position ?

Example 2


Example 3

A skier is moving at 40m/s at the top of a hill. His velocity changes to 10m/s after covering a distance of 600m. What is his acceleration ?


Example 3b

The skier’s girlfriend is also traveling at 40m/s, but, unfortunately, after only 3s, hits a tree and her velocity ‘suddenly’ comes to 0m/s.

How far did she get, given the same deceleration as in the previous question?


Vector Review

• Scalars and Vectors• Vector Components and Arithmetic


Physical quantities are classified as scalars, vectors, etc.

Scalar : described by a real number with units

examples: mass, charge, energy . . .

Vector : described by a scalar (its magnitude) and a direction in space

examples: displacement, velocity, force . . .

Vectors have direction, and obey different rules of arithmetic.


Notation

• Scalars : ordinary or italic font (m, q, t . . .)

• Vectors : - Boldface font (v, a, F . . .)

- arrow notation

- underline (v, a, F . . .)

• Pay attention to notation :

“constant v” and “constant v” mean different things!

.) . . F ,a ,v(


Coordinate Systems

In 2-D : describe a location in a plane

• by polar coordinates :

distance r and angle

• by Cartesian coordinates :

distances x, y, parallel to axes with: x=rcosθ y=rsinθ

These are the x and y components of r

x

y

r

( x , y )

0 x

y


Example 4

A ball is thrown with a speed of 10m/s at an angle of 60o to the horizontal. What are the x and y velocity components?


Addition:

Ax

Ay

A

By

Bx

B

By

Bx

B

Ay

Ax

A

C

Cx

Cy

If A + B = C ,

then:

zzz

yyy

xxx

BAC

BAC

BAC

Three scalar equations from one vector equation!

Tail to Head


Example 5

A=(2i+3j-k) and B=(-i+5j+3k)

a) Find A+B

b) Find 2A

Documents

Physics 1B3-summer Lecture 11 PHYSICS 1B03- MECHANICS Dr. Waldemar Okoń Office: ABB-150 e-mail: [email protected] Office Hours: T,R 1:00-2:00pm