PHYSICS 1B03- MECHANICS
Dr. Waldemar Okoń
Office: ABB-150
e-mail: okon@physics.mcmaster.ca
Office Hours: T,R 1:00-2:00pm
Course web page:
http://physwww.mcmaster.ca/~okon/1b03s/1b03s.html
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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.
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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.
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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…)
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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 in
when you arrive.
Labs start this Thursday !!!
(BSB – B115)
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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.
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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).
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Example:
Concept Quiz
A 2000-kg elevator starts from rest and moves upwards
with a constant acceleration of 1.0 m/s2. The power
required from the motor
a) Increases with time, starting from zero
b) Is large as soon as the elevator starts, then
decreases with time
c) Is constant after the elevator starts to move.
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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.
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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.
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10 min break
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Kinematics in One Dimension
•
•
•
•
Displacement, velocity, acceleration
Graphs
A special case: constant acceleration
Bodies in free fall
Knight: Chapters 1, 2
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• 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
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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
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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) (rate of change of position)
Acceleration a(t) (rate of change of velocity)
• 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.
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Displacement : x  x 2  x 1
x
position x as a function of time t
x2
x
x1
t
t1
Average velocity : v
t2
 x / t
t
(slope of the secant line)
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Instantaneous velocity is the average over an
‘infinitesimal’ time interval :
x dx
t 2  t 1 , t  0 and
 v
t
dt
x
t
t
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.
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Acceleration is the rate of change of velocity:
v v2  v1
AverageAcceleration : a 

t t 2  t1
dv
Instantane
ous Acceleration : a 
dt
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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
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Graphs of x(t), v(t), a(t)
position x
time
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Graphs of x(t), v(t), a(t)
x
t
v
t
a
t
Notice the kinks and
discontinuities – they
rarely happen in the real
world…
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There are more likely graphs of x(t), v(t), a(t)
position x
acceleration a
time
velocity v
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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.
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A Special Case: Constant Acceleration
Using the definitions a 
a  constant
dv
dx
, v
we can derive
dt
dt
Caution: These assume
acceleration is constant.
v(t )  at  v0
x(t ) 
1
2
a
t
 v0t  x0
2
Exercise: eliminate t or a to show that
v 2  v0  2a ( x  x0 )
2
v  v0 x  x0

v
2
t
These are sometimes convenient.
They are valid only for constant
acceleration.
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Example: Free Fall.
(“Free fall” means the only force is gravity; the motion can
be in any direction).
All objects in free fall move with constant downward
acceleration:
a  g  9.80 m / s 2 [downwards ]
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 !!!
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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
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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) 3t1
b) 3t1
c) 9t1
d) None of the above
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10 min break
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Kinematics in One Dimension
• Displacement, velocity, acceleration, free fall
• Examples
Knight: Chapters 1, 2
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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)
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A Special Case: Constant Acceleration
Using the definitions a 
dv
dx
, v
we can derive
dt
dt
a  constant
v(t )  vo  at
x(t )  vot 
1
2
Caution: These assume
acceleration is constant.
at
2
From the above you can get:
v2  v  2ad
2
2
1
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Example 1
A particle’s position is given by the function:
x(t)=(-t3+4t) m
a)
b)
c)
what is the velocity at t=3 s ?
what is the acceleration at 3 s ?
make a sketch of the motion
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Example 2
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 ?
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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 ?
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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?
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Vector Review
• Scalars and Vectors
• Vector Components and Arithmetic
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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.
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Notation
•
Scalars : ordinary or italic font (m, q, t . . .)
•
Vectors : - Boldface font (v, a, F . . .)
- arrow notation
  
( v, a, F . . .)
- underline (v, a, F . . .)
•
Pay attention to notation :
“constant v” and “constant v” mean
different things!
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Coordinate Systems
In 2-D : describe a location in a plane
y
• by polar coordinates :
(x,y)
distance r and angle 
r
y
• by Cartesian coordinates :

0
x
x
distances x, y, parallel to axes
with:
x=rcosθ y=rsinθ
These are the x and y components of r
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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?
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Addition:
If A + B = C ,

A
Ay
Ax

B
By
Bx
then:
Cx  Ax  Bx
Tail to Head
Cy  Ay  By

B

C
Cz  Az  Bz
Three scalar
equations from one
vector equation!
Cy
Bx

A
Ax
By
Ay
Cx
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Example 5
A=(2i+3j-k) and B=(-i+5j+3k)
a) Find A+B
b) Find 2A
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