If you missed the first lecture. . .

filercaliforniaMechanics

Nov 14, 2013 (3 years and 11 months ago)

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Physics 1D03
-

Lecture 2

1

If you missed the first lecture. . .


Find the course webpage:

http://physwww.mcmaster.ca/~okon/1d03/1d03.html


and read the course outline and the first lecture.



Log into Avenue to Learn (http://avenue.mcmaster.ca)

and find Physics 1D03. There you can find out which
lab/tutorial section you are in.




Get a copy of
your

lab/tutorial schedule from the
course web page.

Physics 1D03
-

Lecture 2

2

Kinematics in One Dimension


Displacement, velocity, acceleration


Graphs


A special case: constant acceleration


Bodies in free fall



Serway and Jewett Chapter 2

Physics 1D03
-

Lecture 2

3


Kinematics

: the description of motion


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

Physics 1D03
-

Lecture 2

4

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 (in 1
-
D).



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)

Physics 1D03
-

Lecture 2

5

position
x

as a function of time
t

Average velocity

: (slope of the line)

t
x
v



/

x


t

x
1

x
2

t
1

t
2

t

x

1
2
x
x
x



Displacement

:

Physics 1D03
-

Lecture 2

6

Instantaneous velocity

is the average over an
‘infinitesimal’ time interval :

v
dt
dx
t
x
t
t
t








and

0

,

1
2
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

Physics 1D03
-

Lecture 2

7

Acceleration

is the
rate of change of velocity
:








dt
dv
a
t
t
v
v
t
v
a








:
on
Accelerati

ous
Instantane



:
on
Accelerati

Average

1
2
1
2
Physics 1D03
-

Lecture 2

9

acceleration a

position x

time

velocity v

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

Physics 1D03
-

Lecture 2

10

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.



Physics 1D03
-

Lecture 2

11

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

Physics 1D03
-

Lecture 2

12

Exercise
: eliminate t or a to show that

0
0
2

2
1
0
)
(
)
(
constant

x
t
v
t
a
t
x
v
at
t
v
a






v
t
x
x
v
v
x
x
a
v
v







0
0
0
2
0
2
2
)
(
2
Caution
: These assume
acceleration

is constant.

These are sometimes convenient,
but not necessary. They are valid
only for constant acceleration.

Use the definitions and derive

A Special Case:

Constant Acceleration

dt
dx
v
dt
dv
a



,
Physics 1D03
-

Lecture 2

13

All objects in free fall move with
constant downward
acceleration,



This was demonstrated by Galileo around 1600 A.D.

“g”

is called the “acceleration due to gravity” or the
“gravitational field of the Earth”.

Example:
Free Fall.

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

]
[downwards

s
/
m

80
.
9
2


g
a
Physics 1D03
-

Lecture 2

14

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/s
2

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”.

Physics 1D03
-

Lecture 2

15

Quiz

A block is dropped from rest. It takes a time
t
1

to
fall the first third of the distance. How long does it
take to fall the entire distance?

a)

t
1

b)
3t
1

c)
9t
1

d)
None of the above

3
Physics 1D03
-

Lecture 2

16

Quiz

You throw a set of keys up to a window 4.00m
above you. If the keys just make it to your friend
on a balcony 1.0s later, what was their initial
velocity ?

a)
40 m/s

b)
9.8 m/s

c)
4.5 m/s