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Transcript
```Friday, September 9, 1998
Chapter 3 -- Projectile Motion
Relative Motion
Chapter 4 -- Newton’s Laws
Force and Mass
Think about the following two demonstrations
Assume that the vertical component of the
velocity is equal in both cases. Would the
balls
(a) Hit the ground simultaneously
(b) The ball thrown vertically only
hits first.
(c) The ball thrown with both Vx and
Vy hits first.
Consult with Neighbors!
After the ball leaves my hand, the ONLY
acceleration it experiences (in the absence
of air resistance) is that due to gravity!
Gravity acts downward, affecting only the
vertical component of the velocity, Vy.
The horizontal component of the velocity...
REMAINS UNCHANGED!!!
(At least until the ball hits the ground!)
Vx = constant
H
0
x
y  y0  v0 y t  gt
1
2
The bullet:
In the absence of gravity, the bullet
would arrive at the dot at time
So
y(t )  v0 y t  H
*
*
2
x
t 
v0 x
*
H
x
Without Gravity:
y(t )  v0 y t  H
*
*
Now let’s put gravity back into the problem.
How will this change things?
Does the time it takes the bullet to travel the
horizontal distance x change?
H
x
Still true:
x
t 
v0 x
*
y(t )  v0 y t  g(t )  H  g(t )
*
*
1
2
* 2
1
2
* 2
So, that tells us the position off the ground
the bullet will be when it reaches the
horizontal position of the criminal. Now,
how far off the ground is the criminal?
H
x
The criminal starts falling from a
height H and falls until the bullet
arrives at his horizontal position at
x
t 
v0 x
*
yc (t )  y0c  v0 yct  g(t )  H  0  g(t )
*
1
2
*
* 2
yc (t )  H  g(t )
*
1
2
* 2
1
2
* 2
No! We’re not talking about how
fast you run from your folks when
you learn mom’s made her favorite
goulash for dinner!
Think about two cars on the highway, one
driving 50 mph and the other driving 60 mph.
How fast does the faster car APPEAR to be
travelling to a passenger in the slow car?
10 mph!
What type of motion does
the tennis ball appear to
have to me? To you?
To me: FREE FALL
To you: Parabolic Motion
As I walk at an angle to the wall in the front
of the classroom, what is the speed of my
That speed represents the “component” of my
velocity that is parallel to the wall.
It is often helpful in solving physics problems
to look at the PROJECTIONS of vector quantities
onto useful coordinate systems…(e.g. LAB
last night)!
y
 
v vy

vx
x
  
1  2
x  x0  v0t  2 at
  
v  v0  at
Careful! These do NOT quite match the
ones in the book!
Newton’s Laws
What is a force?
What is mass?
How are these quantities related to acceleration?
Definition IV:
“An impressed force is an action exerted upon a
body in order, to change its state, either of rest, or
of uniform motion in a right line.”
Object sitting still
Object moving with uniform velocity
Law I:
“Every body continues in its state of rest, or
of uniform motion in a right line, unless it is
compelled to change that state by forces
impressed upon it.”
Hmmm…I guess I had better IMPRESS you if
I’m ever going to get you guys to START liking
physics, eh???
Law I:
“Every body continues in its state of rest, or
of uniform motion in a right line, unless it is
compelled to change that state by forces
impressed upon it.”
What does this really mean?
We leave the room and return 10 minutes later.
Where will the keys be?
We leave again and return 10 minutes later.
Where will the keys be?
Unless there’s SOME outside force that acts
upon the keys, they’re not going anywhere!!
We’re in outer space…far away from
or galaxy, or star...
Our spaceship is moving with const