Physics of Technology
PHYS 1800
Lecture 6
Introduction
Projectile Motion
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 1
PHYSICS OF TECHNOLOGY
Spring 2009 Assignment Sheet
Date
Day
Lecture
Chapter
Jan 5
M
Class Admin: Intro.Physics Phenomena
1
6
T
Problem solving and math
App. B, C
7
W
Units, Scalars, Vectors,
1
9
F*
Speed and Velocity
2
Jan 12
M
Acceleration
2
14
W
Free Falling Objects
3
16
F*
Projectile Motion
3
Jan 19
M
Martin Luther King
No Class
21
W
Newton’s Laws
4
23
F*
Mass and Weight
4
Jan 26
M
Motion with Friction
4
28
W
Review
1-4
1-4
29
Th
Test 1
30
F
Circular Motion
5
Feb 2
M
Planetary Motion and Gravity
5
4
W
Energy
6
6
F*
Harmonic Motion
6
Feb 9
M
Momentum
7
11
W
Impulse and Collisions
7
13Introduction
F*
Rotational
8
Section
0 Motion
Lecture 1 Slide 2
Feb 16
M
Presidents Day
No Class
17
Tu
Angular Momentum (Virtual Monday)
8
18
W
Review
5-8
19
5-8
H
Test 2
INTRODUCTION TO Modern Physics PHYX 2710
20
F*
Static Fluids, Pressure
9
Fall 2004
Feb 23
M
Flotation
9
25
W
Fluids in Motion
9
27
F*
Temperature and Heat
10
Mar 2
M
First Law of Thermodynamics
10
Physics of Technology—PHYS 1800
4
W Spring 2009Heat flow and Greenhouse Effect
10
Projectile Motion
*Homework
Handout
6
F*
Climate Change
-
Homework Due
-
1
2
3
4
5
-
6
Lecture 6 Slide 2
7
Physics of Technology
PHYS 1800
Lecture 5
Projectile Motion
Introduction
Section 0
Lecture 1
Slide 3
Review of Free Fall
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 3
Describing (Special) Motion
Position—where you are in space (L-meter)
Speed—how fast position is changing with time (LT-1
or m/s)
Acceleration—how fast speed is changing with time
(LT-2 or m/s2)
1 Slide 4
We willIntroduction
focusSection
on0 aLecture
special
case of constant
acceleration due to gravity, termed FREE FALL.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 4
Acceleration
Acceleration is the rate at which velocity changes.
– Our bodies don’t feel velocity, if the velocity is constant.
– Our bodies feel acceleration.
• A car changing speed or direction.
• An elevator speeding up or slowing down.
Acceleration can be either a change in the object’s
speed or direction of motion.
Change in velocity V2 - V1
=
Average acceleration =
t
Time
interval
Introduction Section 0 Lecture 1 Slide
5
r
r
a = DV m s 2
t
In this Chapter acceleration is a constant, a=g=9.8 m/s2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 5
Acceleration Due to Gravity
• Earth exerts a gravitational force on objects that is
attractive (towards Earth’s surface).
• Near Earth’s surface, this force produces a
constant acceleration downward.
– To measure this acceleration, we need to slow down the
action.
– Galileo was the first to accurately measure this
acceleration due to gravity.
– By rolling objects down an inclined plane, he slowed the
motion enough to establish that the gravitational
acceleration
uniform,
Introduction Section 0is Lecture
1 Slide or
6 constant with time.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 6
Physics of Technology
PHYS 1800
Lecture 6
Projectile Motion
Introduction
Section 0
Review:
Slide 7
Influence of Gravity
Tossing a Ball
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 7
Tracking a Falling Object
• The distance increases in
proportion to the square of the
time:
1 2 1
2
d = at = 10 m/s 1 s = 5 m
2
2

Introduction
Section 0
Lecture 1
Slide 8
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 8
Throwing a ball downward
• Let the ball be thrown downward instead of being
dropped.
– It will have a starting velocity different from zero.
– It will reach the ground more rapidly.
– It will have a larger velocity when it reaches the ground.
a=g
v f = v0  at or
a=
v f - vo
t
 v f  vo   v f  vo   vo vo 
t = 
t   - t
d = vavg t = 
Introduction Section 0 Lecture
 2 1  Slide 9 2   2 2 
1 2
 vo  vo   v f vo 
d =
t   - t = v0t  at
2
 2   2 2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 9
Beyond Free Fall: Throwing a Ball Upward
What if the ball is thrown
upward?
Gravitational acceleration is
always directed downward,
toward the center of the Earth.
Here, the acceleration is in the
opposite direction to the
Introduction Section 0 Lecture 1 Slide 10
original
upward velocity.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 10
• Let the initial velocity be 20
m/s upward.
– It immediately starts
experiencing a downward
acceleration due to gravity, of
approximately 10 m/s.
– Every second, the velocity
decreases by 10 m/s.
• After 2 s, the ball has reached
its highest point.
– Its velocity changes direction,
from upward to downward,
passing through a value of 0
m/s. Introduction Section 0 Lecture 1 Slide 11
• Now, the downward
acceleration increases the
downward velocity.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 11
What is the ball’s acceleration
at the top of its path
(at t=2 s)?
a)
b)
c)
d)
e)
zero.
+10 m/s
-10 m/s
+10 m/s2
-10 m/s2
Gravity does not “turn off” at the top!
The ball’sIntroduction
velocity Section
is still0 changing,
as12it
Lecture 1 Slide
changes from going up to going down.
For a moment the velocity is zero, but
the gravitational acceleration is a
constant throughout the path.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 12
• The velocity-vs-time plot starts with +20
m/s (upward) at time t=0 and changes at
a steady rate of -10 m/s2 (decreasing 10
m/s each second).
• Positive velocities correspond to upward
motion; negative velocities correspond to
downward motion.
• The slope is constant and negative (for
constant downward acceleration).
Introduction
Section 0
Lecture 1
Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 13
Physics of Technology
PHYS 1800
Lecture 6
Projectile Motion
Introduction
Section 0
Lecture 1
Slide 14
Simple Compound Motions—Projectile Motion
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 14
Does this represent a realistic trajectory?
a)
b)
c)
Yes.
No.
Maybe.
The coyote would not go straight
horizontally, pause, and then fall
straight down. There are many
examplesIntroduction
in movies
and on
Section 0 Lecture 1
television of unrealistic
trajectories.
Can you think of any others?
Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 15
What does the trajectory look like?
The acceleration of the
horizontal motion is zero (in the
absence of air resistance).
The object moves with
constant horizontal velocity.
It travels equal horizontal
distances in equal time
intervals.
The acceleration in the
vertical direction is constant.
Its vertical velocity increases
downward just like the falling
ball.
Introduction
Sectiontime
0 Lecture 1
In each
successive
interval, it falls a greater
distance than in the previous
time interval.
Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 16
What does the trajectory look like?
The total velocity at any
point is found by adding the
vertical component of the
velocity, at that point, to the
horizontal component of the
velocity at that point.
The horizontal velocity
remains constant, because
there is no acceleration in
that direction.
The length of the horizontal
velocity vector
doesn’t
Introduction
Section 0 Lecture 1
change.
The downward (vertical) velocity
gets larger and larger, due to
the acceleration due to gravity.
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 17
What does the trajectory look like?
Trajectories for different initial
velocities of a ball rolling off a
table:
The largest initial velocity is v3.
The smallest initial velocity is v1.
The ball travels
greater horizontal
distances when
projected with a
larger initial
horizontal velocity.
Introduction
Section 0
Lecture 1
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 18
Which of these three balls would hit the floor first if
all three left the tabletop at the same time?
a)
b)
c)
d)
The ball with initial
velocity v1.
The ball with initial
velocity v2.
The ball with initial
velocity v3.
They would all hit at the
same time.
Since all three balls undergo the
same downward
acceleration, and
Introduction Section 0 Lecture 1
they all start with a vertical
velocity of zero, they would all
fall the same distance in the
same time!
Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 19
Projectile Motion
• Treating the vertical motion independently of the
horizontal motion, and then combining them to find
the trajectory, is the secret.
– A horizontal glide combines with a vertical plunge to
produce a graceful curve.
– The downward gravitational acceleration behaves the
same as for any falling object.
– There is no acceleration in the horizontal direction if air
resistance can be ignored.
– The projectile moves with constant horizontal velocity
while it is accelerating downward.
Introduction
Section 0
Lecture 1
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 20
Hitting a Target
If the rifle is fired directly at the target in
a horizontal direction, will the bullet hit
the center of the target?
Does the bullet fall during its flight?
Introduction
Section 0
Lecture 1
Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 21
Hitting a Target
 The trajectory depends on the initial velocity.
 The trajectory depends on the launch angle.
Introduction
Section 0
Lecture 1
Slide 22
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 22
Hitting a Target
For the lowest angle, the horizontal
velocity is much greater than the initial
vertical velocity.
The ball does not go very high, so its time
of flight is short.
Introduction
Section 0
Lecture 1
Slide 23
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 23
Hitting a Target
For the highest angle, the initial vertical
velocity is much greater than the
horizontal velocity.
The ball goes higher, so its time of flight is
longer, but it does not travel very far
horizontally.
Introduction
Section 0
Lecture 1
Slide 24
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 24
Hitting a Target
The intermediate angle of 45° divides
the initial velocity equally between the
vertical and the horizontal.
The ball stays in the air longer than at low
angles, but also travels with a greater
horizontal velocity than at high angles.
Introduction
Section 0
Lecture 1
Slide 25
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 25
Physics of Technology
Next Lab/Demo:
Forces
Thursday 1:30-2:45
ESLC 53
Ch 3
Next Class:
Wednesday 10:30-11:20
Slide 26
BUS
318 room
Read Ch 4
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Projectile Motion
Lecture 6 Slide 26