Transcript Lecture 4 - USU Department of Physics

Physics of Technology
PHYS 1800
Lecture 3
Introduction
Section 0
Motion
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 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 Motion 10
*Homework
Handout
6
F*
Climate Change
-
Homework Due
-
1
2
3
4
5
-
6
Lecture 3 Slide 2
7
Physics of Technology
PHYS 1800
Lecture 3
Motion
Introduction
Section 0
Lecture 1
Slide 3
Units of Motion
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 3
What Do We Need To Measure?
What is the minimum about things we need to know?
Where things are—a length, L
When things are there—a time, T
How thing interact with gravity—a mass, M
How things interact with E&M—a charge, Q
Introduction
Section 0
Lecture 1
Slide 4
How thing inter act with weak nuclear force
How things interact with strong nuclear force
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 4
Describing 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)
Introduction
Section 0
Lecture 1
Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 5
Units of Motion
Need a distance unit:
m, cm, mm, km
ft, in, mi
light years, furlongs
Need a time unit:
sec, min, hr, day, year
ms, ns, fs
fortnights
Speed:
A distance divided by time (DT-1)
m/s, mi/hr, mm/yr, furlongs/fortnight
Acceleration:
A distance divided by time squared
Introduction Section 0 Lecture 1 Slide 6
(DT-2)
A speed divided by time (DT-2)
m/s2, mi/hr2, mm/yr2, furlongs/fortnight2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 6
Examples of Distance Units
Consider the lowly penny:
Value
0.75 in
2 cm
Scientific notation
7.5 · 10-1 in
2 cm
0.02 m
Notes on units
“natural unit”
“natural” unit,
metric unit (note prefix)
SI unit, metric unit
0.00002 km
metric unit (note prefix)
2 · 10-5 km
2 · 10-2 m
1.2 · 10-5 mile
0.000012 mile
0.01 fathom
“odd” unit
1 · 10-2 fathom
0.000000000000000000002 light year
“odd” unit
2 · 10-20 light year
Introduction
Section 0
0.000000002
angstrom
Lecture 1
Slide
7
“odd”
unit
2 · 10-8 angstrom
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 7
Dimensions of Motion
Distance:
Dimensions;
Scalar
Symbol:
Units:
(L)
d
m, cm, km, in, ft, light years, furlongs
Time:
Dimensions;
Scalar
Symbol:
Units:
Speed:
(T)
t
s (or sec), min, hr, day, year, ms, ns, fs, fortnights
A distance divided by time
(LT-1)
Dimensions;
Scalar
Symbol:
Units:
Introduction
Acceleration:
s
m/s, mi/hr, mm/yr, furlongs/fortnight
Section 0
Lecture 1
Slide 8
A distance divided by time squared
A speed divided by time
Dimensions;
(LT-2)
INTRODUCTION TO Modern Physics PHYX 2710
Scalar
Fall 2004
Symbol:
a
Units:
m/s2, mi/hr2, mm/yr2, furlongs/fortnight2
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 8
Physics of Technology
PHYS 1800
Lecture 3
Motion
Introduction
Section 0
Lecture 1
Slide 9
Speed and Velocity
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 9
What Is Speed?
Speed is how fast something is moving.
– Speed is always some distance divided by some time.
– The units of speed may be miles per hour, or meters
per second, or kilometers per hour, or inches per
minute, etc.
Rate is one quantity divided by another quantity.
– For example: gallons per minute, pesos per dollar,
points per game.
– So average speed is the rate at which distance is
Introduction Section 0 Lecture 1 Slide 10
covered
over time.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 10
What Is Speed?
Average speed is total distance divided by total
time.
distance traveled
average speed =
time of travel
Instantaneous speed is the speed at that precise
instant in time.
is the rate at which distance is being covered at a
 – Itgiven
instant in time.
Introduction
Lecture 1 Slide the
11
– It is
foundSection
by 0calculating
average speed, over a
short enough time that the speed does not change
much.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 11
Average Speed
Kingman to Flagstaff:
120 mi  2.4 hr
= 50 mph
Flagstaff to Phoenix:
140 mi  2.6 hr
= 54 mph
Total trip:
120 mi + 140 mi
= 260 mi
2.4 hr + 2.6 hr
= 5.0 hr
Introduction Section 0 Lecture
260 mi  5.0 hr
= 52 mph
1
Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 12
Instantaneous Velocity
Instantaneous velocity is a vector quantity having:
a size (magnitude) equal to the instantaneous
speed at a given instant in time, and
a direction equal to the direction of motion at that
instant.
Introduction
Section 0
Lecture 1
Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 13
Instantaneous Speed: a car traveling on a local highway
 A steep slope
indicates a rapid
change in velocity
(or speed), and thus
a large acceleration.
 A horizontal line
has zero slope and
represents zero
acceleration.
Introduction
Section 0
Lecture 1
Slide 14
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 14
What Does a Speedometer Measure?
The speedometer
tells us how fast
we are going at a
given instant in
time.
A speedometer
measures
instantaneous speed.
Introduction we’ll
Section 0 see
Lecture 1
(In a moment,
why a speedometer
doesn’t measure
velocity.)
Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 15
Which quantity is the highway patrol more
interested in?
Average speed?
Instantaneous speed?
The speed limit indicates the maximum legal
instantaneous speed.
To
estimate the time a trip may take, you want to
Introduction Section 0 Lecture 1 Slide 16
use average speed.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 16
Velocity
Velocity involves direction of motion as well as how fast
the object is going.
– Velocity is a vector quantity.
– Vectors have both magnitude and direction.
– Velocity has a magnitude (the speed) and also a direction
(which way the object is moving).
A change in velocity can be a change in the object’s speed
or direction of motion.
A speedometer doesn’t indicate direction, so it indicates
instantaneous speed but not velocity.
Introduction
Section 0
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 17
A car goes around a curve at constant
speed. Is the car’s velocity changing?
Yes
No
At position A, the car has the
velocity indicated by the arrow
(vector) v1.
At position B, the car has the
0 Lecture
1
velocityIntroduction
indicatedSection
by the
arrow
(vector) v2, with the same
magnitude (speed) but a
different direction.
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 18
Changing Velocity
 A force is required to produce a
change in either the magnitude
(speed) or direction of velocity.
 For the car to round the curve,
friction between the wheels and the
road exerts a force to change the
car’s direction.
 For a ball bouncing from a wall,
the wall exerts a force on the ball,
causing the
ball toSection
change
direction.
Introduction
0 Lecture
1 Slide
19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 19
Why Velocity Is So Useful
Velocity is a vector and represents a bodies speed and direction.
• A force must act on a body to change its velocity (i.e. its speed,
direction or both).
• The force causes the body to accelerate resulting in a change in
its velocity.
• Acceleration is a vector and represents the rate of change of
velocity with time.
Introduction
Section 0
Lecture 1
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 20
Physics of Technology
PHYS 1800
Lecture 3
Motion
Introduction
Section 0
Lecture 1
Slide 21
Acceleration
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 21
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
22
r
r
a = DV m s 2
t
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 22
Instantaneous Acceleration
 Instantaneous acceleration is the
acceleration at that precise instant in time.
It
is the rate at which velocity is changing at
a given instant in time.
It is found by calculating the average
speed, over a short enough time that the
speed does not change much.
Introduction
Section 0
Lecture 1
Slide 23
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 23
Acceleration: Vector Direction
The direction of acceleration vector is given by the direction of the change in the
velocity vector, DV.
V2
V1
car
accelerating
- Acceleration
V1
DV
+
V2
=
a
vector in same direction as velocity when velocity is increasing.
V1
car
deceleratin
g
Introduction
Section 0
V1
Lecture 1
V2
+
DV
a
=
Slide 24
- When the velocity is decreasing the change in
motion (ie. to slow car down)
V2
DV
is in the opposite direction to
INTRODUCTION TO Modern Physics PHYX 2710
- Acceleration vector is opposite direction when velocity is decreasing.
- Deceleration is negative acceleration.
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 24
Example: Negative Acceleration
Jet preparing to land
Initial velocity V1=200 km/hr (=55.6 m/s)
Final velocity V2=120 km/hr (=33.3 m/s)
Time interval t=5 sec
DV
V2 - V1
a = t =
t
33 . 3 - 55 . 6
2
m
/
s
=
a
5
Acceleration:
Introduction
= - 4 . 46 m /s 2
a
Section 0 Lecture 1 Slide 25
toward runway
In general:
- Whenever the velocity is changing we say the object is
accelerating (positive or negative).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 25
Return to car on a bend
Car moved at a constant speed but its direction continuously
changed – thus its velocity was changing.
• But we now know that velocity changes are produced by an
acceleration.
• Thus when the car rounds the bend at a constant speed it is
accelerating!!
• Direction of acceleration is given by DV direction.
V1
Acceleration
Direction
0
Question:Introduction
what isSection
DV ?
V1
+ DV
=
Lecture 1
Slide 26
V1
V2
DV
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
V2
V2
Result: the vector
acts
towards the center of
curvature of the bend!
DV
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 26
Thus the acceleration is also directed towards the center of curvature.
This is why the car does NOT change speed but you still feel a force on your body
as you round the bend… (change in direction).
• Force is due to friction of tires on road enabling the car to change direction.
Example:
For a given speed the acceleration experienced (force) depends on the curvature
of the bend.
shallow
sharp
V1
V2
DV
V1
V2
V1
V1
Introduction
DV
Section 0
V2
a=
Lecture 1
DV
t
Slide 27
= Large
V2
a=
INTRODUCTION TO Modern Physics PHYX 2710
DV
t
= Small
Fall 2004
Skiing - sudden turns create large accelerations & large associated forces!
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 27
Physics of Technology
PHYS 1800
Lecture 3
Motion
Introduction
Section 0
Lecture 1
Slide 28
Graphing Motion
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 28
Graphing Motion
Objectives: Understand what position, speed and acceleration are
Learn to graph them versus time
Develop some intuition for common situations
Introduction
Time
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Slide 29
Time
Acceleration 
Standing still
Constant speed (different magnitudes)
Constant acceleration (different magnitudes)
Constant deceleration (different magnitudes)
Arbitrary motion
Speed 
Distance 
Consider:
Time
Motion
Lecture 3 Slide 29
Acceleration 
Speed 
Distance 
Standing Still
Time
Time
Introduction
Section 0
Lecture 1
Time
Slide 30
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 30
Acceleration 
Speed 
Distance 
Constant Speed
Time
Time
Introduction
Section 0
Lecture 1
Time
Slide 31
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 31
Acceleration 
Speed 
Distance 
Constant Speeds
Time
Time
Introduction
Section 0
Lecture 1
Time
Slide 32
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 32
Acceleration 
Speed 
Distance 
Constant Acceleration
Time
Time
Introduction
Section 0
Lecture 1
Time
Slide 33
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 33
Physics of Technology
PHYS 1800
Lecture 3
Motion
Introduction
Section 0
Lecture 1
Slide 39
Vectors: Velocity and Acceleration
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 39
Scalars and Vectors
Scalar: Measure of quantity or size
Sometimes called “magnitude”.
Examples: Length, volume, mass, temperature, speed…
Vectors: Many measurements in physics require a knowledge
of the magnitude and direction of quantity.
These are termed vector quantities.
Examples: Velocity, acceleration, force, electric field…
Direction is an essential feature of a vector quantity.
Example:
Flying
1000
km/hr
due North is quite different to
Introduction
Section 0atLecture
1 Slide
40
the same speed due East!
Vectors require 2 pieces of information MAGNITUDE and
DIRECTION.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 40
Physics of Technology
Next Lab/Demo:
Free Fall
Tuesday 1:30-2:45
ESLC 53
Ch 2
Next Class:
Wednesday 10:30-11:20
Slide 44
BUS
318 room
Review Ch 3
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Motion
Lecture 3 Slide 44