Transcript Introduction to Modern Physics PHYX 2710

Physics of Technology
PHYS 1800
Lecture 11
Introduction
Circular Motion and
Gravitational Force
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 1
PHYSICS OF TECHNOLOGY
Spring 2009 Assignment Sheet
Date
Day
Lecture
Jan 5
M
Class Admin: Intro.Physics Phenomena
6
T
Problem solving and math
7
W
Units, Scalars, Vectors,
9
F*
Speed and Velocity
Jan 12
M
Acceleration
14
W
Free Falling Objects
16
F*
Projectile Motion
Jan 19
M
Martin Luther King
21
W
Newton’s Laws
23
F*
Mass and Weight
Jan 26
M
Motion with Friction
28
W
Review
29
Th
Test 1
30
F
Circular Motion
Feb 2
M
Planetary Motion and Gravity
4
W
Energy
6
F*
Harmonic Motion
Feb 9
M
Momentum
11
W
Impulse and Collisions
13Introduction
F*
Rotational
Section
0 Motion
Lecture 1 Slide 2
Feb 16
M
Presidents Day
17
Tu
Angular Momentum (Virtual Monday)
18
W
Review
19
H
Test 2
INTRODUCTION TO Modern Physics PHYX 2710
20
F*
Static Fluids, Pressure
Fall 2004
Feb 23
M
Flotation
25
W
Fluids in Motion
27
F*
Temperature and Heat
Mar 2
M
First Law of Thermodynamics
Physics of Technology—PHYS 1800
4
W Spring 2009Heat flow and Greenhouse
CircularEffect
Motion and
*Homework
Handout
6
F*
Climate Change
Chapter
Homework Due
1
App. B, C
1
2
2
3
3
1
No Class
4
4
2
4
1-4
1-4
5
3
5
6
6
4
7
7
8
5
No Class
8
5-8
5-8
9
9
9
10
6
10
10
Gravitational
Force
7
Lecture 11 Slide 2
Physics of Technology
PHYS 1800
Lecture 11
Circular Motion and
Gravitational Force
Introduction
Section 0
Lecture 1
Slide 3
Introduction and Review
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 3
Describing Motion and Interactions
Position—where you are in space (L or meter)
Velocity—how fast position is changing with time (LT-1 or m/s)
Acceleration—how fast velocity is changing with time (LT-2 or m/s2)
Force— what is required to change to motion of a body (MLT-2 or kgm/s2)
We will focus on a special kind of force, termed a central forces [e.g.,
gravity, Coulombic (charge) or centripetal forces].
Introduction
Section 0
Lecture 1
Slide 4
Important: Velocity, acceleration and force are VECTORS!!!
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 4
The Math Approach
• We are going to explore a different kind of force that is no
longer constant, but is proportional to 1/r.
ag
 k/r
v f  v0  at or a 
v f  vo
t
 v f  vo   v f  vo   vo vo 
t  
t    t
d  vavg t  
 2   2  2 2
 v1f Slidev5o 
vo 0 Lecture
1 2
 vo Section
Introduction
d 
t    t  v0t  at
2
 2   2 2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 5
Newton’s Laws in Review
•
1st Law —a special case of the 2nd Law for statics,
with a=0 or Fnet=0
• An objects velocity remains unchanged, unless
a force acts on the object.
•
2nd Law (and 1st Law)—How motion of a object is
effected by a force.
– The acceleration of an object is directly
proportional to the magnitude of the imposed
force and inversely proportional to the mass of
the object. The acceleration is the same
direction as that of the imposed force.
F  ma
units: 1 newton = 1 N = 1 kg m s2
•
Introduction
Section 0
Lecture 1
Slide 6
3rd Law —Forces come from interactions with
other objects.
• 
For every action (force), there is an equal but
opposite reaction (force).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 6
Fstring  10 N (t o the right)
Net Forces
 It is the total force or net force
that determines an object’s
acceleration.
 If there is more than one vector
acting on an object, the forces are
added together as vectors, taking
into account their directions.
ftable  2 N (t o the left )
Fnet  10 N  2 N
 8 N (t o the right)
a
Fnet 8 N

m 5 kg
 1.6 m s2 (t o t he right
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Slide 7

Circular Motion and Gravitational Force
Lecture 11 Slide 7
Free Body Diagrams
• Fancy Science: Vector analysis of complex force
problems is facilitated by use of a free body
diagram.
• Common Sense: A picture is worth a 100 words.
(A scale picture is worth an A!)
• Key is to:
•
•
•
•
•
Isolate a single body and draw all the forces acting on it.
Add up all the arrows (vectors).
Introduction Section 0 Lecture 1 Slide 8
What’s left is the net force.
Net force (and masses)  a.
A plus initial conditions motion!
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 8
Does the circular
motion of the moon
around the Earth ...
... have anything
inIntroduction
common
with
Section 0 Lecture 1
circular motion on
Earth?
Slide 9
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 9
A ball is whirled on the end of a string with
constant speed when the string breaks. Which
path will the ball take?
a)
b)
c)
d)
Path 1
Path 2
Path 3
Path 4
Path 3, in the direction of the
tangent
to point A. Neglecting
Introduction Section 0 Lecture 1 Slide
gravity, the body would move in
the direction it was moving
when the force disappeared, in
accordance with the first law.
10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 10
If the string breaks, the ball flies off in a straight-line path in
the direction it was traveling at the instant the string broke.
• If the string is no
longer applying a force
to the ball, Newton’s
First Law tells us that
the ball will continue to
move in a straight line.
• Circular motion is
called centripetal
Introduction Section 0
motion, with the string
providing a centripetal
force.
Lecture 1
Slide 11
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 11
Centripetal Acceleration
• Centripetal acceleration is the rate of
change in velocity of an object that is
associated with the change in direction of the
velocity.
– Centripetal
acceleration is
always
perpendicular to
the velocity.
– Centripetal
acceleration always
Introduction
points
towardSection
the 0 Lecture
center of the curve
(It’s a central force!).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
1
Slide 12
v2
ac 
r
Circular Motion and Gravitational Force
F~1/r
A central
force!
Lecture 11 Slide 12
Centripetal Acceleration
• Centripetal acceleration is the rate of
change in velocity of an object that is
associated with the change in
direction of the velocity.
v2
ac 
r
– Centripetal acceleration is always
perpendicular to the velocity.
– Centripetal acceleration always points
toward the center of the curve.
• The centripetal force refers to any
force or combination of forces that
produces a centripetal acceleration.
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009

Fc  ma c
Slide 13

Circular Motion and Gravitational Force
Lecture 11 Slide 13
A Simple Demonstration of Centripetal Force
(with commentary by Newton)
• The horizontal component
of T produces the centripetal
acceleration.
• The vertical component of T is equal
to the weight of the ball.
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
• At higher speeds, the string is closer
to horizontal because a large
Slide 14
horizontal component of T is needed
to provide the required centripetal
force.
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 14
Centripetal Forces—Negotiating a Flat Curve
• The centripetal force is the total force that produces a
centripetal acceleration.
– The centripetal force may be due to one or more individual forces,
such as a normal force and/or a force due to friction.
• The Static force of friction is the frictional force acting
when there is no motion along the surfaces.
– No skidding or sliding
• The Kinetic
force of friction is the frictional force acting
Introduction Section 0 Lecture 1 Slide 15
when there is motion along the surfaces.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 15
Centripetal Forces—Leaning Into a Curve
• The friction between the
tires and road produces the
centripetal acceleration on a
level curve.
• On a banked curve, the
horizontal
component
of
Introduction
Section 0 Lecture
the normal force also
contributes to the
centripetal acceleration.
1
Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 16
What forces are involved in riding a Ferris wheel?
Depending on the position:
•
Weight of the rider
• Normal force from seat
• Gravity
Introduction
Section 0
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 11 Slide 17