Transcript Introduction to Modern Physics PHYX 2710

Physics of Technology
PHYS 1800
Lecture 8
Introduction
Mass & Weight
Motion with Friction
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 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
Effect
Mass
& Weight
*Homework
Handout
6
F*
Climate Change
Chapter
1
App. B, C
1
2
2
3
3
No Class
4
4
4
1-4
1-4
5
5
6
6
7
7
8
No Class
8
5-8
5-8
9
9
9
10
10
10Friction
-
Homework Due
-
1
2
3
4
5
-
6
Lecture 8-9 Slide 2
7
Physics of Technology
PHYS 1800
Lecture 8
Mass & Weight
Motion with Friction
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
Mass & Weight
Friction
Lecture 8-9 Slide 3
Dennison’s Laws of Motion
1. Stuff happens (or not).
2. The bigger they are the harder
they fall.
3. You get what you give.
Introduction
Section 0
Lecture 1
Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 4
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 5
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
Mass & Weight
Friction
Lecture 8-9 Slide 5
Newton’s First Law of Motion
An object
remains at rest,
or in uniform
motion in a
straight line,
unless it is
compelled to
change by an
externally
imposedIntroduction
force. Section 0
Lecture 1
Slide 6
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 6
Newton’s Second Law of Motion
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.
Introduction
Section 0
Lecture 1
Slide 7
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 7
Newton’s Second Law of Motion
 Note that a force is proportional to an object’s
acceleration, not its velocity.
 Precise definitions of some commonly used terms:
 The mass of an object is a quantity that tells us how much
resistance the object has to a change in its motion.
 This resistance to a change in motion is called inertia.
F  ma
Introduction
Section 0
Lecture 1
Slide 8
units: 1 newton = 1 N = 1 kg m s2
Force has dimensions of (MLT-2)
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 8
Physics of Technology
PHYS 1800
Lecture 8
Mass & Weight
Motion with Friction
Introduction
Section 0
Lecture 1
Slide 9
Mass & Weight
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 9
Mass and Weight
• What exactly is mass?
• Is there a difference between
mass and weight?
• If something is weightless in
space, does it still have mass?
Introduction
Section 0
Lecture 1
Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 10
Mass, Weight, and Inertia
• A much larger force is
required to produce the
same acceleration for the
larger mass.
• Inertia is an object’s
resistance to a change in
its motion.
• Mass is a measure of
an object’s inertia.
Introduction
Section 0
Lecture 1
Slide 11
• The units of mass are
kilograms (kg).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 11
Mass, Weight, and Inertia
• An object’s weight is
the gravitational force
acting on the object.
• Weight is a force,
measured in units of
newtons (N).
• In the absence of
Section 0 Lecture
gravity,Introduction
an object
has
no weight but still has
the same mass.
1
Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 12
Mass Standard
How do we determine what the magnitude of a gravitational
force (weight) is?
The International
Prototype Kilogram
(“IPK”) is the kilogram.
It sits next to an inchbased ruler for scale.
The IPK is made of a
platinum-iridium alloy
Introduction Section 0 Lecture
and is stored
in a vault
at the BIPM in Sèvres,
France.
1
Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 13
Mass, Weight, and Inertia
• Objects of different mass
experience the same
gravitational acceleration on
Earth:
g = 9.8 m/s2
• By Newton’s 2nd Law, F =
ma, the weight is W = mg.
• Different gravitational forces
(weights) act on falling
objects Introduction
of different
Sectionmasses,
0 Lecture 1 Slide
but the objects have the same
acceleration.
14
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 14
Weight
Example: A body of mass 100 kg on the moon
weighs:
W = m . g = 100 x 9.8 / 6 = 163 N
(Compared with 980 N on Earth)
Note: In English (imperial) system, weight (W) is
measured in lbs (pounds) – which is also a force.
1 lbs = 4.45 N so, W = 163 N = 36.6 lbs only!
Introduction
Section 0
Lecture 1
Slide 15
A mass of 1 kg therefore weighs 2.2 lbs near
Earth’s surface (or 9.8 N).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 15
Physics of Technology
PHYS 1800
Lecture 8
Mass & Weight
Motion with Friction
Introduction
Section 0
Lecture 1
Slide 16
A closer Look at Forces
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 16
A Closer Look at the Table
• The forces acting
on the book are W
(gravitational force
from Earth) and N
(normal force from
table).
• Normal force refers
to the perpendicular
force a surface
Introduction Section 0
exerts on an object.
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 17
Third-Law Action/Reaction Pair
An uncompressed spring and the same spring supporting a
book.
The compressed spring exerts an upward force on the book.
Introduction
Section 0
Lecture 1
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 18
Compression on an Atomic Scale
Bonds between atoms in a compressed solid can be treated as
compressed springs.
+
+
+
+
Ultimately the forces come from electrostatic interactions
between electrons and protons (and a little quantum mechanics).
+
+
Section 0
Lecture 1
Slide 19
+
+
Introduction
Fspring=-k Δx
+
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 19
Third-Law Action/Reaction Pair
The car pushes against the road, and the road,
in turn, pushes against the car.
Introduction
Section 0
Lecture 1
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 20
What is friction?
• A resistive force opposing motion.
• So far we have assumed many examples with no
friction but friction is a very important force in our
lives…
• No surface is perfectly smooth when viewed at the
atomic level!
• Frictional forces arise between two surfaces in
contact because they tend to dig into each other.
Introduction
Section 0
Lecture 1
Slide 21
Two objects in contact supported by
a few high spots or “prominences”.
INTRODUCTION TO Modern Physics PHYX 2710
contact points
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 21
What is friction?
• Friction is known to be independent of surface area – counter
intuitive!
• Reasoning: If reduce area, the number of contact points reduces.
This causes the pressure to increase at these points, which in turn
flattens them more and results in an increase in contact area.
• Overall effect: total “contact area” about the same!
• There are no simple “laws of friction”, as it is affected by several
factors, eg:
– Surface quality (roughness)
– Type of material
Introduction Section 0 Lecture 1 Slide 22
– Presence
of lubricants…
• Lubricants act to separate the two surfaces and allow them to
“float” – greatly reducing the friction.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 22
Physics of Technology
PHYS 1800
Lecture 8
Mass & Weight
Motion with Friction
Introduction
Section 0
Lecture 1
Slide 23
Introduction and Review
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 23
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 24
• 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
Mass & Weight
Friction
Lecture 8-9 Slide 24
Does a sky diver continue to accelerate?
Air resistance R is a force
directed upward, that
opposes the gravitational
force W
R increases as the sky
diver’s velocity increases
When R has increased to
the magnitude of W, the net
force is zero so the
acceleration is zero
Introduction Section 0 Lecture 1 Slide 25
The velocity is then at its
maximum value, the
terminal velocity
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 25
Example: Sea Lion splash!
Fk
N
Fk
N
F|| =mg sinθ
θ
F||
mg cosθ
θ
Free body
diagram
θ
W=mg
W=mg
Resolve the weight force into two components –
parallel and perpendicular to ramp.
Result: - Down slope force F|| = m g sin θ
- Normal force
N = m g cos θ
Introduction
Section 0
Lecture 1
Slide 26
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 26
N
Fk
Net force down slope:
F||=mg sinθ
Fnet = F|| - Fk
mg cosθ
=ma
but friction, Fk = μk N
= μk mg cosθ
θ
W=mg
Thus: Fnet = m g sinθ – μk m g cosθ = m a
a = g (sinθ - μk cosθ)
For θ = 23º, μk= 0.26, g = 9.81 m/s2, then
a = 9.81 (sin 23º - 0.26 x cos23º)
a = 1.5 m/s2 (note: ‘a’ is independent of mass)
Introduction
Section 0
Lecture 1
Slide 27
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 27
Physics of Technology
PHYS 1800
Lecture 8
Mass & Weight
Motion with Friction
Introduction
Section 0
Lecture 1
Slide 28
More Complex Problems in Statics and Dynamics
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 28
Newton Provided Both the Ideas and the Methods
Hart’s list of most influential people in the
history of the world:
Newton (2)*
Einstein (10)
Galileo Galilei (12)*
Aristole (13)***
Copernicus (19) *
Kepler (75) *
*(even though they got the wrong answer on the test)
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Simmon’s list of most influential scientists in
the history of the world
Newton (1)* (and 2 and 6 and 40)
Einstein (2)
Slide 29
Galileo Galilei (7)*
Copernicus (9)
Kepler (10)
Tyco Brahe (22)
Aristole (an honorable mentioned)***
Mass & Weight
Friction
Lecture 8-9 Slide 29
How does this trajectory happen?
Key: - resolve motion into its HORIZONTAL and VERTICAL
components.
VH = constant
VTOTAL
VG (due to gravity)
But we know VG increases with time due to gravity acceleration!
VH (constant)
At any instant the total
velocity is vector sum of VH
and VG
Resultant TRAJECTORY
Introduction Section 0 Lecture 1 Slide 30
STEEPENS with increasing
time.
Uniform increase
in VG
with
time
As NO horizontal acceleration the ball moves
equal distances horizontally in equal time (assuming NO air resistance).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Mass & Weight
Friction
Lecture 8-9 Slide 30
Physics of Technology
Next Lab/Demo:
Forces
Thursday 1:30-2:45
ESLC 53
Ch 3
Next Class:
Wednesday 10:30-11:20
Slide 31
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
Mass & Weight
Friction
Lecture 8-9 Slide 31