Transcript Introduction to Modern Physics PHYX 2710

Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 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
Conservation 10
of Energy
*Homework
Handout
6
F*
Climate Change
-
Homework Due
-
1
2
3
4
5
-
6
Lecture 14 Slide 2
7
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Section 0
Lecture 1
Slide 3
Introduction
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 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 kg-m/s2)
Introduction
Section 0
Lecture 1
Slide 4
In this chapter we will develop on of the most useful concepts
in science…ENERGY…and learn what it means to
conserve energy.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 4
Defining Work
• Work is equal to the force applied times the
distance moved.
– Work = Force x Distance:
– Work output = Work input
W=Fd
• units: 1 joule (J) = 1 Nm = 1 kg m2 / s2 [ML2T-2]
Introduction
Section 0
Lecture 1
Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 5
Work and Power
• Only forces parallel to the motion do work.
• Power is the rate of doing work
– Power = Work divided by Time:
P=W/t
units: 1 watt (W) = 1 J / s = 1 kg m2 / s3 [ML2T-3]
Introduction
Section 0
Lecture 1
Slide 6
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 6
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Section 0
Lecture 1
Slide 7
Kinetic Energy
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 7
Kinetic Energy
• Kinetic energy is the energy associated with an
object’s motion.
– Doing work on an object increases its kinetic energy.
– Work done = change in kinetic energy
1 2
KE  mv
2
Introduction
Section 0
Lecture 1
Slide 8
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 8
Kinetic Energy
• Negative work is the work done by a force acting
in a direction opposite to the object’s motion.
– For example, a car skidding to a stop
– What force is acting to slow the car?
Introduction
Section 0
Lecture 1
Slide 9
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 9
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Section 0
Lecture 1
Slide 10
Potential Energy
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 10
Potential Energy
• If work is done but no kinetic
energy is gained, we say that
the potential energy has
increased.
– For example, if a force is
applied to lift a crate, the
gravitational potential energy
of the crate has increased.
– The work done is equal to the
force (mg) times the distance
Section 0 Lecture 1 Slide 11
liftedIntroduction
(height).
– The gravitational potential
energy PEgravity=mgh.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 11
Potential Energy
Work is done on a large crate to tilt the crate so that
it is balanced on one edge, rather than sitting squarely
on the floor as it was at first. Has the potential
energy of the crate increased?
a) Yes
b) No
Yes. The weight of the crate
has been lifted slightly. If it is
Introduction
Lectureand
1 Slide 12
released
it willSection
fall 0back
convert the potential energy
into kinetic energy.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 12
Potential Energy
• The term potential
energy implies storing
energy to use later for
other purposes.
– For example, the
gravitational potential
energy of the crate can
be converted to kinetic
energy and used for
Introduction Section 0 Lecture 1 Slide 13
other
purposes.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 13
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Lecture 1 Slide 14
Conservation
of Energy
Section 0
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 14
Conservation of Energy
Energy 
Energy: The potential to do work.
Conservation of Energy: The total
energy of a closed system remains
constant.
– Energy can be converted from one
form to another.
– Not all forms of energy can be fully
recovered.
Introduction
Section 0
Lecture 1
Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Time 
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 15
Work Input ≤ Work Out
A lever is used to lift a rock. Will the work done by
the person on the lever be greater than, less than, or
equal to the work done by the lever on the rock?
a)
b)
c)
d)
Greater than
Less than
Equal to
Unable to tell
from this graph
Introduction
Section 0
Lecture 1
Slide 16
The work done by the person can never be less than the work done by
the lever on the rock. If there are no dissipative forces they will be equal.
This is a consequence of the conservation of energy.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 16
Work Input ≤ Work Out
– Work done in pulling a sled up a hill produces
an increase in potential energy of the sled and
rider.
– This initial energy is converted to kinetic
energy as they slide down the hill.
Introduction
Section 0
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 17
Work Input ≤ Work Out
• Conservative forces are forces for which the energy
can be completely recovered.
– Gravity and elastic forces are conservative.
– Friction is not conservative.
Introduction
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Slide 18
– Any work done by frictional forces is negative.
– That work removes mechanical energy from the system.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 18
A sled and rider with a total mass of 40 kg are perched at the top of the hill
shown. Suppose that 2000 J of work is done against friction as the sled travels
from the top (at 40 m) to the second hump (at 30 m). Will the sled make it to
the top of the second hump if no kinetic energy is given to the sled at the start
of its motion?
a)
b)
c)
yes
no
It depends.
Yes.
The
difference
between the potential
energy at the first point
and the second point, plus
Introduction Section 0 Lecture
loss to friction is less than
the kinetic energy given at
the start of the motion.
1
Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 19
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Hooke’s
Potential Energy
Section 0 Law
Lecture 1and
Slide Spring
20
Introduction
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 20
Potential Energy of a Spring
• An elastic force is a force that results from
stretching or compressing an object.
• Elastic potential energy is the energy gained
when work is done to stretch a spring.
– The spring constant, k, is a number describing the
stiffness of the spring.
Introduction
Section 0
Lecture 1
Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 21
Hooke’s Law and Potential Energy
• Hooke’s Law: The increase in elastic potential
energy is equal to the work done by the
average force needed to stretch the spring.
PE  work done = average force distance
1
average force = kx
2
1 2
PE  kx
Introduction
2 Section 0
Lecture 1
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INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 22
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Lecture 1 Slide 23
Energy
and Oscillations
Section 0
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 23
• A restoring force is a force
that exerts a push or a pull
back towards equilibrium.
• A restoring force that increases
in direct proportion to the
distance from equilibrium
results in simple harmonic
motion.
Introduction
Section 0
Lecture 1
Slide 24
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 24
Springs and Simple Harmonic Motion
• Simple harmonic motion occurs when the energy of a
system repeatedly changes from potential energy to
kinetic energy and back again.
Energy added by doing work
to stretch the spring is
Introductionback
Section and
0 Lecture
1 Slide 25
transformed
forth
between potential energy
and kinetic energy.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 25
The horizontal position x of the mass on the spring is plotted
against time as the mass moves back and forth.
• The period T is
the time taken for
one complete
cycle.
• The frequency f
is the number of
cycles per unit
time. F=1/T
• The amplitude
is
Introduction Section 0
the maximum
distance from
equilibrium.
Lecture 1
Slide 26
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
X(t) = A sin (2π f t)
Conservation of Energy
Lecture 14 Slide 26
Energy and Oscillations
Why does a
swinging
pendant return
to the same
point after
each swing?
Introduction
Section 0
Lecture 1
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INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 27
Energy and Oscillations
The force
does work to
move the ball.
This
increases the
ball’s energy,
affecting its
motion.
Introduction
Section 0
Lecture 1
Slide 28
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 28
• Conservative forces are forces for which the
energy can be completely recovered.
– Gravity and elastic forces are conservative.
– Friction is not conservative.
Introduction
Section 0
Lecture 1
Slide 29
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 29
Conservation of Energy
• Conservation of
energy means the total
energy (the kinetic plus
potential energies) of a
system remain
constant.
– Energy is conserved if
there are no forces doing
work
on Section
the system.
Introduction
0 Lecture 1 Slide 30
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 30
Physics of Technology
Next Lab/Demo:
Energy & Oscillations
Momentum and Collisions
Thursday 1:30-2:45
ESLC 53
Ch 6 and 7
Next Class:
Wednesday 10:30-11:20
BUS 318 room
Review
Ch 6
Slide 31
Read Ch 7
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Conservation of Energy
Lecture 14 Slide 31