Conservation of Energy
Introduction Section 0 Lecture 1 Slide 1
Lecture 14 Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 2
Lecture 14 Slide 2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet
*Homework Handout
Date Day Lecture Chapter Homework Due Jan 5 6 7 9
M T W F*
Class Admin: Intro.Physics Phenomena Problem solving and math Units, Scalars, Vectors, Speed and Velocity
1 App. B, C 1 2
-
Jan 12 14 16
M W F*
Acceleration Free Falling Objects Projectile Motion
2 3 3
1
Jan 19 21 23
M W F*
Martin Luther King Newton’s Laws Mass and Weight
No Class 4 4
2
Jan 26 28 29 30
M W Th F
Motion with Friction Review Test 1 Circular Motion
4 1-4 1-4 5
3
Feb 2 4 6
M W F*
Planetary Motion and Gravity Energy Harmonic Motion
5 6 6
4
Feb 9 11 13
M W F*
Momentum Impulse and Collisions Rotational Motion
7 7 8
5
Feb 16 17 18 19 20
M Tu W H F*
Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure
No Class 8 5-8 5-8 9
-
Feb 23 25 27
M W F*
Flotation Fluids in Motion Temperature and Heat
9 9 10
6
Mar 2 4 6
M W F*
First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change
10 10 -
7
Mar 9-13 M-F Spring Break No Classes Mar 16 18 20
M W F*
Heat Engines Power and Refrigeration Electric Charge
11 11 12
8
Mar 23 25 26 27
M W H F*
Electric Fields and Electric Potential Review Test 3 Electric Circuits
12 13 9-12 13
-
Mar 30 Apr 1 3
M W F
Magnetic Force Review Electromagnets Motors and Generators
14 9-12 14
9
Apr 6 8 10
M W F*
Making Waves Sound Waves E-M Waves, Light and Color
15 15 16
10
Apr 13 15 17
M W F*
Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes
17 17 17
11
Apr 20 22 24
M W F
Review Seeing Atoms The really BIG & the really small
1-17 18 (not on test) 21 (not on test)
No test week 12
May 1 F Final Exam: 09:30-11:20am
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 3
Lecture 14 Slide 3
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Introduction
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 4
Lecture 14 Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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)
In this chapter we will develop on of the most useful concepts in science…ENERGY…and learn what it means to conserve energy.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 5
Lecture 14 Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
• Work is equal to the force applied times the distance moved.– Work = Force x Distance: W = F d– Work output = Work input
• units: 1 joule (J) = 1 Nm = 1 kg m2 / s2 [ML2T-2]
Defining Work
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 6
Lecture 14 Slide 6
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
• 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]
Work and Power
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 7
Lecture 14 Slide 7
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Kinetic Energy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 8
Lecture 14 Slide 8
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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
2
2
1mvKE
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 9
Lecture 14 Slide 9
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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?
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 10
Lecture 14 Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Potential Energy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 11
Lecture 14 Slide 11
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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 lifted (height).
– The gravitational potential energy PEgravity=mgh.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 12
Lecture 14 Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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) Yesb) No
Yes. The weight of the crate has been lifted slightly. If it is released it will fall back and convert the potential energy into kinetic energy.
Potential Energy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 13
Lecture 14 Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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 other purposes.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 14
Lecture 14 Slide 14
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Conservation of Energy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 15
Lecture 14 Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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.
Conservation of Energy
Time
Ene
rgy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 16
Lecture 14 Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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) Greater thanb) Less thanc) Equal tod) Unable to tell
from this graph
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.
Work Input ≤ Work Out
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 17
Lecture 14 Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
– 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.
Work Input ≤ Work Out
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 18
Lecture 14 Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
– Any work done by frictional forces is negative.– That work removes mechanical energy from the system.
• Conservative forces are forces for which the energy can be completely recovered.– Gravity and elastic forces are conservative.– Friction is not conservative.
Work Input ≤ Work Out
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 19
Lecture 14 Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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) yesb) noc) It depends.
Yes. The difference between the potential energy at the first point and the second point, plus loss to friction is less than the kinetic energy given at the start of the motion.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 20
Lecture 14 Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Hooke’s Law and Spring Potential Energy
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 21
Lecture 14 Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 22
Lecture 14 Slide 22
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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
average force = 1
2kx
PE 1
2kx 2
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 23
Lecture 14 Slide 23
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 14
Conservation of Energy
Energy and Oscillations
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 24
Lecture 14 Slide 24
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
• 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.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 25
Lecture 14 Slide 25
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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 transformed back and forth between potential energy and kinetic energy.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 26
Lecture 14 Slide 26
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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 the maximum distance from equilibrium.
X(t) = A sin (2π f t)
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 27
Lecture 14 Slide 27
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Why does a swinging pendant
return to the same point after each
swing?
Energy and Oscillations
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 28
Lecture 14 Slide 28
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
The force does work to
move the ball. This increases the ball’s
energy, affecting its
motion.
Energy and Oscillations
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 29
Lecture 14 Slide 29
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
• Conservative forces are forces for which the energy can be completely recovered.– Gravity and elastic forces are conservative.– Friction is not conservative.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 30
Lecture 14 Slide 30
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
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 the system.
Conservation of Energy
Introduction Section 0 Lecture 1 Slide 31
Lecture 14 Slide 31
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
Next Lab/Demo: Energy & OscillationsMomentum and CollisionsThursday 1:30-2:45
ESLC 53 Ch 6 and 7
Next Class: Wednesday 10:30-11:20BUS 318 roomReview Ch 6Read Ch 7