Transcript PPT

Physics 218
Lecture 15
Dr. David Toback
Physics 218, Lecture XV
1
Checklist for Today
•Things due awhile ago:
– Read Chapters 7, 8 & 9
•Things that were due Monday:
– Problems from Chap 7 on WebCT
•Things that are due Yesterday in
Recitation
– Chapter 8
– Reading for Lab
Physics 218, Lecture XV
2
The Schedule
This week: (3/3)
• Chapter 7 due in WebCT
• 5th and 6th lectures (of six) on Chapters 7, 8 & 9
• Chapter 8 in recitation
Next week: (3/10) Spring Break!!!
Following Week: (3/17)
• Chapter 8 due in WebCT
• Reading for Chapters 10 & 11
• Lecture on Chapters 10 & 11
• Chapter 9 and Exam 2 Review in recitation
Following Week: (3/24)
• Chapter 9 due in WebCT
• Exam 2 on Tuesday
• Recitation on Chapters 10 & 11
• Reading for Chapters 12 & 13 for Thursday
• Lecture 12 & 13 on Thursday
Physics 218, Lecture XV
3
Chapters 7, 8 & 9 Cont
Before:
– Work and Energy
– The Work-Energy relationship
– Potential Energy
– Conservation of Mechanical Energy
– Conservation of Energy
This time:
– Summary
– More Problems
Physics 218, Lecture XV
4
Physics 218, Lecture XV
5
Law of Conservation of Energy
• Mechanical Energy NOT always
conserved
• If you’ve ever watched a roller
coaster, you see that the friction
turns the energy into heating the
rails, sparks, noise, wind etc.
• Energy = Kinetic Energy + Potential
Energy + Heat + Others…
– Total Energy is what is
conserved!
Physics 218, Lecture XV
6
Law of Conservation of Energy
• Even if there is friction, Energy is
conserved
• Friction does work
– Can turn the energy into heat
– Changes the kinetic energy
• Total Energy = Kinetic Energy + Potential
Energy + Heat + Others…
– This is what is conserved
• Can use “lost” mechanical energy to
estimate things about friction
Physics 218, Lecture XV
7
Roller Coaster with Friction
A roller coaster of mass m starts at rest
at height y1 and falls down the path with
friction, then back up until it hits height
y2 (y1 > y2).
Assuming we don’t know anything about the
friction or the path, how much work is
done by friction on this path?
Physics 218, Lecture XV
8
Energy Summary
If there is net work done on an object, it
changes the kinetic energy of the object
(Gravity forces a ball falling from height h
to speed up  Work done.)
Wnet = DK
If there is a change in the potential energy,
some one had to do some work: (Ball falling
from height h speeds up→ work done → loss
of potential energy. I raise a ball up, I do
work which turns into potential energy for
the ball)
DUTotal = WPerson =-WGravity
Physics 218, Lecture XV
9
Energy Summary
If work is done by a non-conservative force
it does negative work (slows something
down), and we get heat, light, sound etc.
EHeat+Light+Sound.. = -WNC
If work is done by a non-conservative
force, take this into account in the total
energy. (Friction causes mechanical
energy to be lost)
K1+U1 = K2+U2+EHeat…
K1+U1 = K2+U2-WNC
Physics 218, Lecture XV
10
Friction and Springs
A block of mass
m is traveling on
a rough surface.
It reaches a
spring (spring
constant k) with
speed Vo and
compresses it a
total distance D.
Determine m
Physics 218, Lecture XV
11
Robot Arm
A robot arm has a funny
Force equation in 1dimension

3x
FX  F0  1  2
x
0

2




where F0 and X0 are
constants. The robot
picks up a block at X=0
(at rest) and throws it,
releasing it at X=X0.
What is the speed of
the block?
Physics 218, Lecture XV
12
Bungee Jump
You are standing on a
platform high in the air
with a bungee cord
(spring constant k)
strapped to your leg.
You have mass m and
jump off the platform.
1.How far does the cord
stretch, l in the picture?
2.What is the equilibrium
point around which you
will bounce?
Physics 218, Lecture XV
l
l
13
Coming up…
•Next week: Spring Break
•Week after Spring Break
– Homework in WebCT Monday:
• Chapter 8
– Reading for Lecture:
• Chaps 10 & 11: Momentum
– Recitation:
• Chap 9 and Exam review
Physics 218, Lecture XV
14
Physics 218, Lecture XV
15
Roller Coaster
You are in a roller coaster car of mass M
that starts at the top, height Z, with an
initial speed V0=0. Assume no friction.
a) What is the speed at the bottom?
b) How high will it go again?
c) Would it go as high if there were friction?
Z
Physics 218, Lecture XV
16
Energy
• Potential Energy & Conservation
of Energy problems
• The relationship between
potential energy and Force
• Energy diagrams and
Equilibrium
Physics 218, Lecture XV
17
Energy Review
If there is net work on an object, it changes the
kinetic energy of the object (Gravity forces a ball
falling from height h to speed up  Work done.)
Wnet = DK
If there is a change in the potential energy, some
one had to do some work: (Ball falling from height
h speeds up→ work done → loss of potential
energy. I raise a ball up, I do work which turns
into potential energy for the ball)
DUTotal = WPerson =-WGravity
Physics 218, Lecture XV
18
Energy Review
If work is done by a non-conservative force it is
negative work (slows something down), and we get
heat, light, sound etc.
EHeat+Light+Sound.. = -WNC
If work is done by a non-conservative force, take
this into account in the total energy. (Friction
causes mechanical energy to be lost)
K1+U1 = K2+U2+EHeat…
K1+U1 = K2+U2-WNC
Physics 218, Lecture XV
19
Potential Energy Diagrams
• For Conservative forces
can draw energy
diagrams
• Equilibrium points
– Motion will move
“around” the
equilibrium
– If placed there with
no energy, will just
stay (no force)
Fx  
Physics 218, Lecture XV
dU
dx
0
20
Stable vs. Unstable Equilibrium Points
The force is zero at both maxima and minima but…
– If I put a ball with no velocity there would
it stay?
– What if it had a little bit of velocity?
Physics 218, Lecture XV
21
Roller Coaster with Friction
A roller coaster car of mass m starts at rest at
height y1 and falls down the path with friction,
then back up until it hits height y2 (y1 > y2).
Assuming we don’t know anything about the friction
or the path, how much work is done by friction
on this path?
Physics 218, Lecture XV
22
Roller Coaster with Friction
A roller coaster car of mass m starts at rest at
height y1 and falls down the path with friction,
then back up until it hits height y2 (y1 > y2). An
odometer tells us that the total scalar distance
traveled is d.
Assuming we don’t know anything about the friction
or the path, how much work is done by friction
on this path?
Assuming that the magnitude and angle of the
force of friction, F, between the car and the
track is constant, find |F|.
Physics 218, Lecture XV
23
Bungee Jump
A jumper of mass m
sits on a platform
attached to a bungee
cord with spring
constant k. The cord
has length l (it
doesn’t stretch until
it has reached this
length).
How far does the cord
stretch Dy?
Physics 218, Lecture XV
l
24
A football is thrown
A 145g football starts at rest and is thrown
with a speed of 25m/s.
1. What is the final kinetic energy?
2. How much work was done to reach this
velocity?
We don’t know the forces exerted by the
arm as a function of time, but this allows
us to sum them all up to calculate the
work
Physics 218, Lecture XV
25