Transcript PPT

Physics 218
Lecture 10
Dr. David Toback
Physics 218, Lecture X
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Checklist for Today
•Things that were due last Tuesday:
– Reading for Chapter 6
•Things that were due Yesterday:
– Chaps. 3 and 4 HW on WebCT
– Progress on 5&6 problems
•Things due for Today
– Reading for Chap 7
•Things due for Wednesday’s Recitation:
– Problems from Chap 5&6
– No Lab
•Things for Thursday:
– Read Chapters Physics
7, 8
9 X
218,&
Lecture
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Overview: Chapters 7, 8 & 9
Combine Chapter 7, 8 & 9 into six
lectures
Today we’ll cover Work:
• The math
• Intuitive understanding
• Multiple ways to calculate work
Next time:
• How much energy does it take to
accomplish a task?
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Why are we learning this stuff?
This is Fundamental to Engineering
• How much work can a machine
do? (today)
• How much energy does it take
to accomplish a task? (next
time)
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The plan…
Need to start with
some math…
Scalar product
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How do we Multiply Vectors?
• First way: Scalar Product or Dot Product
– Why Scalar Product?
• Because the result is a scalar
(just a number)
– Why a Dot Product?
• Because we use the notation A.B
A.B = |A||B|CosQ
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First Question:
A.B = |A||B|CosQ What is ˆi  ˆi ?
What is ˆ
i  ĵ ?
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Harder Example

A  AX

B  BX
ˆ
i AY ĵ
ˆ
i  BY ĵ


What is A  B using Unit Vector notation?
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Back to Work
• The word “Work” means something
specific in Physics (Kinda like Force)
• The amount of Work we do is the
amount of Forcing we do over some
distance
• Example: If we are accelerating a car
for 1 mile, then there is a force and a
distance  We do Work
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Calculating the work
• Work is done only if the
force (or some component of
it) is in the same (or
opposite) direction as the
displacement
• Work is the force done
Parallel to the displacement
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Work for Constant Forces
The Math: Work can be complicated.
Start with a simple case
Do it differently than the book
For constant forces, the work is:
.
W=F d
…(more on this later)
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1 Dimension Example
You pull a box with a constant force of
30N for 50m where the force and the
displacement are in the same direction
How much work is done on the box?
W = F.d = 30N . 50m= 1500 N . M
= 1500 Joules
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What if the Force
and the Displacement
aren’t in the same
direction?
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2 Dim: Force Parallel to Displacement
W = F||d = F.d = Fdcosq where q is the
angle between the net Force and the net
displacement. You can think of this as the
force component in the direction of the
displacement.
Force
Force
Rotate
Displacement
Displacement
F|| = Fcosq
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Work done and Work experienced
• Something subtle: The amount of
work YOU do on a body may not be
the same as the work done ON a
body
• Only the NET force on the object
is used in the total work calculation
• Add up all the work done on an
object to find the total work done!
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Examples
• Holding a bag of groceries in
place
– Is it heavy?
– Will you get tired holding it?
– Are you doing “Work?”
• Moving a bag of groceries with
constant speed across a room
– Is it heavy?
– Will you get tired doing it?
– Are you doing “Work?”
• Lifting a bag of groceries a
height h with constant speed
– Work by you?
– Work on the bag? Physics 218, Lecture X
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Groceries: With the math
• Holding a bag of groceries
– W=F.d = Fdcosq =(0)*(0)*cosq = 0
• Moving a bag of groceries with constant speed
across a room
– Force exerted by you= mg, Net Force on bag = 0
– Work on bag= F.d = Fdcosq =0*dcosq =0
– Work exerted by you =Fdcosq =mgd*cos(900)=0
• Lifting a bag of groceries a height h with constant
speed
– Work on bag = Fd*cosq = (0)*h*(00) = 0
– Work by you =Fdcosq =(mg)hcos(00)=mgh
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Work in Two Dimensions
You pull a crate of mass M a distance X along a
horizontal floor with a constant force. Your pull has
magnitude FP, and acts at an angle of Q. The floor
is rough and has coefficient of friction m.
Determine:
• The work done by each force
• The net work on the crate
Q
X
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What if the Force is
changing direction?
What if the Force is
changing magnitude?
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What if the force or direction isn’t constant?
I exert a force over a distance for awhile, then
exert a different force over a different distance
(or direction) for awhile. Do this a number of
times. How much work did I do?
Need to
add up all
the little
pieces of
work!
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Find the work: Calculus
To find the total work, we must sum up all the little
pieces of work (i.e., F.d). If the force is continually
changing, then we have to take smaller and smaller
lengths to add. In the limit, this sum becomes an
integral.
b


 F  dx
a
Fancy sum
notationIntegral
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Use an Integral for a Constant Force
Assume a constant Force, F,
doing work in the same direction,
starting at x=0 and continuing for
a distance d. What is the work?
W 

d
0

d

F  dx   Fdx  Fx|xx0d  Fd  F 0  Fd
0
Region of integration
W=Fd
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Non-Constant Force: Springs
• Springs are a good
example of the types of
problems we come back
to over and over again!
• Hooke’s Law


F  kx
Some constant
Displacement
• Force is NOT
CONSTANT overPhysics
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Work done to stretch a Spring
How much work
do you do to
stretch a
spring (spring
constant k),
at constant
velocity, from
x=0 to x=D?
D
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Exam 1 Results
• Overall:
• Mean=71.5%
• People who took mini=76
• People who didn’t = 54
•1A, and 1B, 4C’s, 2D and 10 F’s
• Straight curve for now
• >90% A
• >80% B etc.
• If you got less than a 50% you
REALLY need some help
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This Week
• Next Lecture: More on Work
and Energy
• Finish the reading for Chapters
7, 8 & 9
• Recitation on Chapters 5 & 6
• Ch 5 & 6 due Monday on WebCT
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Examples
• While you are lifting up a bottle with mass m,
the bottle moves a distance d with constant
velocity. As you lift it:
– What is the force you exert?
– What is the work done by you?
– What is the work done by gravity?
– What is the net work?
• You push a box with Force F on a rough floor
with coefficient of friction m for a distance d,
and the box moves with constant velocity. As it
moves:
– What is the work done by you?
– What is the work done by friction?
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– What is the net
work?
Does the Earth do work on the
Moon?
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Simple Case
Start with our spherical cow:
– Constant Forces in a single
direction
• Work is the force done Parallel to
the displacement
• Work is done only if the force (or
some component of it) is in the
same (or opposite) direction as the
displacement
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Hiker
A hiker carries a backpack
of mass M with constant
speed up a hill of angle Q
and height h.
Determine:
• The work done by the
hiker
• The work done by gravity
• The work on the backpack
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Simple Example with Unit Vectors
A woman pulls
a box of mass
M with Force
FP in the Q
direction for a
distance d.
Ignore friction
Find the work
using unit
vectors
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