PHY 113 A General Physics I
9-9:50 AM MWF Olin 101
Plan for Lecture 11:
Chapter 7 -- The notion of work
1. Definition of work
2. Examples of work
3. Potential energy and work;
conservative forces
4. Comments about Exam 1
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PHY 113 A Fall 2012 -- Lecture 11
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PHY 113 A Fall 2012 -- Lecture 11
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Comments about Exam 1
 Scores 70 ≤ G ≤ 100
 Please keep working hard, even if your
score is 90 ≤ G ≤ 100
 Please make an appointment to see me
if your score is 70 ≤ G ≤ 90
 Solutions will be posted on the web on
the course website (you will have to
login with your WFU login and
password)
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PHY 113 A Fall 2012 -- Lecture 11
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Energy  work, kinetic energy
Force  effects acceleration
rf
Wi  f   F  dr
A related quantity is Work
ri
F
dr
ri
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rj
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Definition of vector “dot” product
q
A  B  AB cos q
Note that if q  90 , then A  B  0
o
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Definition of vector “dot” product
q
A  B  AB cos q
Example :
A  5, B  15, q  120
o
A  B  (5)(15) cos120  37.5 (scalar)
o
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Definition of vector “dot” product -- continued
q
Suppose A  Ax ˆi  Ay ˆj and B  Bx ˆi  B y ˆj
A  B  Ax Bx  Ay B y
Note that the result of a vector dot product is a scalar.
Example : A  2ˆi  4ˆj and B  1ˆi  3ˆj
A  B  2 1   4 3  10
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PHY 113 A Fall 2012 -- Lecture 11
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F
Definition of work:
dr
rf
ri
rj
Wi  f   F  dr
ri
Units of work :
Work  Newtons meters  Joules 
1 J  0.239 cal
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Units of work:
work = force · displacement = (N · m) = (joule)
•Only the component of force in the direction of the
displacement contributes to work.
•Work is a scalar quantity.
•If the force is not constant, the integral form must be used.
•Work can be defined for a specific force or for a combination
of forces
rf
W1   F1  dr
ri
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rf
W2   F2  dr
rf
W1 2   (F1  F2 )  dr  W1  W2
ri
PHY 113 A Fall 2012 -- Lecture 11
ri
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iclicker question: A ball with a weight of 5 N follows the
trajectory shown. What is the work done by gravity from the
initial ri to final displacement rf?
2.5m
rf
ri
1m
1m
(A) 0 J
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10 m
(B) 7.5 J
(C) 12.5 J
(D) 50 J
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Gravity does
negative work:
Gravity does
positive work:
ri
rf
r  0
r  0
mg
mg
ri
W=mg(rfri)<0
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rf
W=mg(rfri)>0
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rf
Wi  f   F  dr
Work done by a variable force:
ri
In this case :
rf
xf
ri
xi
Wi  f   F  dr   Fx dx
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Example:
rf
xf
ri
xi
Wi  f   F  dr   Fx dx  (5 N )(4m)  12 5 N 2m   25 J
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Example – spring force:
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Fx = - kx
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F
Positive work
x
Negative work
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Detail:
rf
xf
Wi  f   F  dr   Fx dx 
ri
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xi
xf
  kx dx  
xi
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2
kx
2 xf
xi

  12 k x 2f  xi2

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More examples:
Suppose a rope lifts a weight of 1000N by 0.5m at a constant
upward velocity of 4.9m/s. How much work is done by the
rope?
(A) 500 J (B) 750 J
(C) 4900 J (D) None of these
Suppose a rope lifts a weight of 1000N by 0.5m at a constant
upward acceleration of 4.9m/s2. How much work is done by
the rope?
(A) 500 J (B) 750 J
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(C) 4900 J (D) None of these
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iclicker exercise:
Why should we define work?
A. Because professor like to torture
students.
B. Because it is always good to do work
C. Because it will help us understand
motion.
D. Because it will help us solve the energy
crisis.
Next time we will discuss the Work-Kinetic energy
theorem.
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n
q
FP
fk
mg
xi
xf
Assume FP sinq <<mg
Work of gravity?
Work of FP?
Work of fk?
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0
FP cos q (xf-xi)
mkn (xf-xi)=mk(mg- FP sin q (xf-xi)
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A man must lift a refrigerator of weight mg to a
height h to get it to the truck.
For which method does the man do more work:
A. Vertically lifting the refrigerator at constant
speed to height h?
B. Moving the refrigerator up the ramp of length
L at constant speed with h=L sin q.
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iclicker exercise:
Which of the following statements about friction
forces are true.
A. Friction forces always do positive work.
B. Friction forces always do negative work.
C. Friction forces can do either positive or
negative work.
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