Chapter 5.1-5.4
Energy and Work
Kinetic and Potential Energy
•Mechanical Energy
•Kinetic (associated with motion)
•Potential (associated with position)
•Chemical Energy
•Electromagnetic Energy
•Nuclear Energy
Energy can be transformed from one form to another
But not destroyed--Conserved
Work/Energy can be used in place of Newton’s laws to solve
certain problems more simply
Units of Energy and Work
• SI
– Newton • meter = Joule
•N•m=J
• J = kg • m2 / s2
• US Customary
– foot • pound
• ft • lb
–no special name
Work Can Be Positive or Negative
• Work done on box is
positive when lifting the box
• Work is negative if lowering
the box
– The force would still be
upward, but the
displacement would be
downward
OR
Box does positive work on
student when lowered
Work
W ≡ (F cos θ)∆x = F•∆x
F is the magnitude of the net force
• ∆ x is the magnitude of the
object’s displacement
r
r
• θ is the angle between F and ∆x
This gives no information
about
the time it took for the
displacement to occur
the velocity or acceleration
of the object
Work is a scalar quantity
Work is Zero when force and
displacement are perpendicular
Carrying a bucket of water
• Displacement is horizontal
• Force is vertical
• cos 90° = 0
So no work done!
Two Kinds of Forces
Conservative and Non-Conservative
• A force is conservative if work done on object
moving between two points is independent of the
path the object takes between the points
– The work depends only upon the initial and final
positions of the object
– Any conservative force can have a potential energy
function associated with it
Examples of conservative forces include:
Gravity
(ideal) Spring force
Electromagnetic forces
1
• A force is nonconservative if the work it
does on an object depends on the path taken
by the object between its final and starting
points.
• Examples of nonconservative forces
– kinetic friction and air drag
•The blue path is shorter than the
red path
•The work required is less on the
blue path than on the red path
Work and Potential Energy
Conservative force
potential energy function
Evaluating the difference of the function at any two
points in an object’s path gives the negative of the
work done by the force between those two points
Example will be gravity
•Friction depends on the path and
so is a non-conservative force
Work and Gravitational Potential Energy
Problem Solving with Conservation of Energy
• PE = mgy
Won −book = PEi − PE f = mgyi − mgy f = mg ( yi − y f )
Units of Potential Energy, Work, and
Kinetic Energy are same joules
Work-Energy Theorem
Wnc = (KEf − KEi )
+(PEf − PEi ) = 0
(if conservative)
• Define the system- Verify only conservative forces present
• Select the location of zero gravitational potential energy
Do not change this location while solving problem
• Identify two points the object of interest moves between
At one point information is given
At other point you want to find out something
• Apply the conservation of energy equation to the system
Conservation of Energy
KEi + PEi = KE f + PE f
In-class quiz 11-3
In-class quiz 11-4
A diver drops (does not jump) from a board 10 m
above the water. If he weights 700 N, what is his
speed just as he hits the water?
What acceleration did we measure in the experiment we ran
last class period and what was predicted by the
Atwood’s Machine formula (in m/s2)?
A.
B.
C.
D.
E.
A. 700
m/s
B. 35 m/s
C. 14 m/s
D. 10 m/s
E. 0 m/s
0.26 and 0.32
0.32 and 0.26
0.26 and 0.19
0.19 and 0.26
0.19 and 0.32
a=
m2 − m1
g
m2 + m1
∆y = 166cm
∆t = 4.2 sec or 3.6 sec
m1 = 150 gm
v f = 2 gyi
m2 = 160 gm
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