Work/Energy
Work-Energy Theorem
Conservation of Kinetic Energy
Work-Energy Theorem
Work-Energy Diagram
1
Work/Energy
Work-Energy Theorem
Conservation of Kinetic Energy
If no work is done on an object, its kinetic energy does not
change.
1
1
2
2
K  mv2  mv1  0
2
2
1
1
2
2
mv2  mv1
2
2
THIS IS ONLY TRUE WHEN THERE IS NO WORK BEING DONE!
Total work equals zero only if…
2
1. There is no net force on the object or ...
2. The net force and infinitesimal displacement are
perpendicular to each other.
Work/Energy
Work-Energy Theorem
Examples of Conservation of Kinetic Energy

f

N

T

w

Fnet

ds
THIS IS ONLY TRUE WHEN THERE IS NO WORK BEING DONE!
Total work equals zero only if…
3
1. There is no net force on the object or …
2. The net force and infinitesimal displacement are
perpendicular to each other.
Work/Energy
Work-Energy Theorem
Work- Energy Theorem
If there is work done on an object, then the change in
kinetic energy is equal to the work done.

f

N

w
4
Wtotal

T
Wtotal  K
1
1
2
 T  f  r  mv f  mv0 2
2
2
Work/Energy
Work-Energy Theorem
Work and Energy
Work and energy are calculated from
simple equations
W  F r
1 2
K  mv
2
5
Work/Energy
Work-Energy Theorem
Work- Energy Theorem
Wtotal  K
6
Work/Energy
Work-Energy Theorem
Work-Energy Diagrams
Work
The work is equal to the change
in the kinetic energy of the
system
K initial
K final
0.5 J
2J
1.5 J
 
7
Kinetic Energy
Total Work
Work/Energy
Work-Energy Theorem
Work- Energy Theorem
Wtotal  K
In terms of potential energy, we have
Wnonconservative  Wconseravtive  K
Wnonconservative  U  K
Wnonconservative  K  U
8
Work/Energy
Work-Energy Theorem
Including Potential Energy
The total work done on a
systems is ALWAYS equal to
the change in its kinetic energy
Work-Energy Theorem
W  K
Wnonconservative  Wconservative  K
T, N, f
w, Fsp , Fg
Wnonconservative  K  Wconservative
9
Wnonconservative  K  U g  U sp
Work/Energy
Work-Energy Theorem
The nonconservative work is
equal to the change in the total
energy of the system
Work-Energy Diagrams
Work
K initial
U initial
0.5 J
Total
Energy
1.0 J
1.5 J
K final
2.0 J
U final
-1.0 J
1.0 J
-0.5 J
Initial
 
Final
 
 
Kinetic Energy
Potential Energy
Total Energy
10
Nonconservative Work