Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 25
Second exam Tuesday, October 25
7 pm – 8 pm
Sections 530, 531 105 HELD
Sections 532, 565 107 HELD
Section 566 109 HELD
Work Energy Theorem
x2 y 2
F

dx 
total
x
x1 y1
x2 y 2
F

dy 
total
y
x1 y1
mV
2
final
2
2
initial
mV

2
If a force can be written as the gradient
(slope) of some scalar function, that force is
conservative.
1D case:
dU
Fx  
dx
U(x) is called the  potential energy
function for the force F
If such a function exists, then the force is
conservative
W
conservative
does NOT depend on path!
1D case:
dU
F 
dx
x2
W
conservative
  Fdx 
x1
x2
dU
 
dx   [U ( x2 )  U ( x1 )]
dx
x1
W
con
W
 [U ( x2 )  U ( x1 )]
con
does NOT depend on path!
If Fx(x) is known, you can find the potential energy function as
U ( x)    Fx ( x) dx  C
nc
12
If W
 0, K 2  U 2  K1  U1
or
nc
1 2
W
 K 2  U 2  K1  U1
Newton’s 2nd Law


F  ma
Fx  max
Fy  ma y
Work does not depend on the choice of
coordinates! You can calculate work of
each force in the most convenient system
of coordinates.
Do not forget to work with components!
Usually there are several ways to solve the
problem.
Indicate the law or the theorem you use!