Physics I
Class 10
Potential Energy and
Kinetic Energy in
Spring Systems
Rev. 17-Feb-06 GB
10-1
Two Common Potential Energy
Functions (Review)
Gravitational Potential Energy
U g  m g (y  y0 )  m g h
(y0 is our choice to make the problem easier)
Spring Potential Energy
U s  12 k ( x  x 0 ) 2
(x0 is the equilibrium position and k is the spring constant)
10-2
Conservation of Energy (Review)
Recall the Work-Kinetic Energy Theorem:
 K  Wnet
And for conservative forces we have
Wcons   U
If the non-conservative forces are zero or negligible, then
Wnet  Wcons
Putting it together,
 K   U
or
| K   U  0|
Another way to say this is the total energy, K+U, is conserved.
10-3
Flow of Energy in a Pendulum
10-4
Flow of Energy in a Spring System
Kinetic and Potential Energy
K=0
U = max
y = 10 cm
v=0
K = max
K = max
v
U=0
v
y = 0 cm
y = 0 cm
U=0
K=0
y = -10 cm
U = max
v=0
10-5
Hooke’s Law for an Ideal Spring
Fspr ing (N)
+1
y (cm)
0
+10
+20
Fspring = –k (y–y0)
Problem of the Day #1:
Find k and y0 from the graph.
10-6
Net Force = Gravity + Spring
Shifts the Equilibrium Point
Fgr av
y (cm)
-10
10
Fnet
new equilibrium point
y (cm)
Fspr ing
-10
10
y (cm)
-10
10
10-7
Potential Energy of Net Force
Fnet
y (cm)
-10
10
-1
U(y=0.1) = –W(0 to 0.1) = ?
Problem of the Day #2
Calculate U(0.1).
10-8
Class #10
Take-Away Concepts
1.
Potential Energy defined for a conservative force:
 
U ( A )    F  dx
A
0
2.
Combined Potential Energy of Gravity Plus Spring:
U total  12 k ( y  y 0 ) 2 [y0 is the new equilibrium position.]
3.
Conservation of energy in the spring system:
 K   U
or
| K   U  0 |
10-9
Activity #10
Energy in a Spring System
Objective of the Activity:
1.
2.
Use LoggerPro to study mechanical energy in a
spring system.
Consider how kinetic energy, potential energy,
and total mechanical energy vary with position.
10-10