1. Ch 8 Conservation of Energy
8-1 The Nonisolated System: Conservation of Energy
Mechanical Energy E = K + U
Esystem = T (T stands for energy transfer)
8-2 The Isolated System: Conservation of Energy
W = K
For a conservative force WC = -U
-U = K
K + U = 0 = Esystem
If several potential energies:
E = K + U1 + U2 + U3 + ……
Esystem = K + U1 + U2 + U3 + …
E is constant or conserved

2. Method for Energy Approach
Draw a picture
Write down equations for the energies and works involved
E = K + U
K = mv2/2
Ug = mgy (near surface of Earth – pick zero for Ug)
Us = kx2/2 (Us =0 for x=0)
Pick before (B) and after (A) and label on the picture
Set EA = EB or E = 0

3. P8.6 (p.219)
P8.57 (p.224)

4. CT1: A block initially at rest is allowed to slide down a frictionless ramp and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times as high must a new ramp be?
A. 1
B. 2
C. 3
D. 4
E. 5
F. 6

5. CT2: A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring?
A. 96 m
B. 48 m
C. 24 m
D. 12 m
E. 6 m
F. 3 m
G. impossible to determine

6. 8.3,4 Changes in Mechanical Energy for Nonconservative Forces
WTOT = WC + WNC = K
-U + WNC = K
WNC = K + U
WNC = E
Friction is just another nonconservative force!
The work of friction is always negative.

7. Method for Energy Approach
Draw a picture
Write down equations for the energies and works involved
E = K + U
K = mv2/2
Ug = mgy (near surface of Earth – pick zero for Ug)
Us = kx2/2 (Us =0 for x=0)
Work of non-conservative forces
Pick before (B) and after (A) and label on the picture
Set Wnc = E (If Wnc = 0, then EA = EB or E = 0 and mechanical energy is conserved)

8. P8.21 (p.220)
P8.55 (p.224)

9. P = dE/dt Units: J/s = Watt PAV = W/t P = lim F·r/t = F·v
8.5 Power
P = dE/dt Units: J/s = Watt
PAV = W/t
P = lim F·r/t = F·v    
t0

10. P8.32 (p.221)

11. CT3 A. B. C. D. E.

12. P8.44 (p.223)