SLIDE 1
Three pillars of Newtonian mechanics p
Newtonian Mechanics ion of aw of ion of m Conservati Energy Newton’s L Motion Conservat Momentum N M
Class 8: Kinetic energy work done and Class 8: Kinetic energy, work - - PowerPoint PPT Presentation
Class 8: Kinetic energy work done and Class 8: Kinetic energy, work - - PowerPoint PPT Presentation
Class 8: Kinetic energy work done and Class 8: Kinetic energy, work done, and conservative force Three pillars of Newtonian mechanics p Newtons L N aw of Motion M Newtonian Mechanics Conservati ion of Energy Conservat ion of Momentum m
SLIDE 2
SLIDE 3
Ki ti E Kinetic Energy
2
1 T
2
mv 2 T =
SLIDE 4
W k d Work done
1 `B
Work done by F
s d F W
B B A
v ⋅ = =
∫
s d F W
A B A
∫
→
F ds
A B
s d F
- s
d F ⋅ = ⋅
∫ ∫
v v
A F
A B B A B A
W W
→ → =
⇒
for the same path.
SLIDE 5
Conservative Force If F is a function of position: F(r) B If WA→B is path i d d i
1 `
independent, F is conservative. If WA→B is path d d F i A dependent, F is non‐ conservative.
SLIDE 6
Conservative Force If F(r) is conservative
- 1. WA→A = 0
2. F = × ∇ v A
SLIDE 7
Two Important Equations for Vector Analysis Two Important Equations for Vector Analysis
) F ( . 1 = × ∇ ⋅ ∇ v ) ( 2. = Φ ∇ × ∇
SLIDE 8
Potential Energy If F(r) is conservative, there exist a scalar f i U( ) h function U(r) so that
U F ∇ v
U i ll d h i l i
U
- F