Upload
others
View
6
Download
0
Embed Size (px)
Citation preview
11/23/15 1 Physics 131
■ Theme Music: Cannonball Adderly Work Song
■ Cartoon: Mike Peters Mother Goose & Grimm
November 23, 2015 Physics 131 Prof. E. F. Redish
Mechanical energy
conservation
11/23/15 Physics 131 3
Δ 12 mv
2 +U( ) = 0
Quiz 9
11/23/15 4 Physics 131
#1A 86%B 9%C 5%D 0%
#2 #3a 31% a 26%b 16% b 60%c 75% c 9%d 36% d 5%e 61% e 0%
f 1%
Basic principle
Starting with an equation is often the right way to solve a qualitative question and remind yourself about basic principles.
11/23/15 6 Physics 131 !Fnet ⋅ Δ!r = Δ 1
2 mv2( )
A1v1 = A2v2Δp = 8µL
πR4⎛⎝⎜
⎞⎠⎟Q
11/23/15 13 Physics 131
Foothold ideas: Potential Energy
■ For some forces work only depends on the change in position. Then the work done can be written U is called a potential energy.
■ For gravity, Ugravity = mgh For a spring, Uspring = ½ kx2
For electric force, Uelectric = kCQ1Q2/r12
F ⋅ Δr = −ΔU
Using Mechanical Energy Conservation
■ If resistive forces can be ignored, mechanical energy is conserved (exchanges with hidden internal energy such as thermal or chemical can be ignored)
■ KE may refer to one or more objects PE may refer to one or more interactions.
■ If only one object’s KE is important and only one interaction matters, this can make things really easy.
11/23/15 15 Physics 131
KEi + PEi = KEf + PEf
Which Energies add to give Total Mechanical Energy?
YES Potential Energies
(Conservative Interactions)
YES Kinetic Energy
(in general, all objects)
NO Work done by Interactions
that cross System Boundary 11/23/15 Physics 131 16
Foothold ideas: Energies between charge clusters ■ Atoms and molecules are made up of charges. ■ The potential energy between two charges is
■ The potential energy between many charges is
11/23/15 19 Physics 131
U12elec = kCQ1Q2
r12
U12...Nelec =
kCQiQj
riji< j=1
N
∑