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

∑