1.1. BASEBALL,F=MA,ANDTHEPRINCIPLEOFLEASTACTION 11
Problem: Dyre’sDilemma^2
Indiscussingthemotionofthebaseball, wehave beenignoringalotofdetails
aboutbaseballs,suchasthecompositionoftheinterior,thepatternofthestitching,
andthebrand-nameprintedonthesurface. Instead,thebaseballhasbeentreated
as thoughit were essentially a structurelesspoint of massm. Itis necessaryto
makeidealizationslikethisinphysics;therealworldisotherwisetoocomplicatedto
describe. Butsometimesanidealizationmissessomethingcrucial.Seeifyoucanfind
whatgoeswronginthefollowingargument,whichtriestoprovethatarollingwheel
(or,forthatmatter,arollingbaseball)cannevercometorestthroughfrictionwith
theground.
”Proof”: AsshowninFig.[1.3],theforwardmomentumofawheelinthepositive
x-directioncanonlybeeliminatedbyaforceappliedintheoppositedirection. But
theonlyplacethisforcecouldbeappliedbyfrictionisthepointwherethewheel
touchestheground. Andaforceinthenegativex-direction,appliedatthispoint,
willhavetheeffectofmakingthewheelspinfaster!Therefore,thewheelwillnever
cometorestduetofriction. QED.
Isthisreasoningcorrect?CanyousolveDyre’sDilemma?(^2) IowethisexercisetoDr.JeppeDyre,RoskildeUniversity,Denmark.