1J40-001
Changingaflattire–torque
PROMPTSEMBEDDED
STATEMENTOFTHEPROBLEM
Youhaveaflattireonyourcarand,inordertochangethetire,youneedtoremovethelug
nutsthatsecurethewheeltothecar.Ifthe30-cmlongwrenchyouareusingtoremovethe
nutsisata55°angletothehorizontalandyouapplyaforceof120Ndirectlydownonthe
endofthewrench,whatisthemagnitudeofthetorqueyouexertonthelugnut?
STRATEGY
Forthisproblem,weareinterestedintheappliedtorqueτ.Torqueistherotationalanalog
toforce;itistheeffectivenessofaforcetocauseanobjecttorotateaboutapivotpoint.To
solvefortorque,weneedtoconsider1)themagnitudeoftheappliedforce,F,2)howfar
fromthepivotpointtheforceisapplied,r,and3)theanglethattheforceisapplied,θ.
Lookupthedefinitionoftorquesinyourtext.Inyourownwords,explainhowtorquediffers
fromforce.
IMPLEMENTATION
Let’sdrawadiagramandlabeltheappliedforcevector𝐹,the
vector𝑟thatgoesfromthepivotpointtothewheretheforceis
applied,andtheangleθbetween𝑟and𝐹.Notethattheangleθis
not55°,but(180°-35°)=145°.
Whydowenotusethe55°angle?Howdidwefindtheangleof
145°?Couldwehaveused35°?
r = 30 cm
F = 120 N
r
F
y
55°
x
Therelationbetweenτ,r,F,andθis:
𝜏 = 𝑟×𝐹 = 𝑟𝐹 sin 𝜃
WhatisaCrossProduct?Whatistheresultofacrossproduct?
WecanfindthemagnitudeofthetorqueusingrFsinθ,butdoestorquehaveadirection?
CALCULATION
1J40-001
Changingaflattire–torque
PROMPTSEMBEDDED
Themagnitudeofthetorqueexertedonthelugnutsis
𝜏 = 𝑟𝐹 sin 𝜃= 0.30 m 120 N 𝑠𝑖𝑛 145 = 20.6 N m.
Theunitsoftorquearenewton-meters(N·m).
Theunitsoftorquearenewton-meters(Nm).HowdoesthisunitdifferfromtheSIunitfor
energyandwork?
Howwouldthemagnitudeofthetorqueexertedonthelugnutschangeiftheforcewas
appliedinthemiddleofthehandleratherthantheend?
HowwouldIhavewantedtoorienttheangleofmyappliedforcetomaximizethemagnitude
ofthetorqueexertedonthelugnuts?