1M10-002Sailboat–kineticenergyandwork–PROMPTSAFTER
STATEMENTOFTHEPROBLEM
A3,000-kgsailboatistravellingat25m/swhenaconstantnetforceof1200Nstartsacting
onit,inthedirectionofmotion.Whatisthespeedoftheboatafterithastravelled200m
undertheactionofthisforce?
STRATEGY
Whenaforceactsonamovingobject,workisdoneonthe
object.Theworkdoneontheobjectresultsinthechange
oftheobject’skineticenergyK,definedas
1
𝐾 = 𝑚𝑣 ! 2
wheremisthemassoftheobjectandvisitsspeed.
Thenetworkdoneontheobjectandthechangeinthe
kineticenergyarerelatedbythework-energytheorem
1
1
𝑊!"# = ∆𝐾 = 𝑚𝑣!! − 𝑚𝑣!! 2
2
Tofindtheanswertothequestionposedintheproblem:
1.wefindthenetworkdoneontheboat,2.setitequalto
thechangeinkineticenergyoftheboat,and3.solvethe
resultingequationfortheunknownfinalspeed.
IMPLEMENTATION
1.Network: 𝑊!"# = 𝐹!"# ∙ Δ𝑥 = 𝐹!"# ∆𝑥 cos 𝜃
!
!
!
!
2. 𝑚𝑣!! −
3.𝑣! =
𝑚𝑣!! = 𝑊!"# ! !!"# ! !!!!
!
System
y
v0
x0
n
x
xf
Fnet
Free-Body Diagram
Fg
msailboat = 3000 kg
(xf - x0) = 200 m
vf = ?
v0 = 25 m/s
Fnet = 1200 N
1M10-002Sailboat–kineticenergyandwork–PROMPTSAFTER
CALCULATION
𝑊!"# = 1200 N 200 m cos 0° = 240,000 Nm = 240,000 J (joules)
𝑣! =
480,000 J + 3000 kg (25
3000 kg
m !
)
s ! = 28 m
s
SELF-EXPLANATIONPROMPTS
1. Statethework-energytheoreminyourownwords.
2. TheworkdonebyaconstantforceF,actingalongthedirectionofmotionovera
distanceΔxequals𝐹𝛥𝑥.Fromkinematics,weknowthatifanobjectstartsfromrestand
accelerateswithaccelerationaoveradistanceΔx,2𝑎∆𝑥 = 𝑣 ! ;andfromNewton’s
SecondLaw,weknowthat𝑎 =
!
!
!
.Combinethethreeequationsandshowthatthework
donebytheforceequals 𝑚𝑣 ! .
!
3. Usethesameprocedureasabovetoshowthattheworkdonetoincreasethespeedof
massmfromv1tov2isequaltothechangeinitskineticenergy.