Problem 9.98

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Problem 9.98 [Difficulty: 2]
Given: Bike and rider at terminal speed on hill with 8% grade.
W 210 lbf A 5 ft
2
 Vt 50
ft
s
 CD 1.25
Find: (a) Verify drag coefficient
(b) Estimate distance needed for bike and rider to decelerate to 10 m/s after reaching level road
Solution:
Basic
equations:
FD CD
1
2
 ρ V
2
 A (Drag)
Assumptions: (1) Standard air
(2) Neglect all losses other than aerodynamic drag
The angle of incline is: θ atan 9 %( ) 5.143 deg Summing forces in the x-direction: ΣFx FG FD 0
Expanding out both force terms: M g sin θ( ) CD
1
2
 ρ Vt
2
 A Solving this expression for the drag coefficient:
CD
2 W sin θ( )
ρ Vt
2
 A
 CD 1.26
The original estimate for the
drag coefficient was good.
Once on the flat surface: ΣFx FD
W
g t
Vd
d







W
g
V
s
Vd
d






 Therefore:
W
g
V
s
Vd
d






 CD
1
2
 ρ V
2
 A
Separating variables: ds
2 W
CD ρ g A

dV
V
 Integrating both sides yields: Δs
2 W
CD ρ g A
 ln
V2
V1






 Δs 447 ft