Driving in Circles Examples
Example 1
A 1200 kg car is driving around a circular portion of road of radius 65 m at a constant
speed of 15 m as in the diagram. What is the minumum coefficien t of static friction
s
required to keep the car on the road?


 Fx  max
From above

FN
F fs   mac
But
 F fs   s FN
F fs
r  65 m

a
v  15 m
s

Fg
FN  Fg
v2
ac 
r
mv 2
 s FN 
r
mv 2
 s mg 
r
FN  Fg
FN  mg
Driving in Circles Examples
Example 1
A 1200 kg car is driving around a circular portion of road of radius 65 m at a constant
speed of 15 m as in the diagram. What is the minumum coefficien t of static friction
s
required to keep the car on the road?
2
v
s g 
r
From above

FN

F fs
r  65 m

a
v  15 m
s

Fg
FN  Fg
v2
s 
rg

15 m

2
s
s 
65 m  9.8 N kg 


 s min  0.35
Driving in Circles Examples
Example 2
A circular curve of highway is designed for traffic moving at 60.km . If the radius of
h
the curve is 150 m, at what angle must the road be banked for the car to successfully
negotiate it with no friction?
From above
r  150 m

a
v  60 km
Do not rotate the axis as
the car is moving in a
horizontal circle


FNx Fg  FNy


FNy FN
h

Fg
Driving in Circles Examples
Example 2
A circular curve of highway is designed for traffic moving at 60.km . If the radius of
h
the curve is 150 m, at what angle must the road be banked for the car to successfully
negotiate it with no friction?


 Fx  max
FNy  Fg
FNy  mg

FNx   mac

FNx


FNy FN

Fg
FNx
But
mv 2

r
FNx
tan  
FNy
FNx  FNy tan 
mv 2
FNy tan  
r
Driving in Circles Examples
Example 2
A circular curve of highway is designed for traffic moving at 60.km . If the radius of
h
the curve is 150 m, at what angle must the road be banked for the car to successfully
negotiate it with no friction?


FNx


FNy FN

Fg
mv 2
mg tan  
r
v2
tan  
rg
" Design Speed" of a
banked curve (F f  0)
Driving in Circles Examples
Example 2 continued
A circular curve of highway is designed for traffic moving at 60.km . If the radius of
h
the curve is 150 m, at what angle must the road be banked for the car to successfully
negotiate it with no friction?
v2
tan  
rg
" Design Speed" of a
banked curve (F f  0)
2


v
1
  tan  
 rg 


2
m
 (16.67 )

1
s
  tan 

 150 m  9.8 N  
kg  


  11
But
1000 m
1h
km
m
v  60.



16
.
67
h 1 km 3600 s
s