Lecture 14
Reminder: Particle in Uniform Circular Motion
v2
ac =
r
v2
å F = mac = m r
Centripetal “force”
Clicker question
Time=1min
You are a civil engineer who has been given the assignment to design a
curved roadway in such a way that a car will not have to rely on friction
to round the curve without skidding.
Suppose the designated speed for the road
is to be 13.4 m/s (30.0 mi/h) and the radius
of the curve is 35.0 m. You need to
determine the angle at which the roadway
on the curve should be banked.
A) 10°
B) 15°
C) 22°
D) 28°
E) 35°
Clicker question
Time=1min
You are a civil engineer who has been given the assignment to design a
curved roadway in such a way that a car will not have to rely on friction
to round the curve without skidding.
Suppose the designated speed for the road
is to be 13.4 m/s (30.0 mi/h) and the radius
of the curve is 35.0 m. You need to
determine the angle at which the roadway
on the curve should be banked.
A) 10°
B) 15°
C) 22°
D) 28°
E) 35°
Clicker question
Time=1min
You are a civil engineer who has been given the assignment to design a
curved roadway in such a way that a car will not have to rely on friction
to round the curve without skidding.
Suppose the designated speed for the road
is to be 13.4 m/s (30.0 mi/h) and the radius
of the curve is 35.0 m. You need to
determine the angle at which the roadway
on the curve should be banked.
A) 10°
B) 15°
C) 22°
D) 28°
E) 35°
Next: What if it was on Mars?
!!"#$ = 3.72 (/* %
Clicker question
How slow should the driver negotiate a
200m radius curve so that the flower
on the car dashboard doesn’t slide?
The static coefficient of friction is 0.2.
A)
B)
C)
D)
10 m/s
20 m/s
30 m/s
40 m/s
Time=1min
Example: Car on Curved Banked Road
What is the maximum safe speed on a curved banked
road with a given angle + and static friction ,$ ?
Example: Car on Curved Banked Road
What is the maximum safe speed on a curved banked
road with a given angle + and static friction ,$ ?
-. #
Σ"! = $ sin ( − *" cos ( =
/
Σ"$ = $ cos ( − *" sin ( − -0 = 0
Example: Car on Curved Banked Road
What is the maximum safe speed on a curved banked
road with a given angle + and static friction ,$ ?
-. #
Σ"! = $ sin ( − *" cos ( =
/
Σ"$ = $ cos ( − *" sin ( − -0 = 0
-. #
sin ( − 2" cos ( =
/$
-0
cos ( − 2" sin ( =
$
Example: Car on Curved Banked Road
What is the maximum safe speed on a curved banked
road with a given angle + and static friction ,$ ?
-. #
Σ"! = $ sin ( − *" cos ( =
/
Σ"$ = $ cos ( − *" sin ( − -0 = 0
-. #
sin ( − 2" cos ( =
/$
-0
cos ( − 2" sin ( =
$
tan ( − 2"
.#
=
≡7
1 − 2" tan ( /0
tan ( =
7 + 2"
1 + 72"
Clicker question
Time=1min
According to Newton, any two objects attract each other
due to gravity with a force
!%
#=$ !
&
The mass of Sun is ! = 2x1030 Kg.
Earth is 150 billion m away from the Sun.
How many 24 hours is in an Earthian year?
A) 110 B) 230 C) 365 D) 480
$ = 6.7x10-11 m3/Kg s2
Clicker question
Time=1min
According to Newton, any two objects attract each other
due to gravity with a force
!%
#=$ !
&
The mass of Sun is ! = 2x1030 Kg.
Venus is 110 billion m away from the Sun.
How many 24 hours is in a Venusian year?
A) 110 B) 230 C) 365 D) 480
$ = 6.7x10-11 m3/Kg s2
Nonuniform Circular Motion
  
a = ar + ar



å F = å Fr + å Ft
Example
A bead slides at constant speed along a curved wire
lying on a horizontal surface as shown in the figure.
Draw the vectors representing the force exerted by the
wire on the bead at points A, B, and C.
Example
A bead slides at constant speed along a curved wire lying
on a horizontal surface as shown in the figure.
Suppose the bead speeds up with constant tangential
acceleration as it moves toward the right. Draw the vectors
representing the force on the bead at points A, B, and C.
Fictitious forces: Centrifugal force
Fictitious forces: Centrifugal force
Fictitious forces: Centrifugal force
Fictitious forces: Coriolis force
Quiz
Time=10min
End of Lecture 14