Transcript CarExitRamp

Car on an exit ramp
a classic rotational motion & friction problem
Rhine
The Problem
v
Suppose a car enters a flat
(not banked) on-ramp at a
constant speed of 50 mph (or,
more generally, v). Assume S
= 0.50 (or more generally, S).
If the car maintains this
speed...
Top View
a) What is the minimum safe
radius that you, the civil
engineer, should have used for
the off ramp design?
b) If the driver were to enter
the turn at a higher speed,
what would happen?
v
c) Re-work the problem with a
banked curve (bank angle of 
= 10, or more generally, )
Assumptions and intuition
v
As the car is going through the
turn, is the car’s velocity
changing or not?
Top View
What type of force (or
acceleration) is required for an
object to follow a curved path?
v
Solving the problem
v
Top View
i) Draw a FBD – of the FRONT VIEW of the car, as if
it was headed straight toward you. Why do you need
to use this orientation??
ii) Apply Newton’s Second Law:
iii) solve the problem for r
v
Banked off-ramp (bank angle = )
i) Redraw the FBD (FRONT VIEW of the car)
v
Top View
ii) Apply Newton’s Second Law:
iii) solve the problem for r
v