Question

4) Consider a car traveling with speed around a curve of radius r . a) Derive an equation that best expresses the angle () at which a road should be banked so that no friction is required. b) If the speed signpost says 42 mile/h, and the angle of the bank is 18°, what is the radius (r) of the curve. (2 points)

You must show how tan is derived mathematically.

Answer #1

A 1000-kg car is traveling around a curve having a radius of 100
m that is banked at an angle of 15.0°. If 30m/s is the maximum
speed this car can make the curve without sliding, what is the
coefficient of friction between the road and the tires?

A curve of radius 20 m is banked so that a 1100 kg car traveling
at 30 km/h can round it even if the road is so icy that the
coefficient of static friction is approximately zero. The
acceleration of gravity is 9.81 m/s 2 .
Find the minimum speed at which a car can travel around this
curve without skidding if the coefficient of static friction
between the road and the tires is 0.3. Answer in units of m/s.

A car rounds a 50 meter radius curve that is banked such that a
car rounding it does not need friction at a speed of 12 m/s. What
is the bank angle of the road?
The coefficient of kinetic friction between the tires and the
road is 0.5 and the coefficient of static friction between the
tires and the road is 0.8. If the same road were flat (instead of
banked), determine the maximum speed with which the coar could...

An auto mobile traveling at 60 mph rounds a curve banked at 10
degrees. The radius of the curve is 200 ft. (a) What is the minimum
coefficient of friction that will keep the car on the road? (b)
What would the bank angle need to be in order for the car to stay
on the road without any friction?

If a curve with a radius of 81 m is properly banked for a car
traveling 67 km/h , what must be the coefficient of static friction
for a car not to skid when traveling at 82 km/h ?

If a curve with a radius of 82 m is properly banked for a car
traveling 75 km/h , what must be the coefficient of static friction
for a car not to skid when traveling at 100 km/h ?

A car is traveling around a banked curve without friction which
is banked at 28 degrees. It is originally moving at 14 m/s. A
constant acceleration of 2.5 m/s2 in the direction is applied in
the direction that it is moving which causes the car to speed up.
If this acceleration is applied for 2.7 seconds, how far did the
car move up the road (the incline) in meters?

A car merges onto the freeway on a banked curve. The car
maintains a constant velocity 푣 while driving on the curve, which
is banked at angle theta and has a radius of curvature R. The car
has mass m and the coefficient of static friction between the car’s
tires and the road is meu(s). What is the maximum and minimum speed
that the car can go around the banked curve without slipping? Hint:
The car tends to slip up...

A curve of radius 20 m is banked so that a 1000 kg car traveling
at 60 km/h can round it even if the road is so icy that the
coefficient of static friction is approximately zero. The
acceleration of gravity is 9.81 m/s 2 . ? Find the minimum speed at
which a car can travel around this curve without skidding if the
coefficient of static friction between the road and the tires is
0.2. Answer in units of...

1) A car is traveling around a circular portion of road banked
at an incline of 20 degrees to the horizonal. If the radius of the
turn is 75 m and the coefficient of static friction is 0.75 A) What
is the maximum speed the car can take the turn without losing
traction? B) At what speed would the static friction be zero?

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