Question

A curve of radius 30 m is banked so that a 950-kg car traveling at 25 miles per hour can round it even if the road is so icy that the coefficient of static friction is approximately zero. You are commissioned to tell the local police the range of speeds at which a car can travel around this curve without skidding. Neglect the effects of air drag and rolling friction. If the coefficient of static friction between the snowy road and the tires is 0.300, what is the range of speeds you tell them? a) Under icy (frictionless) conditions, what is the banking angle of the curve? No free-body diagram, no credit! b) Now with friction: Draw 2 free body diagrams for the minimum and maximum speeds. Be sure to choose a “smart” orientation for the coordinate axes. c) What are the minimum and maximum safe speeds for the value of friction given for the curve?

Answer #1

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 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...

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...

A curve of radius 68 m is banked for a designed speed of 85km/h.
If the coefficient of static friction is 0.30, at what range of
speeds can a car safely make the curve? (You must show schematic
and free-body diagrams, and apply Newton's 2nd law of motion.)

A curve of radius 90 m is banked for a design speed of 80 km/h.
If the coefficient of static friction is 0.30 (wet pavement), at
what range of speeds can a car safely make the curve?
Minimum- ? km/h
Maximum - ? km/h

A road with a radius of 75.0 m is banked so that a car can
navigate the curve at a speed of 15.0 m/s without any friction. If
the banking angle is reduced to zero when a car is going 20.0 m/s
on this curve, what minimum coefficient of static friction is
needed if the car is to navigate the curve without slipping?

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...

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 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?

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