magnetism

1
Physics

• The term cornering describes, without, numbers a
  cars ability to go fast around a curve.
• The physics of a flat curve has a built in
  cornering limiting factor.
• This factor is the centripetal acceleration. The
  centripetal acceleration can be found fromac -
  v2/R

2
Physics

• Where ac equals the centripetal acceleration, v
  equals the car's velocity around the curve, and R
  represents the radius of the curve.
• A curve that as a posted speed limit of 25 m/s
  and has a radius of 50 m requires a centripetal
  acceleration of 6.5 m/s2.
• In terms of g's this is 0.66 g's, (6.5/9.8
  0.66 ).

3
Physics

• The centripetal force needed for a car to make it
  around a flat corner supplied by the friction
  between the car's tires and the road. This value
  is described in magazines such as Car and Driver
  as the car's lateral acceleration

4
Physics

• To find the car's lateral acceleration, a car
  turns a circle of a given radius.
• Then it accelerates slowly until it begins to
  slip to the outside of the circle.
• This is the point where the friction between the
  tires and the road have exerted the maximum
  amount of friction.
• The cars maximum lateral acceleration can be
  calculated from the formula for centripetal
  acceleration shown above.

5
Physics

• The curve decides how much centripetal
  acceleration is needed to safely navigate the
  curve.
• It decides it by the velocity the curve is going
  to be traveled and the radius of the curve.
• Use the equation, V2/R.

6
Physics

• If a car requires 0.66 g's to make it around a
  curve without slipping.
• Then the car's lateral acceleration has to be
  greater than or equal to the curve's calculated
  centripetal acceleration then it will go around
  the curve without slipping.

7
Physics

• If the lateral acceleration of the car is less
  than the centripetal acceleration then the car
  will slip to the outside of the curve until the
  radius is big enough to allow the curves
  centripetal acceleration to be equal to the car's
  lateral acceleration.

8
Physics

• EXAMPLE 11. A curve has a posted speed limit of
  25 mph, 11.16 m/s. The curves radius is 40
  meters. With what centripetal acceleration can
  a car travel around the curve without slipping?
• Ac v2/R ac (11.16)2/40m 3.11m/s2
• 3.11m/s2/9.8m/s2 0.317gs

9
Physics

• This means that a car can travel around the curve
  without slipping if the tires exert a frictional
  force of 3.11 m/s2, 0.318 g's.
• In car and driver this frictional force is
  described as the "lateral acceleration.
• The limiting factor is 0.317 gs for this
  curve.

10
Physics

• EXAMPLE 2While traveling down a road at 25 m/s,
  a car needs to negotiate a curve of radius 19 m.
• What centripetal force is needed to make the
  curve and what will happen if the friction
  between the cars tires and the road is not
  equal to or greater than the needed centripetal
  force needed for the curve.

11
Physics

• Solution
• ac v2/R
• ac(25)2/19 32.8m/s2
• gs 32.89/9.80 3.36gs

12
Physics

• 3.36 gs! There are no passenger cars that do
  this.
• The car will not make it around the curve. The
  driver will have the wheels turned but the car
  will continue to slide.

13
Physics

• If the curve were banked, the car would slide to
  the outside of the curve until the centripetal
  acceleration needed to negotiate the curve equals
  the centripetal acceleration the car can exert.
• Suppose the car can exert a centripetal
  acceleration of 0.88 gs

14
Physics

• 0.88gs .88(9.8m/s2) 8.62m/s2
• 8.624m/s2 252/R
• Therefore R 72.47m. The car will slide outwards
  along the banked curve until the radius of the
  turn equals 72.47 meters, or until a fence stops
  the car.

15
Physics

• What is the maximum velocity that a Lamborghini
  Diablo can go around a curve if it the curve has
  a radius of 50 m?2 What is the maximum velocity
  that a Range Rover can go around a curve if it
  the curve has a radius of 50 m?3. a How much
  centripetal acceleration is needed so a car can
  go around a curve at 21 m/s if the curves radius
  is 50 m? (Answer in gs and m/s2)b Which cars
  can navigate the curve without slipping?4. What
  is the smallest radius curve that a Nissan
  300ZX can travel around at 25 m/s. 5. How fast
  could a Geo Metro Lsi take the same curve as
  the Nissan in 4?6. Detective Columbo was
  looking at an accident when he noticed something.
  He saw that the car traveled around a curve of
  radius 30 m at 15.43 m/s, 34.6 mph, before the
  car began to slip to the outside. Columbo sends
  this information to you in the crime lab. It is
  up to you to send him a list of possible cars
  that the perpetrator may have been driving. Using
  physics, which possible cars could the suspect
  have been driving?7. In a court trial a suspect
  is accused of fleeing the scene of an accident.
  The suspects car is a dark green Toyota 4Runner
  4WD . A witness testified that they saw a dark
  green vehicle traveling about 30 mph around the
  nearby corners. Could he have been at the scene
  of the crime?

16
Physics

• What is the maximum velocity that a Lamborghini
  Diablo can go around a curve if it the curve has
  a radius of 50 m?2 What is the maximum velocity
  that a Range Rover can go around a curve if it
  the curve has a radius of 50 m?

17
Physics

• 3. a How much centripetal acceleration is needed
  so a car can go around a curve at 21 m/s if the
  curves radius is 50 m? (Answer in gs and
  m/s2)b Which cars can navigate the curve without
  slipping?4. What is the smallest radius curve
  that a Nissan 300ZX can travel around at 25
  m/s.

18
Physics

• 5. How fast could a Geo Metro Lsi take the same
  curve as the Nissan in 4?gt

19
Physics

• 6. Detective Columbo was looking at an accident
  when he noticed something. He saw that the car
  traveled around a curve of radius 30 m at 15.43
  m/s, 34.6 mph, before the car began to slip to
  the outside. Columbo sends this information to
  you in the crime lab. It is up to you to send him
  a list of possible cars that the perpetrator may
  have been driving. Using physics, which possible
  cars could the suspect have been driving?

20
Physics

• 7. In a court trial a suspect is accused of
  fleeing the scene of an accident. The suspects
  car is a dark green Toyota 4Runner 4WD . A
  witness testified that they saw a dark green
  vehicle traveling about 30 mph around the nearby
  corners. Could he have been at the scene of the
  crime?