Uniform Circular Motion Page 3
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Click for the questions that go with this reading
 

For any object to curve, or turn in part of a circle, its inertia must be changed. This is done by applying a force. This force is called a centripetal force and it can be supplied by may sources -friction, gravity, etc.

Car enthusiasts refer to this centripetal force as a "lateral force." The greater the lateral force the greater the speed a car can travel around a curve. Car magazines such as, "Car and Driver," report this lateral force as a lateral acceleration in g's. To use it with standard physics equations it must be converted to m/s2.

Lateral g's are calculated by driving car clockwise and then counterclockwise around a dry circular test track. The car speeds up while maintaining its path along the circular track. When the car skids out of control its velocity is noted and the centripetal acceleration is calculated.

Most street cars can provide a lateral g of 0.6 to 0.90. ("g's" scale the acceleration.) That is a wide range of g's. A lateral acceleration of "1g" means that the car is producing a sideways acceleration equal to its weight. There are some sports car that produce more than 1g laterally. That's an exercise you can do with an Internet search.

This video can be found on YouTube at https://youtu.be/2z-kuZizGBw

 
 
Example 1

A 2016 Mazda 3 has a lateral acceleration of 0.81 g's.
(a) How fast can this car "take" a city street corner with a radius of 20.0 m without sliding?
(b) An circular ramp with a radius of 80.0 m is used to exit the highway the speed limit is 45 mph, 20.12 m/s. Can this same car travel around the curve at 90 mph, 40.24 m/s? (In reality the situation is not this simple, the off ramp is coated with droplets of leaked, slippery, car fluids. Small pebbly pieces of car tire act like marbles on the ramp and the ramp is usually

a lower friction cement surface. But for the sake of this simple problem, ignore all this.)

 

Solution

"Lateral" means "side" or "sideways." In this case the acceleration is pointed from from the side of the car with of value of 0.81 g's. Whenever the acceleration is perpendicular to the motion, the acceleration is called a "centripetal acceleration" and it will cause the car to curve or travel in a circle if the speed does not change. The "lateral" acceleration is the "centripetal" acceleration of the car.

The use of the term lateral in the description of a car's motion is the way car enthusiasts describe the car's centripetal acceleration.

 

Part a's solution

This video can be found on YouTube at https://youtu.be/Mpfa7x13NUM

 

Example 2

2 cars are traveling around a 90° of a circular curve as shown above. The two cars start side by side and end the curve traveling side by side. The yellow car on the inside of curve is traveling at 11.0 m/s. What is the speed of the red car on the outside of the curve?

Strategy

  • Need to find the time for the red car on the outside knowing only the radius.
  • The two cars have the same period because they start side by side and finish side by side.
  • Even thought this is only 1/4 of a circle, the speed if the cars is the same. It does not matter if they travel an entire circle of 1/4 of a circle. it will be the same.
  • Find the period of the yellow car. This is the same as the red car since they stay side by side.
  • Use this to calculate the red car's speed.
Solution

This video can be found on YouTube at https://youtu.be/3PxSKM_6xXA

Example Cars and their centripetal, (also called the lateral,) accelerations

Model/Year

Max Lateral Accel (g)

Model/Year

Max Lateral Accel (g)

GMC Sierra Club Cab 1500/'96

0.60

Mazda Miata/'96

0.88

Ford  '90

0.64

BMW 328i Sport/'96

0.91

Hyundai Excel GLS '90

0.66

Ford Mustang Cobra R/'95

0.96

Jeep Grand Wagoneer '90

0.7

Dodge Viper SRT-10 /’18

1.05

Mercedes-Benz 420SEL '90

0.72

Ford Shelby Mustang GT350R/’18

1.10

Ford Taurus LX Wagon/'96

0.74

Dodge Viper ACR (Mk V) /’18

1.15

Toyota 4Runner/’96

0.76

Porsche 911 GT3 (9)/’18

1.18

Honda Accord EX V-6/'95

0.78

Chevrolet Corvette ZR1/’18

1.24

Lexus LS 400/'95

0.80

F-1 race car /’17

8 <–Not a typo

Infiniti 130 V'96

0.82

Lamborghini Diablo

0.93

Nissan 300ZX '90

0.86

Range Rover

0.63

Porsche 928 GT '90

0.86

 

 

Here is a more recent list of the best cornering cars and their lateral accelerations, fastestlaps.com/makes

 
 
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by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

The owner of this website does not collect cookies when the site is visited. However, this site uses and or embeds Adobe, Apple, GoDaddy, Google, and YouTube products. These companies collect cookies when their producs are used on my pages. Click here to go to them to find out more about how they use their cookies. If you do not agree with any of their policies then leave this site now.