Minimum coefficient of friction to keep cars from sliding off the road

Click For Summary
SUMMARY

The discussion focuses on calculating the minimum coefficient of friction required to prevent cars from sliding off a banked circular highway curve designed for a speed of 61 km/h and a radius of 201 m. Given that traffic is moving at 44 km/h on a rainy day, the necessary calculations involve the equations Fk=ukFn and Fs, max=usFn, along with the centripetal force equation F=mv^2/R. The angle of banking, θ, was determined to be 4.32° using the formula tanθ=v^2/gR, where v is the speed, g is the acceleration due to gravity, and R is the radius of the curve.

PREREQUISITES
  • Understanding of centripetal force and its application in circular motion
  • Knowledge of frictional forces, specifically static and kinetic friction
  • Familiarity with basic trigonometry, particularly tangent functions
  • Ability to apply Newton's laws of motion in practical scenarios
NEXT STEPS
  • Calculate the minimum coefficient of friction using the derived angle and speed values
  • Explore the effects of varying speeds on the required coefficient of friction
  • Investigate the impact of road conditions (e.g., wet vs. dry) on friction coefficients
  • Learn about the design principles of banked curves in highway engineering
USEFUL FOR

Students in physics or engineering, traffic safety analysts, and highway design professionals will benefit from this discussion as it provides insights into the dynamics of vehicle motion on banked curves and the role of friction in maintaining safety on roadways.

rockchalk1312
Messages
38
Reaction score
0
A banked circular highway curve is designed for traffic moving at 61 km/h. The radius of the curve is 201 m. Traffic is moving along the highway at 44 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)


Fk=ukFn
Fs, max=usFn
F=mv^2/R


Honestly no idea at how to attempt it. Although I did find that θ needed to be:
tanθ=v^2/gR
tanθ=12.2^2/(9.8)(201)
θ=4.32°

Thank you for any help!
 
Physics news on Phys.org


As always, the first step is to draw a diagram showing all the forces acting on the car.
 

Similar threads

Distance travelled by a car considering only air friction?
  • · Replies 4 ·
Replies
4
Views
2K
Cars rounding a slippery banked corner in the rain
  • · Replies 20 ·
Replies
20
Views
3K
How to find coefficient of friction *Without* mass?
  • · Replies 3 ·
Replies
3
Views
22K
Banked Curve-Determine smallest static coefficient of friction
  • · Replies 9 ·
Replies
9
Views
4K
What Is the Minimum Stopping Distance to Prevent Crate Sliding?
  • · Replies 3 ·
Replies
3
Views
4K
Friction question (intro level)
  • · Replies 1 ·
Replies
1
Views
1K
Coefficient of kinetic friction between a car and the road
  • · Replies 12 ·
Replies
12
Views
4K
A banked curve and coefficient of friction
  • · Replies 1 ·
Replies
1
Views
12K
How Do You Calculate the Minimum Coefficient of Friction for a Banked Curve?
  • · Replies 1 ·
Replies
1
Views
3K
Centripal Force - Friction needed to keep a car tracking a curve
  • · Replies 6 ·
Replies
6
Views
3K