Centripetal Force: Banked Curve

Click For Summary
SUMMARY

The discussion centers on calculating the speed of a 1200 kg car navigating a banked curve at an angle of 42.5 degrees and a radius of 150 meters, with a frictional force of 9000 N. Two different methods yield conflicting results: one calculation suggests a speed of 54 m/s, while another, based on the Wikipedia formula for banked turns, indicates 67 m/s. The discrepancy arises from the application of the frictional force in the equations governing centripetal motion. Correctly incorporating the frictional force into the calculations is essential for accurate results.

PREREQUISITES
  • Understanding of centripetal force and its equations
  • Knowledge of forces acting on an object on an incline
  • Familiarity with trigonometric functions in physics
  • Ability to manipulate equations involving mass, radius, and friction
NEXT STEPS
  • Review the derivation of the centripetal force equation, Fc = mv²/r
  • Study the application of friction in banked curves using real-world examples
  • Learn how to apply trigonometric functions to forces on inclined planes
  • Explore advanced physics problems involving banked turns and friction
USEFUL FOR

Physics students, educators, and anyone interested in understanding the dynamics of vehicles on banked curves, particularly in relation to centripetal force and frictional effects.

badsniper
Messages
3
Reaction score
0

Homework Statement


A 1200 kg car travels around a curve banked at 42.5 degrees in a circular path of radius = 150m, but the ramp is only 55m long. The force of friction on the car is 9000N, calculate the speed of the car.

So:

radius = 150 m
θ (angle the incline makes with the horizontal) = 42.5
mass = 1200 kg
Friction = 9000 N


Homework Equations



Fc= FNx + FFx

Fc= mv2 / r

The Attempt at a Solution



The car does not move in the y-plane, therefore:

Ff + Fg + FN = 0

FN = (mg + Ffsinθ)/cosθ

Solve for FN and I got 24213.83512 N

Then I used the value of FN to find FNx and added FFx to it.

Then I multiplied by the radius, divided by the mass and took the square root leaving me with 54m/s.

However, when I use the formula found on this page http://en.wikipedia.org/wiki/Banked_turn" I got 67 m/s.

Which one is right? And If I'm wrong, where did I go wrong?
 
Last edited by a moderator:
Physics news on Phys.org
How did you apply the 9000N to the equations on the Wiki site?
 

Similar threads

Centripetal Force Banked Curves
  • · Replies 12 ·
Replies
12
Views
3K
How do I draw a FBD for centripetal force
  • · Replies 6 ·
Replies
6
Views
4K
Banked Curve perfectly banked
  • · Replies 4 ·
Replies
4
Views
8K
Solving Banked Curve Problem: Coefficient of Static Friction
  • · Replies 6 ·
Replies
6
Views
3K
What is the Radius of Curvature for a Banked Curve with Ice on the Road?
  • · Replies 5 ·
Replies
5
Views
3K
A father spins his child on a cart
  • · Replies 10 ·
Replies
10
Views
2K
Solving Banked Curve Friction Problems
  • · Replies 6 ·
Replies
6
Views
5K
Find the Coefficient of friction on a banked curve.
  • · Replies 9 ·
Replies
9
Views
7K
Banked roads -- circular motion and gravitation
  • · Replies 11 ·
Replies
11
Views
3K
Max Speed of Car on Wet Ramp Turn at 20° Bank
  • · Replies 3 ·
Replies
3
Views
2K